Ex8 and minor improvements
This commit is contained in:
Markus Schmidt
parent
2195a9db0a
commit
77bc8c6aa3
50 changed files with 214845 additions and 43 deletions
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@ -19,8 +19,8 @@ Each kernel will be executed 20 times.
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will be used to compute the reported bandwidth.
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will be used to compute the reported bandwidth.
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-------------------------------------------------------------
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-------------------------------------------------------------
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Your clock granularity/precision appears to be 1 microseconds.
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Your clock granularity/precision appears to be 1 microseconds.
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Each test below will take on the order of 46252 microseconds.
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Each test below will take on the order of 59858 microseconds.
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(= 46252 clock ticks)
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(= 59858 clock ticks)
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Increase the size of the arrays if this shows that
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Increase the size of the arrays if this shows that
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you are not getting at least 20 clock ticks per test.
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you are not getting at least 20 clock ticks per test.
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-------------------------------------------------------------
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-------------------------------------------------------------
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@ -29,10 +29,10 @@ For best results, please be sure you know the
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precision of your system timer.
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precision of your system timer.
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-------------------------------------------------------------
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-------------------------------------------------------------
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Function Best Rate MB/s Avg time Min time Max time
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Function Best Rate MB/s Avg time Min time Max time
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Copy: 28478.6 0.047858 0.044946 0.054333
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Copy: 23508.2 0.063228 0.054449 0.074427
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Scale: 20551.4 0.066044 0.062283 0.077807
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Scale: 18323.7 0.089940 0.069855 0.116932
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Add: 22534.2 0.089671 0.085204 0.099586
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Add: 19762.6 0.276166 0.097153 3.054857
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Triad: 22709.5 0.088864 0.084546 0.098536
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Triad: 19559.9 0.123390 0.098160 0.156530
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-------------------------------------------------------------
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-------------------------------------------------------------
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Solution Validates: avg error less than 1.000000e-13 on all three arrays
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Solution Validates: avg error less than 1.000000e-13 on all three arrays
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-------------------------------------------------------------
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-------------------------------------------------------------
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@ -42,19 +42,19 @@ Solution Validates: avg error less than 1.000000e-13 on all three arrays
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Module Error RunTime MFLOPS
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Module Error RunTime MFLOPS
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(usec)
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(usec)
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1 4.0146e-13 0.0021 6622.7552
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1 4.0146e-13 0.0029 4831.3737
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2 -1.4166e-13 0.0006 12723.3419
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2 -1.4166e-13 0.0006 11258.2969
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3 4.7184e-14 0.0027 6253.2599
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3 4.7184e-14 0.0031 5448.3769
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4 -1.2557e-13 0.0026 5758.6323
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4 -1.2557e-13 0.0030 5042.5895
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5 -1.3800e-13 0.0051 5740.4851
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5 -1.3800e-13 0.0060 4867.7339
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6 3.2380e-13 0.0051 5674.2511
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6 3.2380e-13 0.0054 5322.4399
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7 -8.4583e-11 0.0031 3827.0478
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7 -8.4583e-11 0.0031 3907.7854
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8 3.4867e-13 0.0053 5610.0203
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8 3.4867e-13 0.0056 5323.6214
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Iterations = 512000000
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Iterations = 512000000
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NullTime (usec) = 0.0000
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NullTime (usec) = 0.0000
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MFLOPS(1) = 9507.3864
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MFLOPS(1) = 8348.0311
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MFLOPS(2) = 5042.7572
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MFLOPS(2) = 4650.8807
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MFLOPS(3) = 5597.4972
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MFLOPS(3) = 5016.3434
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MFLOPS(4) = 5766.1547
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MFLOPS(4) = 5297.2428
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@ -82,8 +82,12 @@ vector<double> benchmark_D(const vector<double>& coeff, const vector<double>& x)
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double norm2(const vector<double>& x)
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double norm2(const vector<double>& x)
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{
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{
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double s = 0.0;
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double s = 0.0;
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for (unsigned int i = 0; i < x.size(); ++i)
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double xi;
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s += x[i]*x[i];
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for (unsigned int i = 0; i < x.size(); ++i){
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xi = x[i];
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s += xi*xi;
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}
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return sqrt(s);
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return sqrt(s);
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}
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}
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@ -116,7 +120,7 @@ vector<double> matrixMultColumnWise(const vector<double> &A, const vector<double
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double sum = 0.0;
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double sum = 0.0;
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for (unsigned int k = 0; k < L; k++)
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for (unsigned int k = 0; k < L; k++)
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{
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{
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sum += A[k*L+i]*B[k*N+j];
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sum += A[k*M+i]*B[k*N+j];
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}
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}
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C[i*N+j] = sum;
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C[i*N+j] = sum;
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}
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}
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@ -131,6 +131,7 @@ int main(int argc, char **argv)
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double bytesC = (MC * LC + LC * NC + MC * NC)* sizeof(double);
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double bytesC = (MC * LC + LC * NC + MC * NC)* sizeof(double);
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cout << "\n===== Benchmark C =====\n";
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cout << "\n===== Benchmark C =====\n";
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cout << guardC << endl;
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cout << "bytes: " << bytesC << endl;
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cout << "bytes: " << bytesC << endl;
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cout << "Timing in sec. : " << tC << endl;
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cout << "Timing in sec. : " << tC << endl;
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cout << "GFLOPS : " << flopsC / tC / 1024 / 1024 / 1024 << endl;
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cout << "GFLOPS : " << flopsC / tC / 1024 / 1024 / 1024 << endl;
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@ -172,6 +173,7 @@ int main(int argc, char **argv)
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double bytesD = (p + 2 * ND)*sizeof(double);
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double bytesD = (p + 2 * ND)*sizeof(double);
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cout << "\n===== Benchmark D =====\n";
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cout << "\n===== Benchmark D =====\n";
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cout << guardD << endl;
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cout << "bytes: " << bytesD << endl;
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cout << "bytes: " << bytesD << endl;
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cout << "Timing in sec. : " << tD << endl;
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cout << "Timing in sec. : " << tD << endl;
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cout << "GFLOPS : " << flopsD / tD / 1024 / 1024 / 1024 << endl;
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cout << "GFLOPS : " << flopsD / tD / 1024 / 1024 / 1024 << endl;
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@ -208,6 +210,8 @@ int main(int argc, char **argv)
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cout << "GFLOPS : " << 2.0 * NA / tA / 1024 / 1024 / 1024 << endl;
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cout << "GFLOPS : " << 2.0 * NA / tA / 1024 / 1024 / 1024 << endl;
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cout << "GiByte/s : "
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cout << "GiByte/s : "
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<< NA * sizeof(xA[0]) / tA / 1024 / 1024 / 1024 << endl;
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<< NA * sizeof(xA[0]) / tA / 1024 / 1024 / 1024 << endl;
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//a bit faster due to only accessing one vector
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}
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}
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@ -240,6 +244,8 @@ int main(int argc, char **argv)
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cout << "GFLOPS : " << 5.0 * NA / tA / 1024 / 1024 / 1024 << endl;
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cout << "GFLOPS : " << 5.0 * NA / tA / 1024 / 1024 / 1024 << endl;
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cout << "GiByte/s : "
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cout << "GiByte/s : "
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<< 2.0 * NA * sizeof(xA[0]) / tA / 1024 / 1024 / 1024 << endl;
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<< 2.0 * NA * sizeof(xA[0]) / tA / 1024 / 1024 / 1024 << endl;
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//in comparison to benchmark A: a bit slower runtime but more than double the amount of FLOPS therefor also more GFLOPS
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}
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}
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@ -276,11 +282,16 @@ int main(int argc, char **argv)
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double bytesC = (MC * LC + LC * NC + MC * NC)* sizeof(double);
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double bytesC = (MC * LC + LC * NC + MC * NC)* sizeof(double);
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cout << "\n===== Benchmark 5C =====\n";
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cout << "\n===== Benchmark 5C =====\n";
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cout << guardC << endl;
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cout << "bytes: " << bytesC << endl;
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cout << "bytes: " << bytesC << endl;
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cout << "Timing in sec. : " << tC << endl;
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cout << "Timing in sec. : " << tC << endl;
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cout << "GFLOPS : " << flopsC / tC / 1024 / 1024 / 1024 << endl;
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cout << "GFLOPS : " << flopsC / tC / 1024 / 1024 / 1024 << endl;
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cout << "GiByte/s : " << bytesC / tC / 1024 / 1024 / 1024 << endl;
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cout << "GiByte/s : " << bytesC / tC / 1024 / 1024 / 1024 << endl;
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//slower than rowwise access, due to incoherent acces in the vector memory of A
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//Transpose matrix, the it is also row wise-access or reorder loops
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}
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}
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return 0;
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return 0;
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} // memory for x and y will be deallocated by their destructors
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}
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51
sheet3/345/output.txt
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51
sheet3/345/output.txt
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@ -0,0 +1,51 @@
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o main.o main.cpp
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o mylib.o mylib.cpp
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o benchmark.o benchmark.cpp
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g++ main.o mylib.o benchmark.o -g -O0 -llapack -lblas -flto -o main.GCC_
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./main.GCC_
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===== Benchmark A =====
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<xA,yA> = 1.4e+06
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Timing in sec. : 0.00893637
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GFLOPS : 0.291808
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GiByte/s : 2.33446
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===== Benchmark B =====
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340000
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bytes: 2.31472e+07
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Timing in sec. : 0.0133897
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GFLOPS : 0.402029
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GiByte/s : 1.61001
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===== Benchmark C =====
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7.37196e+07
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bytes: 2.4e+07
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Timing in sec. : 8.67235
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GFLOPS : 0.21478
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GiByte/s : 0.00257736
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===== Benchmark D =====
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10500
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bytes: 3.20001e+07
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Timing in sec. : 0.101087
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GFLOPS : 0.515935
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GiByte/s : 0.294821
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===== Benchmark 5A =====
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NORM = 150114
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Timing in sec. : 0.00703533
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GFLOPS : 0.370658
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GiByte/s : 1.48263
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===== Benchmark 5B =====
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<xA,yA> = 1.4e+06
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Timing in sec. : 0.0108377
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GFLOPS : 0.601533
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GiByte/s : 1.92491
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===== Benchmark 5C =====
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7.37196e+07
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bytes: 2.4e+07
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Timing in sec. : 15.2407
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GFLOPS : 0.122215
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GiByte/s : 0.00146658
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@ -139,4 +139,4 @@ int main(int argc, char **argv)
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return 0;
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return 0;
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} // memory for x and y will be deallocated by their destructors
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}
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24
sheet3/6/output.txt
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24
sheet3/6/output.txt
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@ -0,0 +1,24 @@
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o main.o main.cpp
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o mylib.o mylib.cpp
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g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o benchmark.o benchmark.cpp
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g++ main.o mylib.o benchmark.o -g -O0 -llapack -lblas -flto -o main.GCC_
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./main.GCC_
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===== Benchmark A =====
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<xA,yA> = 1.4e+06
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Timing in sec. : 0.000900578
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GFLOPS : 2.89559
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GiByte/s : 23.1647
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===== Benchmark B =====
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1.7e+07
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bytes: 2.31472e+07
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Timing in sec. : 0.000687268
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GFLOPS : 7.83252
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GiByte/s : 31.3669
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===== Benchmark C =====
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bytes: 2.4e+07
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Timing in sec. : 0.0151789
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GFLOPS : 122.713
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GiByte/s : 1.47255
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@ -13,8 +13,7 @@ COMPILER=GCC_
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# COMPILER=PGI_
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# COMPILER=PGI_
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SOURCES = main.cpp benchmark.cpp
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SOURCES = main.cpp
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OBJECTS = $(SOURCES:.cpp=.o)
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OBJECTS = $(SOURCES:.cpp=.o)
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PROGRAM = main.${COMPILER}
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PROGRAM = main.${COMPILER}
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43
sheet3/7/benchmark.cpp
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43
sheet3/7/benchmark.cpp
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#include <iostream>
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#include <vector>
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#include <cmath>
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using namespace std;
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#include <cblas.h>
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// Inner product
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double benchmark_A(const vector<double> &x, const vector<double> &y)
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{
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return cblas_ddot(x.size(),x.data(),1,y.data(),1);
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}
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//Matrix-vector product
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vector<double> benchmark_B(const vector<double> &A, const vector<double> &x)
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{
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unsigned int N = x.size();
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unsigned int M = A.size() / N;
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vector<double> b(M, 0.0);
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cblas_dgemv(CblasRowMajor,CblasNoTrans,M,N,1,A.data(),N,x.data(),1,0.0,b.data(),1);
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return b;
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}
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//Matrix-Matrix product
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vector<double> benchmark_C(const vector<double> &A, const vector<double> &B, unsigned int M)
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{
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unsigned int L = A.size()/M;
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unsigned int N = B.size()/L;
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vector<double> C(M*N,0.0);
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cblas_dgemm(CblasRowMajor,CblasNoTrans,CblasNoTrans,M,N,L,1.0,A.data(),L,B.data(),N,0.0,C.data(),N);
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return C;
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}
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21
sheet3/7/benchmark.h
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21
sheet3/7/benchmark.h
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#ifndef BENCHMARK_H
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#define BENCHMARK_H
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#include <vector>
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using namespace std;
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double benchmark_A(const vector<double> &x,
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const vector<double> &y);
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vector<double> benchmark_B(const vector<double> &A,
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const vector<double> &x);
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vector<double> benchmark_C(const vector<double> &A,
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const vector<double> &B,
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unsigned int M);
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#endif
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Binary file not shown.
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#include <sstream>
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#include <sstream>
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#include <vector>
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#include <vector>
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#include <lapacke.h>
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#include <lapacke.h>
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#include "timing.h"
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#include "benchmark.h"
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using namespace std;
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using namespace std;
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using namespace std::chrono; // timing
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using namespace std::chrono; // timing
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int main()
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int main()
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{
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{
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unsigned int n= 10;
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unsigned int n= 32;
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unsigned int nhrs = 1;
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vector<double> M(n*n,4.0);
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vector<double> M(n*n,4.0);
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@ -32,7 +32,7 @@ int main()
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}
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}
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vector<double> M2 = M;
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|
||||||
LAPACKE_dgetrf(LAPACK_ROW_MAJOR,n,n, M.data(),n,ipiv.data()); //M=PLU
|
LAPACKE_dgetrf(LAPACK_ROW_MAJOR,n,n, M.data(),n,ipiv.data()); //M=PLU
|
||||||
|
|
||||||
|
|
||||||
unsigned int runtimes[] = {1,2,4,8,16,32};
|
|
||||||
|
|
||||||
for(unsigned int i=0; i < 6;i++)
|
|
||||||
|
double time;
|
||||||
|
unsigned int nhrsmax = 1000000;
|
||||||
|
for(unsigned int i=nhrsmax/10; i < nhrsmax;i+=nhrsmax/10)
|
||||||
{
|
{
|
||||||
nhrs = runtimes[i];
|
|
||||||
vector<double> b(n*nhrs,0.0);
|
|
||||||
for (unsigned int j=0; j<n; j++)
|
|
||||||
{
|
|
||||||
for (unsigned int k=0; k<nhrs; k++)
|
|
||||||
{
|
|
||||||
b[j*nhrs+k] = j*nhrs+k;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
LAPACKE_dgetrs(LAPACK_ROW_MAJOR,'N',n,nhrs,M.data(),n,ipiv.data(),b.data(),nhrs);
|
|
||||||
}
|
|
||||||
|
|
||||||
|
unsigned int nhrs = i;
|
||||||
|
|
||||||
|
//FOR CHECKING
|
||||||
|
vector<double> X(n*nhrs,1.0);
|
||||||
|
|
||||||
|
vector<double> b = benchmark_C(M2,X,n);
|
||||||
|
|
||||||
|
tic();
|
||||||
|
LAPACKE_dgetrs(LAPACK_ROW_MAJOR,'N',n,nhrs,M.data(),n,ipiv.data(),b.data(),nhrs);
|
||||||
|
time = toc();
|
||||||
|
cout << "Time for nhrs=" << nhrs << ": " << time << endl;
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
double max_err = 0.0;
|
||||||
|
for (unsigned int j = 0; j < n * nhrs; j++)
|
||||||
|
{
|
||||||
|
double err = b[j] - X[j];
|
||||||
|
err *= err;
|
||||||
|
if (err > max_err) max_err = err;
|
||||||
|
}
|
||||||
|
cout <<"max err^2:" << max_err <<endl;
|
||||||
|
cout <<endl;
|
||||||
|
|
||||||
|
}
|
||||||
|
/*
|
||||||
|
|
||||||
|
Time for nhrs=100000: 0.0605495
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=200000: 0.127608
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=300000: 0.182197
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=400000: 0.202608
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=500000: 0.24484
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=600000: 0.298055
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=700000: 0.362414
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=800000: 0.410004
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time for nhrs=900000: 0.492339
|
||||||
|
max err^2:4.93038e-32
|
||||||
|
|
||||||
|
Time grows slow (linearly)
|
||||||
|
*/
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
BIN
sheet3/7/mylib.o
BIN
sheet3/7/mylib.o
Binary file not shown.
51
sheet3/7/timing.h
Normal file
51
sheet3/7/timing.h
Normal file
|
|
@ -0,0 +1,51 @@
|
||||||
|
//
|
||||||
|
// Gundolf Haase, Oct 18 2024
|
||||||
|
//
|
||||||
|
#pragma once
|
||||||
|
#include <chrono> // timing
|
||||||
|
#include <stack>
|
||||||
|
|
||||||
|
//using Clock = std::chrono::system_clock; //!< The wall clock timer chosen
|
||||||
|
using Clock = std::chrono::high_resolution_clock;
|
||||||
|
using TPoint= std::chrono::time_point<Clock>;
|
||||||
|
|
||||||
|
// [Galowicz, C++17 STL Cookbook, p. 29]
|
||||||
|
|
||||||
|
std::stack<TPoint> MyStopWatch; //!< starting time of stopwatch
|
||||||
|
|
||||||
|
/** Starts stopwatch timer.
|
||||||
|
* Use as @code tic(); myfunction(...) ; double tsec = toc(); @endcode
|
||||||
|
*
|
||||||
|
* The timining can be nested and the recent time point is stored on top of the stack.
|
||||||
|
*
|
||||||
|
* @return recent time point
|
||||||
|
* @see toc
|
||||||
|
*/
|
||||||
|
auto tic()
|
||||||
|
{
|
||||||
|
MyStopWatch.push(Clock::now());
|
||||||
|
return MyStopWatch.top();
|
||||||
|
}
|
||||||
|
|
||||||
|
/** Returns the elapsed time from stopwatch.
|
||||||
|
*
|
||||||
|
* The time point from top of the stack is used
|
||||||
|
* if time point @p t_b is not passed as input parameter.
|
||||||
|
* Use as @code tic(); myfunction(...) ; double tsec = toc(); @endcode
|
||||||
|
* or as @code auto t_b = tic(); myfunction(...) ; double tsec = toc(t_b); @endcode
|
||||||
|
* The last option is to be used in the case of
|
||||||
|
* non-nested but overlapping time measurements.
|
||||||
|
*
|
||||||
|
* @param[in] t_b start time of some stop watch
|
||||||
|
* @return elapsed time in seconds.
|
||||||
|
*
|
||||||
|
*/
|
||||||
|
double toc(TPoint const &t_b = MyStopWatch.top())
|
||||||
|
{
|
||||||
|
// https://en.cppreference.com/w/cpp/chrono/treat_as_floating_point
|
||||||
|
using Unit = std::chrono::seconds;
|
||||||
|
using FpSeconds = std::chrono::duration<double, Unit::period>;
|
||||||
|
auto t_e = Clock::now();
|
||||||
|
MyStopWatch.pop();
|
||||||
|
return FpSeconds(t_e-t_b).count();
|
||||||
|
}
|
||||||
2877
sheet3/8/Doxyfile
Normal file
2877
sheet3/8/Doxyfile
Normal file
File diff suppressed because it is too large
Load diff
54
sheet3/8/Makefile
Normal file
54
sheet3/8/Makefile
Normal file
|
|
@ -0,0 +1,54 @@
|
||||||
|
#
|
||||||
|
# use GNU-Compiler tools
|
||||||
|
COMPILER=GCC_
|
||||||
|
# COMPILER=GCC_SEQ_
|
||||||
|
# alternatively from the shell
|
||||||
|
# export COMPILER=GCC_
|
||||||
|
# or, alternatively from the shell
|
||||||
|
# make COMPILER=GCC_
|
||||||
|
|
||||||
|
MAIN = main
|
||||||
|
SOURCES = ${MAIN}.cpp vdop.cpp geom.cpp\
|
||||||
|
getmatrix.cpp jacsolve.cpp userset.cpp
|
||||||
|
# dexx.cpp debugd.cpp skalar.cpp vecaccu.cpp accudiag.cpp
|
||||||
|
|
||||||
|
OBJECTS = $(SOURCES:.cpp=.o)
|
||||||
|
|
||||||
|
PROGRAM = ${MAIN}.${COMPILER}
|
||||||
|
|
||||||
|
# uncomment the next to lines for debugging and detailed performance analysis
|
||||||
|
CXXFLAGS += -g
|
||||||
|
# -pg slows down the code on my laptop when using CLANG_
|
||||||
|
#LINKFLAGS += -pg
|
||||||
|
#CXXFLAGS += -Q --help=optimizers
|
||||||
|
#CXXFLAGS += -fopt-info
|
||||||
|
|
||||||
|
include ../${COMPILER}default.mk
|
||||||
|
|
||||||
|
#############################################################################
|
||||||
|
# additional specific cleaning in this directory
|
||||||
|
clean_all::
|
||||||
|
@rm -f t.dat*
|
||||||
|
|
||||||
|
|
||||||
|
#############################################################################
|
||||||
|
# special testing
|
||||||
|
# NPROCS = 4
|
||||||
|
#
|
||||||
|
TFILE = t.dat
|
||||||
|
# TTMP = t.tmp
|
||||||
|
#
|
||||||
|
graph: $(PROGRAM)
|
||||||
|
# @rm -f $(TFILE).*
|
||||||
|
# next two lines only sequentially
|
||||||
|
./$(PROGRAM)
|
||||||
|
@mv $(TFILE).000 $(TFILE)
|
||||||
|
# $(MPIRUN) $(MPIFLAGS) -np $(NPROCS) $(PROGRAM)
|
||||||
|
# @echo " "; echo "Manipulate data for graphics."; echo " "
|
||||||
|
# @cat $(TFILE).* > $(TTMP)
|
||||||
|
# @sort -b -k 2 $(TTMP) -o $(TTMP).1
|
||||||
|
# @sort -b -k 1 $(TTMP).1 -o $(TTMP).2
|
||||||
|
# @awk -f nl.awk $(TTMP).2 > $(TFILE)
|
||||||
|
# @rm -f $(TTMP).* $(TTMP) $(TFILE).*
|
||||||
|
#
|
||||||
|
-gnuplot jac.dem
|
||||||
5
sheet3/8/ToDo.txt
Normal file
5
sheet3/8/ToDo.txt
Normal file
|
|
@ -0,0 +1,5 @@
|
||||||
|
// Jan 15, 2019
|
||||||
|
|
||||||
|
geom.h:75 void SetValues(std::vector<double> &v) const; // GH: TODO with functor
|
||||||
|
Set vector values using a functor ff(x,y).
|
||||||
|
See solution in Progs/cds
|
||||||
43
sheet3/8/ascii_read_meshvector.m
Normal file
43
sheet3/8/ascii_read_meshvector.m
Normal file
|
|
@ -0,0 +1,43 @@
|
||||||
|
function [ xc, ia, v ] = ascii_read_meshvector( fname )
|
||||||
|
%
|
||||||
|
% Loads the 2D triangular mesh (coordinates, vertex connectivity)
|
||||||
|
% together with values on its vertices from an ASCII file.
|
||||||
|
% Matlab indexing is stored (starts with 1).
|
||||||
|
%
|
||||||
|
% The input file format is compatible
|
||||||
|
% with Mesh_2d_3_matlab:Write_ascii_matlab(..) in jacobi_oo_stl/geom.h
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% IN: fname - filename
|
||||||
|
% OUT: xc - coordinates
|
||||||
|
% ia - mesh connectivity
|
||||||
|
% v - solution vector
|
||||||
|
|
||||||
|
DELIMETER = ' ';
|
||||||
|
|
||||||
|
fprintf('Read file %s\n',fname)
|
||||||
|
|
||||||
|
% Read mesh constants
|
||||||
|
nn = dlmread(fname,DELIMETER,[0 0 0 3]); %% row_1, col_1, row_2, col_2 in C indexing!!!
|
||||||
|
nnode = nn(1);
|
||||||
|
ndim = nn(2);
|
||||||
|
nelem = nn(3);
|
||||||
|
nvert = nn(4);
|
||||||
|
|
||||||
|
% Read coordinates
|
||||||
|
row_start = 0+1;
|
||||||
|
row_end = 0+nnode;
|
||||||
|
xc = dlmread(fname,DELIMETER,[row_start 0 row_end ndim-1]);
|
||||||
|
|
||||||
|
% Read connectivity
|
||||||
|
row_start = row_end+1;
|
||||||
|
row_end = row_end+nelem;
|
||||||
|
ia = dlmread(fname,DELIMETER,[row_start 0 row_end nvert-1]);
|
||||||
|
|
||||||
|
% Read solution
|
||||||
|
row_start = row_end+1;
|
||||||
|
row_end = row_end+nnode;
|
||||||
|
v = dlmread(fname,DELIMETER,[row_start 0 row_end 0]);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
49
sheet3/8/ascii_write_mesh.m
Normal file
49
sheet3/8/ascii_write_mesh.m
Normal file
|
|
@ -0,0 +1,49 @@
|
||||||
|
function ascii_write_mesh( xc, ia, e, basename)
|
||||||
|
%
|
||||||
|
% Saves the 2D triangular mesh in the minimal way (only coordinates, vertex connectivity, minimal boundary edge info)
|
||||||
|
% in an ASCII file.
|
||||||
|
% Matlab indexing is stored (starts with 1).
|
||||||
|
%
|
||||||
|
% The output file format is compatible with Mesh_2d_3_matlab:Mesh_2d_3_matlab(std::string const &fname) in jacobi_oo_stl/geom.h
|
||||||
|
%
|
||||||
|
% IN:
|
||||||
|
% coordinates xc: [2][nnode]
|
||||||
|
% connectivity ia: [4][nelem] with t(4,:) are the subdomain numbers
|
||||||
|
% edges e: [7][nedges] boundary edges
|
||||||
|
% e([1,2],:) - start/end vertex of edge
|
||||||
|
% e([3,4],:) - start/end values
|
||||||
|
% e(5,:) - segment number
|
||||||
|
% e([6,7],:) - left/right subdomain
|
||||||
|
% basename: file name without extension
|
||||||
|
%
|
||||||
|
% Data have been generated via <https://de.mathworks.com/help/pde/ug/initmesh.html initmesh>.
|
||||||
|
%
|
||||||
|
fname = [basename, '.txt'];
|
||||||
|
|
||||||
|
nnode = int32(size(xc,2));
|
||||||
|
ndim = int32(size(xc,1));
|
||||||
|
nelem = int32(size(ia,2));
|
||||||
|
nvert_e = int32(3);
|
||||||
|
|
||||||
|
|
||||||
|
dlmwrite(fname,nnode,'delimiter','\t','precision',16) % number of nodes
|
||||||
|
dlmwrite(fname,ndim,'-append','delimiter','\t','precision',16) % space dimension
|
||||||
|
dlmwrite(fname,nelem,'-append','delimiter','\t','precision',16) % number of elements
|
||||||
|
dlmwrite(fname,nvert_e,'-append','delimiter','\t','precision',16) % number of vertices per element
|
||||||
|
|
||||||
|
% dlmwrite(fname,xc(:),'-append','delimiter','\t','precision',16) % coordinates
|
||||||
|
dlmwrite(fname,xc([1,2],:).','-append','delimiter','\t','precision',16) % coordinates
|
||||||
|
|
||||||
|
% no subdomain info transferred
|
||||||
|
tmp=int32(ia(1:3,:));
|
||||||
|
% dlmwrite(fname,tmp(:),'-append','delimiter','\t','precision',16) % connectivity in Matlab indexing
|
||||||
|
dlmwrite(fname,tmp(:,:).','-append','delimiter','\t','precision',16) % connectivity in Matlab indexing
|
||||||
|
|
||||||
|
% store only start and end point of boundary edges,
|
||||||
|
nbedges = size(e,2);
|
||||||
|
dlmwrite(fname,nbedges,'-append','delimiter','\t','precision',16) % number boundary edges
|
||||||
|
tmp=int32(e(1:2,:));
|
||||||
|
% dlmwrite(fname,tmp(:),'-append','delimiter','\t','precision',16) % boundary edges in Matlab indexing
|
||||||
|
dlmwrite(fname,tmp(:,:).','-append','delimiter','\t','precision',16) % boundary edges in Matlab indexing
|
||||||
|
|
||||||
|
end
|
||||||
522
sheet3/8/geom.cpp
Normal file
522
sheet3/8/geom.cpp
Normal file
|
|
@ -0,0 +1,522 @@
|
||||||
|
// see: http://llvm.org/docs/CodingStandards.html#include-style
|
||||||
|
#include "geom.h"
|
||||||
|
|
||||||
|
#include <algorithm>
|
||||||
|
#include <cassert>
|
||||||
|
#include <fstream>
|
||||||
|
#include <iostream>
|
||||||
|
#include <list>
|
||||||
|
#include <string>
|
||||||
|
#include <vector>
|
||||||
|
using namespace std;
|
||||||
|
|
||||||
|
Mesh::Mesh(int ndim, int nvert_e, int ndof_e)
|
||||||
|
: _nelem(0), _nvert_e(nvert_e), _ndof_e(ndof_e), _nnode(0), _ndim(ndim), _ia(0), _xc(0)
|
||||||
|
{
|
||||||
|
}
|
||||||
|
|
||||||
|
Mesh::~Mesh()
|
||||||
|
{}
|
||||||
|
|
||||||
|
void Mesh::SetValues(std::vector<double> &v, const std::function<double(double, double)> &func) const
|
||||||
|
{
|
||||||
|
int const nnode = Nnodes(); // number of vertices in mesh
|
||||||
|
assert( nnode == static_cast<int>(v.size()) );
|
||||||
|
for (int k = 0; k < nnode; ++k)
|
||||||
|
{
|
||||||
|
v[k] = func( _xc[2 * k], _xc[2 * k + 1] );
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void Mesh::Debug() const
|
||||||
|
{
|
||||||
|
cout << "\n ############### Debug M E S H ###################\n";
|
||||||
|
cout << "\n ............... Coordinates ...................\n";
|
||||||
|
for (int k = 0; k < _nnode; ++k)
|
||||||
|
{
|
||||||
|
cout << k << " : " ;
|
||||||
|
for (int i = 0; i < _ndof_e; ++i )
|
||||||
|
{
|
||||||
|
cout << _xc[2*k+i] << " ";
|
||||||
|
}
|
||||||
|
cout << endl;
|
||||||
|
}
|
||||||
|
cout << "\n ............... Elements ...................\n";
|
||||||
|
for (int k = 0; k < _nelem; ++k)
|
||||||
|
{
|
||||||
|
cout << k << " : ";
|
||||||
|
for (int i = 0; i < _ndof_e; ++i )
|
||||||
|
cout << _ia[_ndof_e * k + i] << " ";
|
||||||
|
cout << endl;
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void Mesh::Write_ascii_matlab(std::string const &fname, std::vector<double> const &v) const
|
||||||
|
{
|
||||||
|
assert(Nnodes() == static_cast<int>(v.size())); // fits vector length to mesh information?
|
||||||
|
|
||||||
|
ofstream fout(fname); // open file ASCII mode
|
||||||
|
if ( !fout.is_open() )
|
||||||
|
{
|
||||||
|
cout << "\nFile " << fname << " has not been opened.\n\n" ;
|
||||||
|
assert( fout.is_open() && "File not opened." );
|
||||||
|
}
|
||||||
|
|
||||||
|
string const DELIMETER(" "); // define the same delimeter as in matlab/ascii_read*.m
|
||||||
|
int const OFFSET(1); // convert C-indexing to matlab
|
||||||
|
|
||||||
|
// Write data: #nodes, #space dimensions, #elements, #vertices per element
|
||||||
|
fout << Nnodes() << DELIMETER << Ndims() << DELIMETER << Nelems() << DELIMETER << NverticesElements() << endl;
|
||||||
|
|
||||||
|
// Write cordinates: x_k, y_k in seperate lines
|
||||||
|
assert( Nnodes()*Ndims() == static_cast<int>(_xc.size()));
|
||||||
|
for (int k = 0, kj = 0; k < Nnodes(); ++k)
|
||||||
|
{
|
||||||
|
for (int j = 0; j < Ndims(); ++j, ++kj)
|
||||||
|
{
|
||||||
|
fout << _xc[kj] << DELIMETER;
|
||||||
|
}
|
||||||
|
fout << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Write connectivity: ia_k,0, ia_k,1 etc in seperate lines
|
||||||
|
assert( Nelems()*NverticesElements() == static_cast<int>(_ia.size()));
|
||||||
|
for (int k = 0, kj = 0; k < Nelems(); ++k)
|
||||||
|
{
|
||||||
|
for (int j = 0; j < NverticesElements(); ++j, ++kj)
|
||||||
|
{
|
||||||
|
fout << _ia[kj] + OFFSET << DELIMETER; // C to matlab
|
||||||
|
}
|
||||||
|
fout << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Write vector
|
||||||
|
for (int k = 0; k < Nnodes(); ++k)
|
||||||
|
{
|
||||||
|
fout << v[k] << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
fout.close();
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void Mesh::Visualize(std::vector<double> const &v) const
|
||||||
|
{
|
||||||
|
// define external command
|
||||||
|
const string exec_m("matlab -nosplash < visualize_results.m"); // Matlab
|
||||||
|
//const string exec_m("octave --no-window-system --no-gui visualize_results.m"); // Octave
|
||||||
|
//const string exec_m("flatpak run org.octave.Octave visualize_results.m"); // Octave (flatpak): desktop GH
|
||||||
|
|
||||||
|
const string fname("uv.txt");
|
||||||
|
Write_ascii_matlab(fname, v);
|
||||||
|
|
||||||
|
int ierror = system(exec_m.c_str()); // call external command
|
||||||
|
|
||||||
|
if (ierror != 0)
|
||||||
|
{
|
||||||
|
cout << endl << "Check path to Matlab/octave on your system" << endl;
|
||||||
|
}
|
||||||
|
cout << endl;
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// #####################################################################
|
||||||
|
Mesh_2d_3_square::Mesh_2d_3_square(int nx, int ny, int myid, int procx, int procy)
|
||||||
|
: Mesh(2, 3, 3), // two dimensions, 3 vertices, 3 dofs
|
||||||
|
_myid(myid), _procx(procx), _procy(procy), _neigh{{-1, -1, -1, -1}}, _color(0),
|
||||||
|
_xl(0.0), _xr(1.0), _yb(0.0), _yt(1.0), _nx(nx), _ny(ny)
|
||||||
|
{
|
||||||
|
//void IniGeom(int const myid, int const procx, int const procy, int neigh[], int &color)
|
||||||
|
int const ky = _myid / _procx;
|
||||||
|
int const kx = _myid % _procy; // MOD(myid,procx)
|
||||||
|
// Determine the neighbors of domain/rank myid
|
||||||
|
_neigh[0] = (ky == 0) ? -1 : _myid - _procx; // South
|
||||||
|
_neigh[1] = (kx == _procx - 1) ? -1 : _myid + 1; // East
|
||||||
|
_neigh[2] = (ky == _procy - 1) ? -1 : _myid + _procx; // North
|
||||||
|
_neigh[3] = (kx == 0) ? -1 : _myid - 1; // West
|
||||||
|
|
||||||
|
_color = (kx + ky) & 1 ;
|
||||||
|
|
||||||
|
// subdomain is part of unit square
|
||||||
|
double const hx = 1. / _procx;
|
||||||
|
double const hy = 1. / _procy;
|
||||||
|
_xl = kx * hx; // left
|
||||||
|
_xr = (kx + 1) * hx; // right
|
||||||
|
_yb = ky * hy; // bottom
|
||||||
|
_yt = (ky + 1) * hy; // top
|
||||||
|
|
||||||
|
// Calculate coordinates
|
||||||
|
int const nnode = (_nx + 1) * (_ny + 1); // number of nodes
|
||||||
|
Resize_Coords(nnode, 2); // coordinates in 2D [nnode][ndim]
|
||||||
|
GetCoordsInRectangle(_nx, _ny, _xl, _xr, _yb, _yt, GetCoords().data());
|
||||||
|
|
||||||
|
// Calculate element connectivity (linear triangles)
|
||||||
|
int const nelem = 2 * _nx * _ny; // number of elements
|
||||||
|
Resize_Connectivity(nelem, 3); // connectivity matrix [nelem][3]
|
||||||
|
GetConnectivityInRectangle(_nx, _ny, GetConnectivity().data());
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void Mesh_2d_3_square::SetU(std::vector<double> &u) const
|
||||||
|
{
|
||||||
|
int dx = _nx + 1;
|
||||||
|
for (int j = 0; j <= _ny; ++j)
|
||||||
|
{
|
||||||
|
int k = j * dx;
|
||||||
|
for (int i = 0; i <= _nx; ++i, ++k)
|
||||||
|
{
|
||||||
|
u[k] = 0.0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
void Mesh_2d_3_square::SetF(std::vector<double> &f) const
|
||||||
|
{
|
||||||
|
int dx = _nx + 1;
|
||||||
|
for (int j = 0; j <= _ny; ++j)
|
||||||
|
{
|
||||||
|
int k = j * dx;
|
||||||
|
for (int i = 0; i <= _nx; ++i, ++k)
|
||||||
|
{
|
||||||
|
f[k] = 1.0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
std::vector<int> Mesh_2d_3_square::Index_DirichletNodes() const
|
||||||
|
{
|
||||||
|
int const dx = 1,
|
||||||
|
dy = _nx + 1,
|
||||||
|
bl = 0,
|
||||||
|
br = _nx,
|
||||||
|
tl = _ny * (_nx + 1),
|
||||||
|
tr = (_ny + 1) * (_nx + 1) - 1;
|
||||||
|
int const start[4] = { bl, br, tl, bl},
|
||||||
|
end[4] = { br, tr, tr, tl},
|
||||||
|
step[4] = { dx, dy, dx, dy};
|
||||||
|
|
||||||
|
vector<int> idx(0);
|
||||||
|
for (int j = 0; j < 4; j++)
|
||||||
|
{
|
||||||
|
if (_neigh[j] < 0)
|
||||||
|
{
|
||||||
|
for (int i = start[j]; i <= end[j]; i += step[j])
|
||||||
|
{
|
||||||
|
idx.push_back(i); // node i is Dirichlet node
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// remove multiple elements
|
||||||
|
sort(idx.begin(), idx.end()); // sort
|
||||||
|
idx.erase( unique(idx.begin(), idx.end()), idx.end() ); // remove duplicate data
|
||||||
|
|
||||||
|
return idx;
|
||||||
|
}
|
||||||
|
|
||||||
|
void Mesh_2d_3_square::SaveVectorP(std::string const &name, vector<double> const &u) const
|
||||||
|
{
|
||||||
|
// construct the file name for subdomain myid
|
||||||
|
const string tmp( std::to_string(_myid / 100) + to_string((_myid % 100) / 10) + to_string(_myid % 10) );
|
||||||
|
|
||||||
|
const string namep = name + "." + tmp;
|
||||||
|
ofstream ff(namep.c_str());
|
||||||
|
ff.precision(6);
|
||||||
|
ff.setf(ios::fixed, ios::floatfield);
|
||||||
|
|
||||||
|
// assumes tensor product grid in unit square; rowise numbered (as generated in class constructor)
|
||||||
|
// output is provided for tensor product grid visualization ( similar to Matlab-surf() )
|
||||||
|
auto const &xc = GetCoords();
|
||||||
|
int k = 0;
|
||||||
|
for (int j = 0; j <= _ny; ++j)
|
||||||
|
{
|
||||||
|
for (int i = 0; i <= _nx; ++i, ++k)
|
||||||
|
ff << xc[2 * k + 0] << " " << xc[2 * k + 1] << " " << u[k] << endl;
|
||||||
|
ff << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
ff.close();
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void Mesh_2d_3_square::GetCoordsInRectangle(int const nx, int const ny,
|
||||||
|
double const xl, double const xr, double const yb, double const yt,
|
||||||
|
double xc[])
|
||||||
|
{
|
||||||
|
const double hx = (xr - xl) / nx,
|
||||||
|
hy = (yt - yb) / ny;
|
||||||
|
|
||||||
|
int k = 0;
|
||||||
|
for (int j = 0; j <= ny; ++j)
|
||||||
|
{
|
||||||
|
const double y0 = yb + j * hy;
|
||||||
|
for (int i = 0; i <= nx; ++i, k += 2)
|
||||||
|
{
|
||||||
|
xc[k ] = xl + i * hx;
|
||||||
|
xc[k + 1] = y0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void Mesh_2d_3_square::GetConnectivityInRectangle(int const nx, int const ny, int ia[])
|
||||||
|
{
|
||||||
|
const int dx = nx + 1;
|
||||||
|
int k = 0;
|
||||||
|
int l = 0;
|
||||||
|
for (int j = 0; j < ny; ++j, ++k)
|
||||||
|
{
|
||||||
|
for (int i = 0; i < nx; ++i, ++k)
|
||||||
|
{
|
||||||
|
ia[l ] = k;
|
||||||
|
ia[l + 1] = k + 1;
|
||||||
|
ia[l + 2] = k + dx + 1;
|
||||||
|
l += 3;
|
||||||
|
ia[l ] = k;
|
||||||
|
ia[l + 1] = k + dx;
|
||||||
|
ia[l + 2] = k + dx + 1;
|
||||||
|
l += 3;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// #################### still some old code (--> MPI) ############################
|
||||||
|
|
||||||
|
|
||||||
|
// Copies the values of w corresponding to the boundary
|
||||||
|
// South (ib==1), East (ib==2), North (ib==3), West (ib==4)
|
||||||
|
|
||||||
|
void GetBound(int const ib, int const nx, int const ny, double const w[], double s[])
|
||||||
|
{
|
||||||
|
const int //dx = 1,
|
||||||
|
dy = nx + 1,
|
||||||
|
bl = 0,
|
||||||
|
br = nx,
|
||||||
|
tl = ny * (nx + 1),
|
||||||
|
tr = (ny + 1) * (nx + 1) - 1;
|
||||||
|
switch (ib)
|
||||||
|
{
|
||||||
|
case 1:
|
||||||
|
{
|
||||||
|
for (int i = bl, j = 0; i <= br; ++i, ++j)
|
||||||
|
s[j] = w[i];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 3:
|
||||||
|
{
|
||||||
|
for (int i = tl, j = 0; i <= tr; ++i, ++j)
|
||||||
|
s[j] = w[i];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 4:
|
||||||
|
{
|
||||||
|
for (int i = bl, j = 0; i <= tl; i += dy, ++j)
|
||||||
|
s[j] = w[i];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 2:
|
||||||
|
{
|
||||||
|
for (int i = br, j = 0; i <= tr; i += dy, ++j)
|
||||||
|
s[j] = w[i];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
default:
|
||||||
|
{
|
||||||
|
cout << endl << "Wrong parameter ib in " << __FILE__ << ":" << __LINE__ << endl;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// ----------------------------------------------------------------------------------------------------------
|
||||||
|
// Computes w: = w + s at nodes on the boundary
|
||||||
|
// South (ib == 1), East (ib == 2), North (ib == 3), West (ib == 4)
|
||||||
|
|
||||||
|
void AddBound(int const ib, int const nx, int const ny, double w[], double const s[])
|
||||||
|
{
|
||||||
|
int const dy = nx + 1,
|
||||||
|
bl = 0,
|
||||||
|
br = nx,
|
||||||
|
tl = ny * (nx + 1),
|
||||||
|
tr = (ny + 1) * (nx + 1) - 1;
|
||||||
|
switch (ib)
|
||||||
|
{
|
||||||
|
case 1:
|
||||||
|
{
|
||||||
|
for (int i = bl, j = 0; i <= br; ++i, ++j)
|
||||||
|
w[i] += s[j];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 3:
|
||||||
|
{
|
||||||
|
for (int i = tl, j = 0; i <= tr; ++i, ++j)
|
||||||
|
w[i] += s[j];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 4:
|
||||||
|
{
|
||||||
|
for (int i = bl, j = 0; i <= tl; i += dy, ++j)
|
||||||
|
w[i] += s[j];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
case 2:
|
||||||
|
{
|
||||||
|
for (int i = br, j = 0; i <= tr; i += dy, ++j)
|
||||||
|
w[i] += s[j];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
default:
|
||||||
|
{
|
||||||
|
cout << endl << "Wrong parameter ib in " << __FILE__ << ":" << __LINE__ << endl;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// ####################################################################
|
||||||
|
|
||||||
|
Mesh_2d_3_matlab::Mesh_2d_3_matlab(string const &fname)
|
||||||
|
: Mesh(2, 3, 3), // two dimensions, 3 vertices, 3 dofs
|
||||||
|
bedges(0)
|
||||||
|
{
|
||||||
|
ifstream ifs(fname);
|
||||||
|
if (!(ifs.is_open() && ifs.good()))
|
||||||
|
{
|
||||||
|
cerr << "Mesh_2d_3_matlab: Error cannot open file " << fname << endl;
|
||||||
|
assert(ifs.is_open());
|
||||||
|
}
|
||||||
|
|
||||||
|
int const OFFSET(1); // Matlab to C indexing
|
||||||
|
cout << "ASCI file " << fname << " opened" << endl;
|
||||||
|
|
||||||
|
// Read some mesh constants
|
||||||
|
int nnode, ndim, nelem, nvert_e;
|
||||||
|
ifs >> nnode >> ndim >> nelem >> nvert_e;
|
||||||
|
cout << nnode << " " << ndim << " " << nelem << " " << nvert_e << endl;
|
||||||
|
assert(ndim == 2 && nvert_e == 3);
|
||||||
|
|
||||||
|
// Allocate memory
|
||||||
|
Resize_Coords(nnode, ndim); // coordinates in 2D [nnode][ndim]
|
||||||
|
Resize_Connectivity(nelem, nvert_e); // connectivity matrix [nelem][nvert]
|
||||||
|
|
||||||
|
// Read ccordinates
|
||||||
|
auto &xc = GetCoords();
|
||||||
|
for (int k = 0; k < nnode * ndim; ++k)
|
||||||
|
{
|
||||||
|
ifs >> xc[k];
|
||||||
|
}
|
||||||
|
|
||||||
|
// Read connectivity
|
||||||
|
auto &ia = GetConnectivity();
|
||||||
|
for (int k = 0; k < nelem * nvert_e; ++k)
|
||||||
|
{
|
||||||
|
ifs >> ia[k];
|
||||||
|
ia[k] -= OFFSET; // Matlab to C indexing
|
||||||
|
}
|
||||||
|
|
||||||
|
// additional read of boundary information (only start/end point)
|
||||||
|
int nbedges;
|
||||||
|
ifs >> nbedges;
|
||||||
|
|
||||||
|
bedges.resize(nbedges * 2);
|
||||||
|
for (int k = 0; k < nbedges * 2; ++k)
|
||||||
|
{
|
||||||
|
ifs >> bedges[k];
|
||||||
|
bedges[k] -= OFFSET; // Matlab to C indexing
|
||||||
|
}
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// binary
|
||||||
|
//{
|
||||||
|
//ifstream ifs(fname, ios_base::in | ios_base::binary);
|
||||||
|
//if(!(ifs.is_open() && ifs.good()))
|
||||||
|
//{
|
||||||
|
//cerr << "ReadBinMatrix: Error cannot open file " << file << endl;
|
||||||
|
//assert(ifs.is_open());
|
||||||
|
//}
|
||||||
|
//cout << "ReadBinMatrix: file opened" << file << endl;
|
||||||
|
|
||||||
|
|
||||||
|
//}
|
||||||
|
|
||||||
|
// binaryIO.cpp
|
||||||
|
//void read_binMatrix(const string& file, vector<int> &cnt, vector<int> &col, vector<double> &ele)
|
||||||
|
//{
|
||||||
|
|
||||||
|
//ifstream ifs(file, ios_base::in | ios_base::binary);
|
||||||
|
|
||||||
|
//if(!(ifs.is_open() && ifs.good()))
|
||||||
|
//{
|
||||||
|
//cerr << "ReadBinMatrix: Error cannot open file " << file << endl;
|
||||||
|
//assert(ifs.is_open());
|
||||||
|
//}
|
||||||
|
//cout << "ReadBinMatrix: Opened file " << file << endl;
|
||||||
|
|
||||||
|
//int _size;
|
||||||
|
|
||||||
|
//ifs.read(reinterpret_cast<char*>(&_size), sizeof(int)); // old: ifs.read((char*)&_size, sizeof(int));
|
||||||
|
//cnt.resize(_size);
|
||||||
|
//cout << "ReadBinMatrix: cnt size: " << _size << endl;
|
||||||
|
|
||||||
|
//ifs.read((char*)&_size, sizeof(int));
|
||||||
|
//col.resize(_size);
|
||||||
|
//cout << "ReadBinMatrix: col size: " << _size << endl;
|
||||||
|
|
||||||
|
//ifs.read((char*)&_size, sizeof(int));
|
||||||
|
//ele.resize(_size);
|
||||||
|
//cout << "ReadBinMatrix: ele size: " << _size << endl;
|
||||||
|
|
||||||
|
|
||||||
|
//ifs.read((char*)cnt.data(), cnt.size() * sizeof(int));
|
||||||
|
//ifs.read((char*)col.data(), col.size() * sizeof(int));
|
||||||
|
//ifs.read((char*)ele.data(), ele.size() * sizeof(double));
|
||||||
|
|
||||||
|
//ifs.close();
|
||||||
|
//cout << "ReadBinMatrix: Finished reading matrix.." << endl;
|
||||||
|
|
||||||
|
//}
|
||||||
|
|
||||||
|
|
||||||
|
std::vector<int> Mesh_2d_3_matlab::Index_DirichletNodes() const
|
||||||
|
{
|
||||||
|
vector<int> idx(bedges); // copy
|
||||||
|
|
||||||
|
sort(idx.begin(), idx.end()); // sort
|
||||||
|
idx.erase( unique(idx.begin(), idx.end()), idx.end() ); // remove duplicate data
|
||||||
|
|
||||||
|
return idx;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
381
sheet3/8/geom.h
Normal file
381
sheet3/8/geom.h
Normal file
|
|
@ -0,0 +1,381 @@
|
||||||
|
#ifndef GEOM_FILE
|
||||||
|
#define GEOM_FILE
|
||||||
|
#include <array>
|
||||||
|
#include <functional> // function; C++11
|
||||||
|
#include <string>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Basis class for finite element meshes.
|
||||||
|
*/
|
||||||
|
class Mesh
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/**
|
||||||
|
* Constructor initializing the members with default values.
|
||||||
|
*
|
||||||
|
* @param[in] ndim space dimensions (dimension for coordinates)
|
||||||
|
* @param[in] nvert_e number of vertices per element (dimension for connectivity)
|
||||||
|
* @param[in] ndof_e degrees of freedom per element (= @p nvert_e for linear elements)
|
||||||
|
*/
|
||||||
|
explicit Mesh(int ndim, int nvert_e = 0, int ndof_e = 0);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Destructor.
|
||||||
|
*
|
||||||
|
* See clang warning on
|
||||||
|
* <a href="https://stackoverflow.com/questions/28786473/clang-no-out-of-line-virtual-method-definitions-pure-abstract-c-class/40550578">weak-vtables</a>.
|
||||||
|
*/
|
||||||
|
virtual ~Mesh();
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Number of finite elements in (sub)domain.
|
||||||
|
* @return number of elements.
|
||||||
|
*/
|
||||||
|
int Nelems() const
|
||||||
|
{
|
||||||
|
return _nelem;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Global number of vertices for each finite element.
|
||||||
|
* @return number of vertices per element.
|
||||||
|
*/
|
||||||
|
int NverticesElements() const
|
||||||
|
{
|
||||||
|
return _nvert_e;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Global number of degrees of freedom (dof) for each finite element.
|
||||||
|
* @return degrees of freedom per element.
|
||||||
|
*/
|
||||||
|
int NdofsElement() const
|
||||||
|
{
|
||||||
|
return _ndof_e;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Number of vertices in mesh.
|
||||||
|
* @return number of vertices.
|
||||||
|
*/
|
||||||
|
int Nnodes() const
|
||||||
|
{
|
||||||
|
return _nnode;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Space dimension.
|
||||||
|
* @return number of dimensions.
|
||||||
|
*/
|
||||||
|
int Ndims() const
|
||||||
|
{
|
||||||
|
return _ndim;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* (Re-)Allocates memory for the element connectivity and redefines the appropriate dimensions.
|
||||||
|
*
|
||||||
|
* @param[in] nelem number of elements
|
||||||
|
* @param[in] nvert_e number of vertices per element
|
||||||
|
*/
|
||||||
|
void Resize_Connectivity(int nelem, int nvert_e)
|
||||||
|
{
|
||||||
|
SetNelem(nelem); // number of elements
|
||||||
|
SetNverticesElement(nvert_e); // vertices per element
|
||||||
|
_ia.resize(nelem * nvert_e);
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Read connectivity information (g1,g2,g3)_i.
|
||||||
|
* @return convectivity vector [nelems*ndofs].
|
||||||
|
*/
|
||||||
|
const std::vector<int> &GetConnectivity() const
|
||||||
|
{
|
||||||
|
return _ia;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Access/Change connectivity information (g1,g2,g3)_i.
|
||||||
|
* @return convectivity vector [nelems*ndofs].
|
||||||
|
*/
|
||||||
|
std::vector<int> &GetConnectivity()
|
||||||
|
{
|
||||||
|
return _ia;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* (Re-)Allocates memory for the element connectivity and redefines the appropriate dimensions.
|
||||||
|
*
|
||||||
|
* @param[in] nnodes number of nodes
|
||||||
|
* @param[in] ndim space dimension
|
||||||
|
*/
|
||||||
|
void Resize_Coords(int nnodes, int ndim)
|
||||||
|
{
|
||||||
|
SetNnode(nnodes); // number of nodes
|
||||||
|
SetNdim(ndim); // space dimension
|
||||||
|
_xc.resize(nnodes * ndim);
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Read coordinates of vertices (x,y)_i.
|
||||||
|
* @return coordinates vector [nnodes*2].
|
||||||
|
*/
|
||||||
|
const std::vector<double> &GetCoords() const
|
||||||
|
{
|
||||||
|
return _xc;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Access/Change coordinates of vertices (x,y)_i.
|
||||||
|
* @return coordinates vector [nnodes*2].
|
||||||
|
*/
|
||||||
|
std::vector<double> &GetCoords()
|
||||||
|
{
|
||||||
|
return _xc;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Calculate values in vector @p v via function @p func(x,y)
|
||||||
|
* @param[in] v vector
|
||||||
|
* @param[in] func function of (x,y) returning a double value.
|
||||||
|
*/
|
||||||
|
void SetValues(std::vector<double> &v, const std::function<double(double, double)> &func) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Prints the information for a finite element mesh
|
||||||
|
*/
|
||||||
|
void Debug() const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Determines the indices of those vertices with Dirichlet boundary conditions
|
||||||
|
* @return index vector.
|
||||||
|
*/
|
||||||
|
virtual std::vector<int> Index_DirichletNodes() const = 0;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Write vector @p v toghether with its mesh information to an ASCii file @p fname.
|
||||||
|
*
|
||||||
|
* The data are written in C-style.
|
||||||
|
*
|
||||||
|
* @param[in] fname file name
|
||||||
|
* @param[in] v vector
|
||||||
|
*/
|
||||||
|
void Write_ascii_matlab(std::string const &fname, std::vector<double> const &v) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Visualize @p v together with its mesh information via matlab or octave.
|
||||||
|
*
|
||||||
|
* Comment/uncomment those code lines in method Mesh:Visualize (geom.cpp)
|
||||||
|
* that are supported on your system.
|
||||||
|
*
|
||||||
|
* @param[in] v vector
|
||||||
|
*
|
||||||
|
* @warning matlab files ascii_read_meshvector.m visualize_results.m
|
||||||
|
* must be in the executing directory.
|
||||||
|
*/
|
||||||
|
void Visualize(std::vector<double> const &v) const;
|
||||||
|
|
||||||
|
|
||||||
|
protected:
|
||||||
|
void SetNelem(int nelem)
|
||||||
|
{
|
||||||
|
_nelem = nelem;
|
||||||
|
}
|
||||||
|
|
||||||
|
void SetNverticesElement(int nvert)
|
||||||
|
{
|
||||||
|
_nvert_e = nvert;
|
||||||
|
}
|
||||||
|
|
||||||
|
void SetNdofsElement(int ndof)
|
||||||
|
{
|
||||||
|
_ndof_e = ndof;
|
||||||
|
}
|
||||||
|
|
||||||
|
void SetNnode(int nnode)
|
||||||
|
{
|
||||||
|
_nnode = nnode;
|
||||||
|
}
|
||||||
|
|
||||||
|
void SetNdim(int ndim)
|
||||||
|
{
|
||||||
|
_ndim = ndim;
|
||||||
|
}
|
||||||
|
|
||||||
|
private:
|
||||||
|
int _nelem; //!< number elements
|
||||||
|
int _nvert_e; //!< number of vertices per element
|
||||||
|
int _ndof_e; //!< degrees of freedom (d.o.f.) per element
|
||||||
|
int _nnode; //!< number nodes/vertices
|
||||||
|
int _ndim; //!< space dimension of the problem (1, 2, or 3)
|
||||||
|
std::vector<int> _ia; //!< element connectivity
|
||||||
|
std::vector<double> _xc; //!< coordinates
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* 2D finite element mesh of the square consiting of linear triangular elements.
|
||||||
|
*/
|
||||||
|
class Mesh_2d_3_square: public Mesh
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/**
|
||||||
|
* Generates the f.e. mesh for the unit square.
|
||||||
|
*
|
||||||
|
* @param[in] nx number of discretization intervals in x-direction
|
||||||
|
* @param[in] ny number of discretization intervals in y-direction
|
||||||
|
* @param[in] myid my MPI-rank / subdomain
|
||||||
|
* @param[in] procx number of ranks/subdomains in x-direction
|
||||||
|
* @param[in] procy number of processes in y-direction
|
||||||
|
*/
|
||||||
|
Mesh_2d_3_square(int nx, int ny, int myid = 0, int procx = 1, int procy = 1);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Destructor
|
||||||
|
*/
|
||||||
|
~Mesh_2d_3_square() override
|
||||||
|
{}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Set solution vector based on a tensor product grid in the rectangle.
|
||||||
|
* @param[in] u solution vector
|
||||||
|
*/
|
||||||
|
void SetU(std::vector<double> &u) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Set right hand side (rhs) vector on a tensor product grid in the rectangle.
|
||||||
|
* @param[in] f rhs vector
|
||||||
|
*/
|
||||||
|
void SetF(std::vector<double> &f) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Determines the indices of those vertices with Dirichlet boundary conditions
|
||||||
|
* @return index vector.
|
||||||
|
*/
|
||||||
|
std::vector<int> Index_DirichletNodes() const override;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Stores the values of vector @p u of (sub)domain into a file @p name for further processing in gnuplot.
|
||||||
|
* The file stores rowise the x- and y- coordinates together with the value from @p u .
|
||||||
|
* The domain [@p xl, @p xr] x [@p yb, @p yt] is discretized into @p nx x @p ny intervals.
|
||||||
|
*
|
||||||
|
* @param[in] name basename of file name (file name will be extended by the rank number)
|
||||||
|
* @param[in] u local vector
|
||||||
|
*
|
||||||
|
* @warning Assumes tensor product grid in unit square; rowise numbered
|
||||||
|
* (as generated in class constructor).
|
||||||
|
* The output is provided for tensor product grid visualization
|
||||||
|
* ( similar to Matlab-surf() ).
|
||||||
|
*
|
||||||
|
* @see Mesh_2d_3_square
|
||||||
|
*/
|
||||||
|
void SaveVectorP(std::string const &name, std::vector<double> const &u) const;
|
||||||
|
|
||||||
|
// here will still need to implement in the class
|
||||||
|
// GetBound(), AddBound()
|
||||||
|
// or better a generalized way with indices and their appropriate ranks for MPI communication
|
||||||
|
|
||||||
|
private:
|
||||||
|
/**
|
||||||
|
* Determines the coordinates of the dicretization nodes of the domain [@p xl, @p xr] x [@p yb, @p yt]
|
||||||
|
* which is discretized into @p nx x @p ny intervals.
|
||||||
|
*
|
||||||
|
* @param[in] ny number of discretization intervals in y-direction
|
||||||
|
* @param[in] xl x-coordinate of left boundary
|
||||||
|
* @param[in] xr x-coordinate of right boundary
|
||||||
|
* @param[in] yb y-coordinate of lower boundary
|
||||||
|
* @param[in] yt y-coordinate of upper boundary
|
||||||
|
* @param[out] xc coordinate vector of length 2n with x(2*k,2*k+1) as coodinates of node k
|
||||||
|
*/
|
||||||
|
|
||||||
|
void GetCoordsInRectangle(int nx, int ny, double xl, double xr, double yb, double yt,
|
||||||
|
double xc[]);
|
||||||
|
/**
|
||||||
|
* Determines the element connectivity of linear triangular elements of a FEM discretization
|
||||||
|
* of a rectangle using @p nx x @p ny equidistant intervals for discretization.
|
||||||
|
* @param[in] nx number of discretization intervals in x-direction
|
||||||
|
* @param[in] ny number of discretization intervals in y-direction
|
||||||
|
* @param[out] ia element connectivity matrix with ia(3*s,3*s+1,3*s+2) as node numbers od element s
|
||||||
|
*/
|
||||||
|
void GetConnectivityInRectangle(int nx, int ny, int ia[]);
|
||||||
|
|
||||||
|
private:
|
||||||
|
int _myid; //!< my MPI rank
|
||||||
|
int _procx; //!< number of MPI ranks in x-direction
|
||||||
|
int _procy; //!< number of MPI ranks in y-direction
|
||||||
|
std::array<int, 4> _neigh; //!< MPI ranks of neighbors (negative: no neighbor but b.c.)
|
||||||
|
int _color; //!< red/black coloring (checker board) of subdomains
|
||||||
|
|
||||||
|
double _xl; //!< x coordinate of lower left corner of square
|
||||||
|
double _xr; //!< x coordinate of lower right corner of square
|
||||||
|
double _yb; //!< y coordinate or lower left corner of square
|
||||||
|
double _yt; //!< y coordinate of upper right corner of square
|
||||||
|
int _nx; //!< number of intervals in x-direction
|
||||||
|
int _ny; //!< number of intervals in y-direction
|
||||||
|
};
|
||||||
|
|
||||||
|
// #################### still some old code (--> MPI) ############################
|
||||||
|
/**
|
||||||
|
* Copies the values of @p w corresponding to boundary @p ib
|
||||||
|
* onto vector s. South (ib==1), East (ib==2), North (ib==3), West (ib==4).
|
||||||
|
* The vector @p s has to be long enough!!
|
||||||
|
* @param[in] ib my local boundary
|
||||||
|
* @param[in] nx number of discretization intervals in x-direction
|
||||||
|
* @param[in] ny number of discretization intervals in y-direction
|
||||||
|
* @param[in] w vector for all nodes of local discretization
|
||||||
|
* @param[out] s short vector with values on boundary @p ib
|
||||||
|
*/
|
||||||
|
// GH_NOTE: Absicherung bei s !!
|
||||||
|
void GetBound(int ib, int nx, int ny, double const w[], double s[]);
|
||||||
|
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Computes @p w := @p w + @p s at the interface/boundary nodes on the
|
||||||
|
* boundary @p ib . South (ib==1), East (ib==2), North (ib==3), West (ib==4)
|
||||||
|
* @param[in] ib my local boundary
|
||||||
|
* @param[in] nx number of discretization intervals in x-direction
|
||||||
|
* @param[in] ny number of discretization intervals in y-direction
|
||||||
|
* @param[in,out] w vector for all nodes of local discretization
|
||||||
|
* @param[in] s short vector with values on boundary @p ib
|
||||||
|
*/
|
||||||
|
void AddBound(int ib, int nx, int ny, double w[], double const s[]);
|
||||||
|
|
||||||
|
// #################### Mesh from Matlab ############################
|
||||||
|
/**
|
||||||
|
* 2D finite element mesh of the square consiting of linear triangular elements.
|
||||||
|
*/
|
||||||
|
class Mesh_2d_3_matlab: public Mesh
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/**
|
||||||
|
* Reads mesh data from a binary file.
|
||||||
|
*
|
||||||
|
* File format, see ascii_write_mesh.m
|
||||||
|
*
|
||||||
|
* @param[in] fname file name
|
||||||
|
*/
|
||||||
|
explicit Mesh_2d_3_matlab(std::string const &fname);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Determines the indices of those vertices with Dirichlet boundary conditions.
|
||||||
|
* @return index vector.
|
||||||
|
*
|
||||||
|
* @warning All boundary nodes are considered as Dirchlet nodes.
|
||||||
|
*/
|
||||||
|
std::vector<int> Index_DirichletNodes() const override;
|
||||||
|
|
||||||
|
private:
|
||||||
|
/**
|
||||||
|
* Determines the indices of those vertices with Dirichlet boundary conditions
|
||||||
|
* @return index vector.
|
||||||
|
*/
|
||||||
|
int Nnbedges() const
|
||||||
|
{
|
||||||
|
return static_cast<int>(bedges.size());
|
||||||
|
}
|
||||||
|
|
||||||
|
std::vector<int> bedges; //!< boundary edges [nbedges][2] storing start/end vertex
|
||||||
|
|
||||||
|
};
|
||||||
|
|
||||||
|
#endif
|
||||||
348
sheet3/8/getmatrix.cpp
Normal file
348
sheet3/8/getmatrix.cpp
Normal file
|
|
@ -0,0 +1,348 @@
|
||||||
|
#include "getmatrix.h"
|
||||||
|
#include "userset.h"
|
||||||
|
|
||||||
|
#include <algorithm>
|
||||||
|
#include <cassert>
|
||||||
|
#include <cmath>
|
||||||
|
#include <iomanip>
|
||||||
|
#include <iostream>
|
||||||
|
#include <list>
|
||||||
|
#include <vector>
|
||||||
|
using namespace std;
|
||||||
|
|
||||||
|
|
||||||
|
// general routine for lin. triangular elements
|
||||||
|
|
||||||
|
void CalcElem(int const ial[3], double const xc[], double ske[3][3], double fe[3])
|
||||||
|
//void CalcElem(const int* __restrict__ ial, const double* __restrict__ xc, double* __restrict__ ske[3], double* __restrict__ fe)
|
||||||
|
{
|
||||||
|
const int i1 = 2 * ial[0], i2 = 2 * ial[1], i3 = 2 * ial[2];
|
||||||
|
const double x13 = xc[i3 + 0] - xc[i1 + 0], y13 = xc[i3 + 1] - xc[i1 + 1],
|
||||||
|
x21 = xc[i1 + 0] - xc[i2 + 0], y21 = xc[i1 + 1] - xc[i2 + 1],
|
||||||
|
x32 = xc[i2 + 0] - xc[i3 + 0], y32 = xc[i2 + 1] - xc[i3 + 1];
|
||||||
|
const double jac = fabs(x21 * y13 - x13 * y21);
|
||||||
|
|
||||||
|
ske[0][0] = 0.5 / jac * (y32 * y32 + x32 * x32);
|
||||||
|
ske[0][1] = 0.5 / jac * (y13 * y32 + x13 * x32);
|
||||||
|
ske[0][2] = 0.5 / jac * (y21 * y32 + x21 * x32);
|
||||||
|
ske[1][0] = ske[0][1];
|
||||||
|
ske[1][1] = 0.5 / jac * (y13 * y13 + x13 * x13);
|
||||||
|
ske[1][2] = 0.5 / jac * (y21 * y13 + x21 * x13);
|
||||||
|
ske[2][0] = ske[0][2];
|
||||||
|
ske[2][1] = ske[1][2];
|
||||||
|
ske[2][2] = 0.5 / jac * (y21 * y21 + x21 * x21);
|
||||||
|
|
||||||
|
const double xm = (xc[i1 + 0] + xc[i2 + 0] + xc[i3 + 0]) / 3.0,
|
||||||
|
ym = (xc[i1 + 1] + xc[i2 + 1] + xc[i3 + 1]) / 3.0;
|
||||||
|
//fe[0] = fe[1] = fe[2] = 0.5 * jac * FunctF(xm, ym) / 3.0;
|
||||||
|
fe[0] = fe[1] = fe[2] = 0.5 * jac * fNice(xm, ym) / 3.0;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// general routine for lin. triangular elements,
|
||||||
|
// non-symm. matrix
|
||||||
|
// node numbering in element: a s c e n d i n g indices !!
|
||||||
|
[[deprecated("Use CRS_Matrix::AddElem_3(...) instead.")]]
|
||||||
|
void AddElem(int const ial[3], double const ske[3][3], double const fe[3],
|
||||||
|
int const id[], int const ik[], double sk[], double f[])
|
||||||
|
{
|
||||||
|
for (int i = 0; i < 3; ++i)
|
||||||
|
{
|
||||||
|
const int ii = ial[i], // row ii (global index)
|
||||||
|
id1 = id[ii], // start and
|
||||||
|
id2 = id[ii + 1]; // end of row ii in matrix
|
||||||
|
int ip = id1;
|
||||||
|
for (int j = 0; j < 3; ++j) // no symmetry assumed
|
||||||
|
{
|
||||||
|
const int jj = ial[j];
|
||||||
|
bool not_found = true;
|
||||||
|
do // find entry jj (global index) in row ii
|
||||||
|
{
|
||||||
|
not_found = (ik[ip] != jj);
|
||||||
|
++ip;
|
||||||
|
}
|
||||||
|
while (not_found && ip < id2);
|
||||||
|
|
||||||
|
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
|
||||||
|
if (not_found) // no entry found !!
|
||||||
|
{
|
||||||
|
cout << "Error in AddElem: (" << ii << "," << jj << ") ["
|
||||||
|
<< ial[0] << "," << ial[1] << "," << ial[2] << "]\n";
|
||||||
|
assert(!not_found);
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
sk[ip - 1] += ske[i][j];
|
||||||
|
}
|
||||||
|
f[ii] += fe[i];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// ----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// ####################################################################
|
||||||
|
|
||||||
|
CRS_Matrix::CRS_Matrix(Mesh const &mesh)
|
||||||
|
: _mesh(mesh), _nrows(0), _nnz(0), _id(0), _ik(0), _sk(0)
|
||||||
|
{
|
||||||
|
Derive_Matrix_Pattern();
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void CRS_Matrix::Derive_Matrix_Pattern()
|
||||||
|
{
|
||||||
|
int const nelem(_mesh.Nelems());
|
||||||
|
int const ndof_e(_mesh.NdofsElement());
|
||||||
|
auto const &ia(_mesh.GetConnectivity());
|
||||||
|
// Determine the number of matrix rows
|
||||||
|
_nrows = *max_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem);
|
||||||
|
++_nrows; // node numberng: 0 ... nnode-1
|
||||||
|
assert(*min_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem) == 0); // numbering starts with 0 ?
|
||||||
|
|
||||||
|
// Collect for each node those nodes it is connected to (multiple entries)
|
||||||
|
// Detect the neighboring nodes
|
||||||
|
vector< list<int> > cc(_nrows); // cc[i] is the list of nodes a node i is connected to
|
||||||
|
for (int i = 0; i < nelem; ++i)
|
||||||
|
{
|
||||||
|
int const idx = ndof_e * i;
|
||||||
|
for (int k = 0; k < ndof_e; ++k)
|
||||||
|
{
|
||||||
|
list<int> &cck = cc.at(ia[idx + k]);
|
||||||
|
cck.insert( cck.end(), ia.cbegin() + idx, ia.cbegin() + idx + ndof_e );
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// Delete the multiple entries
|
||||||
|
_nnz = 0;
|
||||||
|
for (auto &it : cc)
|
||||||
|
{
|
||||||
|
it.sort();
|
||||||
|
it.unique();
|
||||||
|
_nnz += static_cast<int>(it.size());
|
||||||
|
// cout << it.size() << " :: "; copy(it->begin(),it->end(), ostream_iterator<int,char>(cout," ")); cout << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
// CSR data allocation
|
||||||
|
_id.resize(_nrows + 1); // Allocate memory for CSR row pointer
|
||||||
|
_ik.resize(_nnz); // Allocate memory for CSR column index vector
|
||||||
|
|
||||||
|
// copy CSR data
|
||||||
|
_id[0] = 0; // begin of first row
|
||||||
|
for (size_t i = 0; i < cc.size(); ++i)
|
||||||
|
{
|
||||||
|
//cout << i << " " << nid.at(i) << endl;;
|
||||||
|
const list<int> &ci = cc.at(i);
|
||||||
|
const auto nci = static_cast<int>(ci.size());
|
||||||
|
_id[i + 1] = _id[i] + nci; // begin of next line
|
||||||
|
copy(ci.begin(), ci.end(), _ik.begin() + _id[i] );
|
||||||
|
}
|
||||||
|
|
||||||
|
assert(_nnz == _id[_nrows]);
|
||||||
|
_sk.resize(_nnz); // Allocate memory for CSR column index vector
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void CRS_Matrix::Debug() const
|
||||||
|
{
|
||||||
|
// ID points to first entry of row
|
||||||
|
// no symmetry assumed
|
||||||
|
cout << "\nMatrix (nnz = " << _id[_nrows] << ")\n";
|
||||||
|
|
||||||
|
for (int row = 0; row < _nrows; ++row)
|
||||||
|
{
|
||||||
|
cout << "Row " << row << " : ";
|
||||||
|
int const id1 = _id[row];
|
||||||
|
int const id2 = _id[row + 1];
|
||||||
|
for (int j = id1; j < id2; ++j)
|
||||||
|
{
|
||||||
|
cout.setf(ios::right, ios::adjustfield);
|
||||||
|
cout << "[" << setw(2) << _ik[j] << "] " << setw(4) << _sk[j] << " ";
|
||||||
|
}
|
||||||
|
cout << endl;
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void CRS_Matrix::CalculateLaplace(vector<double> &f)
|
||||||
|
{
|
||||||
|
assert(_mesh.NdofsElement() == 3); // only for triangular, linear elements
|
||||||
|
//cout << _nnz << " vs. " << _id[_nrows] << " " << _nrows<< endl;
|
||||||
|
assert(_nnz == _id[_nrows]);
|
||||||
|
|
||||||
|
for (int k = 0; k < _nrows; ++k)
|
||||||
|
{
|
||||||
|
_sk[k] = 0.0;
|
||||||
|
}
|
||||||
|
for (int k = 0; k < _nrows; ++k)
|
||||||
|
{
|
||||||
|
f[k] = 0.0;
|
||||||
|
}
|
||||||
|
|
||||||
|
double ske[3][3], fe[3];
|
||||||
|
// Loop over all elements
|
||||||
|
auto const nelem = _mesh.Nelems();
|
||||||
|
auto const &ia = _mesh.GetConnectivity();
|
||||||
|
auto const &xc = _mesh.GetCoords();
|
||||||
|
|
||||||
|
for (int i = 0; i < nelem; ++i)
|
||||||
|
{
|
||||||
|
CalcElem(ia.data() + 3 * i, xc.data(), ske, fe);
|
||||||
|
AddElem_3(ia.data() + 3 * i, ske, fe, f);
|
||||||
|
}
|
||||||
|
//Debug();
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void CRS_Matrix::ApplyDirichletBC(std::vector<double> const &u, std::vector<double> &f)
|
||||||
|
{
|
||||||
|
double const PENALTY = 1e6;
|
||||||
|
auto const idx = _mesh.Index_DirichletNodes();
|
||||||
|
int const nidx = static_cast<int>(idx.size());
|
||||||
|
|
||||||
|
for (int row = 0; row < nidx; ++row)
|
||||||
|
{
|
||||||
|
int const k = idx[row];
|
||||||
|
int const id1 = fetch(k, k); // Find diagonal entry of row
|
||||||
|
assert(id1 >= 0);
|
||||||
|
_sk[id1] += PENALTY; // matrix weighted scaling feasible
|
||||||
|
f[k] += PENALTY * u[k];
|
||||||
|
}
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void CRS_Matrix::GetDiag(vector<double> &d) const
|
||||||
|
{
|
||||||
|
assert( _nrows == static_cast<int>(d.size()) );
|
||||||
|
|
||||||
|
for (int row = 0; row < _nrows; ++row)
|
||||||
|
{
|
||||||
|
const int ia = fetch(row, row); // Find diagonal entry of row
|
||||||
|
assert(ia >= 0);
|
||||||
|
d[row] = _sk[ia];
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool CRS_Matrix::Compare2Old(int nnode, int const id[], int const ik[], double const sk[]) const
|
||||||
|
{
|
||||||
|
bool bn = (nnode == _nrows); // number of rows
|
||||||
|
if (!bn)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "number of rows" << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool bz = (id[nnode] == _nnz); // number of non zero elements
|
||||||
|
if (!bz)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "number of non zero elements" << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool bd = equal(id, id + nnode + 1, _id.cbegin()); // row starts
|
||||||
|
if (!bd)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "row starts" << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool bk = equal(ik, ik + id[nnode], _ik.cbegin()); // column indices
|
||||||
|
if (!bk)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "column indices" << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
bool bv = equal(sk, sk + id[nnode], _sk.cbegin()); // values
|
||||||
|
if (!bv)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "values" << endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
return bn && bz && bd && bk && bv;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void CRS_Matrix::Mult(vector<double> &w, vector<double> const &u) const
|
||||||
|
{
|
||||||
|
assert( _nrows == static_cast<int>(w.size()) );
|
||||||
|
assert( w.size() == u.size() );
|
||||||
|
|
||||||
|
for (int row = 0; row < _nrows; ++row)
|
||||||
|
{
|
||||||
|
double wi = 0.0;
|
||||||
|
for (int ij = _id[row]; ij < _id[row + 1]; ++ij)
|
||||||
|
{
|
||||||
|
wi += _sk[ij] * u[ _ik[ij] ];
|
||||||
|
}
|
||||||
|
w[row] = wi;
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
void CRS_Matrix::Defect(vector<double> &w,
|
||||||
|
vector<double> const &f, vector<double> const &u) const
|
||||||
|
{
|
||||||
|
assert( _nrows == static_cast<int>(w.size()) );
|
||||||
|
assert( w.size() == u.size() && u.size() == f.size() );
|
||||||
|
|
||||||
|
for (int row = 0; row < _nrows; ++row)
|
||||||
|
{
|
||||||
|
double wi = f[row];
|
||||||
|
for (int ij = _id[row]; ij < _id[row + 1]; ++ij)
|
||||||
|
{
|
||||||
|
wi -= _sk[ij] * u[ _ik[ij] ];
|
||||||
|
}
|
||||||
|
w[row] = wi;
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
int CRS_Matrix::fetch(int const row, int const col) const
|
||||||
|
{
|
||||||
|
int const id2 = _id[row + 1]; // end and
|
||||||
|
int ip = _id[row]; // start of recent row (global index)
|
||||||
|
|
||||||
|
while (ip < id2 && _ik[ip] != col) // find index col (global index)
|
||||||
|
{
|
||||||
|
++ip;
|
||||||
|
}
|
||||||
|
if (ip >= id2)
|
||||||
|
{
|
||||||
|
ip = -1;
|
||||||
|
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
|
||||||
|
cout << "No column " << col << " in row " << row << endl;
|
||||||
|
assert(ip >= id2);
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
return ip;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// general routine for lin. triangular elements,
|
||||||
|
// non-symm. matrix
|
||||||
|
// node numbering in element: a s c e n d i n g indices !!
|
||||||
|
void CRS_Matrix::AddElem_3(int const ial[3], double const ske[3][3], double const fe[3], vector<double> &f)
|
||||||
|
{
|
||||||
|
for (int i = 0; i < 3; ++i)
|
||||||
|
{
|
||||||
|
const int ii = ial[i]; // row ii (global index)
|
||||||
|
for (int j = 0; j < 3; ++j) // no symmetry assumed
|
||||||
|
{
|
||||||
|
const int jj = ial[j]; // column jj (global index)
|
||||||
|
int ip = fetch(ii, jj); // find column entry jj in row ii
|
||||||
|
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
|
||||||
|
if (ip < 0) // no entry found !!
|
||||||
|
{
|
||||||
|
cout << "Error in AddElem: (" << ii << "," << jj << ") ["
|
||||||
|
<< ial[0] << "," << ial[1] << "," << ial[2] << "]\n";
|
||||||
|
assert(ip >= 0);
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
_sk[ip] += ske[i][j];
|
||||||
|
}
|
||||||
|
f[ii] += fe[i];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
178
sheet3/8/getmatrix.h
Normal file
178
sheet3/8/getmatrix.h
Normal file
|
|
@ -0,0 +1,178 @@
|
||||||
|
#ifndef GETMATRIX_FILE
|
||||||
|
#define GETMATRIX_FILE
|
||||||
|
|
||||||
|
#include "geom.h"
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Calculates the element stiffness matrix @p ske and the element load vector @p fe
|
||||||
|
* of one triangular element with linear shape functions.
|
||||||
|
* @param[in] ial node indices of the three element vertices
|
||||||
|
* @param[in] xc vector of node coordinates with x(2*k,2*k+1) as coodinates of node k
|
||||||
|
* @param[out] ske element stiffness matrix
|
||||||
|
* @param[out] fe element load vector
|
||||||
|
*/
|
||||||
|
void CalcElem(int const ial[3], double const xc[], double ske[3][3], double fe[3]);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Adds the element stiffness matrix @p ske and the element load vector @p fe
|
||||||
|
* of one triangular element with linear shape functions to the appropriate positions in
|
||||||
|
* the symmetric stiffness matrix, stored as CSR matrix K(@p sk,@p id, @p ik)
|
||||||
|
*
|
||||||
|
* @param[in] ial node indices of the three element vertices
|
||||||
|
* @param[in] ske element stiffness matrix
|
||||||
|
* @param[in] fe element load vector
|
||||||
|
* @param[out] sk vector non-zero entries of CSR matrix
|
||||||
|
* @param[in] id index vector containing the first entry in a CSR row
|
||||||
|
* @param[in] ik column index vector of CSR matrix
|
||||||
|
* @param[out] f distributed local vector storing the right hand side
|
||||||
|
*
|
||||||
|
* @warning Algorithm requires indices in connectivity @p ial in ascending order.
|
||||||
|
* Currently deprecated.
|
||||||
|
*/
|
||||||
|
void AddElem(int const ial[3], double const ske[3][3], double const fe[3],
|
||||||
|
int const id[], int const ik[], double sk[], double f[]);
|
||||||
|
|
||||||
|
|
||||||
|
// #####################################################################
|
||||||
|
/**
|
||||||
|
* Square matrix in CRS format (compressed row storage; also named CSR),
|
||||||
|
* see an <a href="https://en.wikipedia.org/wiki/Sparse_matrix">introduction</a>.
|
||||||
|
*/
|
||||||
|
class CRS_Matrix
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/**
|
||||||
|
* Intializes the CRS matrix structure from the given discetization in @p mesh.
|
||||||
|
*
|
||||||
|
* The sparse matrix pattern is generated but the values are 0.
|
||||||
|
*
|
||||||
|
* @param[in] mesh given discretization
|
||||||
|
*
|
||||||
|
* @warning A reference to the discretization @p mesh is stored inside this class.
|
||||||
|
* Therefore, changing @p mesh outside requires also
|
||||||
|
* to call method @p Derive_Matrix_Pattern explicitely.
|
||||||
|
*
|
||||||
|
* @see Derive_Matrix_Pattern
|
||||||
|
*/
|
||||||
|
explicit CRS_Matrix(Mesh const & mesh);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Destructor.
|
||||||
|
*/
|
||||||
|
~CRS_Matrix()
|
||||||
|
{}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Generates the sparse matrix pattern and overwrites the existing pattern.
|
||||||
|
*
|
||||||
|
* The sparse matrix pattern is generated but the values are 0.
|
||||||
|
*/
|
||||||
|
void Derive_Matrix_Pattern();
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Calculates the entries of f.e. stiffness matrix and load/rhs vector @p f for the Laplace operator in 2D.
|
||||||
|
* No memory is allocated.
|
||||||
|
*
|
||||||
|
* @param[in,out] f (preallocated) rhs/load vector
|
||||||
|
*/
|
||||||
|
void CalculateLaplace(std::vector<double> &f);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Applies Dirichlet boundary conditions to stiffness matrix and to load vector @p f.
|
||||||
|
* The <a href="https://www.jstor.org/stable/2005611?seq=1#metadata_info_tab_contents">penalty method</a>
|
||||||
|
* is used for incorporating the given values @p u.
|
||||||
|
*
|
||||||
|
* @param[in] u (global) vector with Dirichlet data
|
||||||
|
* @param[in,out] f load vector
|
||||||
|
*/
|
||||||
|
void ApplyDirichletBC(std::vector<double> const &u, std::vector<double> &f);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Extracts the diagonal elemenst of the sparse matrix.
|
||||||
|
*
|
||||||
|
* @param[in,out] d (prellocated) vector of diagonal elements
|
||||||
|
*/
|
||||||
|
void GetDiag(std::vector<double> &d) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Performs the matrix-vector product w := K*u.
|
||||||
|
*
|
||||||
|
* @param[in,out] w resulting vector (preallocated)
|
||||||
|
* @param[in] u vector
|
||||||
|
*/
|
||||||
|
void Mult(std::vector<double> &w, std::vector<double> const &u) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Calculates the defect/residuum w := f - K*u.
|
||||||
|
*
|
||||||
|
* @param[in,out] w resulting vector (preallocated)
|
||||||
|
* @param[in] f load vector
|
||||||
|
* @param[in] u vector
|
||||||
|
*/
|
||||||
|
void Defect(std::vector<double> &w,
|
||||||
|
std::vector<double> const &f, std::vector<double> const &u) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Number rows in matrix.
|
||||||
|
* @return number of rows.
|
||||||
|
*/
|
||||||
|
int Nrows() const
|
||||||
|
{return _nrows;}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Show the matrix entries.
|
||||||
|
*/
|
||||||
|
void Debug() const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Finds in a CRS matrix the access index for an entry at row @p row and column @p col.
|
||||||
|
*
|
||||||
|
* @param[in] row row index
|
||||||
|
* @param[in] col column index
|
||||||
|
* @return index for element (@p row, @p col). If no appropriate entry exists then -1 will be returned.
|
||||||
|
*
|
||||||
|
* @warning assert() stops the function in case that matrix element (@p row, @p col) doesn't exist.
|
||||||
|
*/
|
||||||
|
int fetch(int row, int col) const;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Adds the element stiffness matrix @p ske and the element load vector @p fe
|
||||||
|
* of one triangular element with linear shape functions to the appropriate positions in
|
||||||
|
* the stiffness matrix, stored as CSR matrix K(@p sk,@p id, @p ik).
|
||||||
|
*
|
||||||
|
* @param[in] ial node indices of the three element vertices
|
||||||
|
* @param[in] ske element stiffness matrix
|
||||||
|
* @param[in] fe element load vector
|
||||||
|
* @param[in,out] f distributed local vector storing the right hand side
|
||||||
|
*
|
||||||
|
* @warning Algorithm assumes linear triangular elements (ndof_e==3).
|
||||||
|
*/
|
||||||
|
void AddElem_3(int const ial[3], double const ske[3][3], double const fe[3], std::vector<double> &f);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Compare @p this CRS matrix with an external CRS matrix stored in C-Style.
|
||||||
|
*
|
||||||
|
* The method prints statements on differences found.
|
||||||
|
*
|
||||||
|
* @param[in] nnode row number of external matrix
|
||||||
|
* @param[in] id start indices of matrix rows of external matrix
|
||||||
|
* @param[in] ik column indices of external matrix
|
||||||
|
* @param[in] sk non-zero values of external matrix
|
||||||
|
*
|
||||||
|
* @return true iff all data are identical.
|
||||||
|
*/
|
||||||
|
bool Compare2Old(int nnode, int const id[], int const ik[], double const sk[]) const;
|
||||||
|
|
||||||
|
private:
|
||||||
|
Mesh const & _mesh; //!< reference to discretization
|
||||||
|
int _nrows; //!< number of rows in matrix
|
||||||
|
int _nnz; //!< number of non-zero entries
|
||||||
|
std::vector<int> _id; //!< start indices of matrix rows
|
||||||
|
std::vector<int> _ik; //!< column indices
|
||||||
|
std::vector<double> _sk; //!< non-zero values
|
||||||
|
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
#endif
|
||||||
5
sheet3/8/gnuplot.rot
Normal file
5
sheet3/8/gnuplot.rot
Normal file
|
|
@ -0,0 +1,5 @@
|
||||||
|
zrot=(zrot+10)%360
|
||||||
|
xrot=(xrot+17)%180
|
||||||
|
set view xrot,zrot
|
||||||
|
replot
|
||||||
|
reread
|
||||||
7
sheet3/8/gprofng_script1
Normal file
7
sheet3/8/gprofng_script1
Normal file
|
|
@ -0,0 +1,7 @@
|
||||||
|
# max 5 lines
|
||||||
|
limit 5
|
||||||
|
# define metrics
|
||||||
|
metrics name:e.llm
|
||||||
|
# show absolute numbers
|
||||||
|
compare on
|
||||||
|
functions
|
||||||
7
sheet3/8/gprofng_script2
Normal file
7
sheet3/8/gprofng_script2
Normal file
|
|
@ -0,0 +1,7 @@
|
||||||
|
# max 5 lines
|
||||||
|
limit 5
|
||||||
|
# define metrics
|
||||||
|
metrics name:e.llm
|
||||||
|
# show absolute numbers
|
||||||
|
compare ratio
|
||||||
|
functions
|
||||||
21
sheet3/8/jac.dem
Normal file
21
sheet3/8/jac.dem
Normal file
|
|
@ -0,0 +1,21 @@
|
||||||
|
set style data lines
|
||||||
|
set parametric
|
||||||
|
set hidden3d
|
||||||
|
set nokey
|
||||||
|
#set xrange [0:1]
|
||||||
|
#set yrange [-0:1]
|
||||||
|
#set zrange [-2:2]
|
||||||
|
set cntrparam levels 15
|
||||||
|
set contour base
|
||||||
|
set title "Solution"
|
||||||
|
xrot=60
|
||||||
|
zrot=0
|
||||||
|
splot "t.dat"
|
||||||
|
#splot "lsg.gnu"
|
||||||
|
pause -1 "Press ENTER to continue."
|
||||||
|
#load "gnuplot.rot"
|
||||||
|
#set title ""
|
||||||
|
#set autosc
|
||||||
|
#set nohidden
|
||||||
|
#set nopara
|
||||||
|
#set key
|
||||||
75
sheet3/8/jacobi.cbp
Normal file
75
sheet3/8/jacobi.cbp
Normal file
|
|
@ -0,0 +1,75 @@
|
||||||
|
<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
|
||||||
|
<CodeBlocks_project_file>
|
||||||
|
<FileVersion major="1" minor="6" />
|
||||||
|
<Project>
|
||||||
|
<Option title="jacobi" />
|
||||||
|
<Option pch_mode="2" />
|
||||||
|
<Option compiler="gcc" />
|
||||||
|
<Build>
|
||||||
|
<Target title="Debug">
|
||||||
|
<Option output="bin/Debug/jacobi" prefix_auto="1" extension_auto="1" />
|
||||||
|
<Option object_output="obj/Debug/" />
|
||||||
|
<Option type="1" />
|
||||||
|
<Option compiler="gcc" />
|
||||||
|
<Compiler>
|
||||||
|
<Add option="-g" />
|
||||||
|
</Compiler>
|
||||||
|
</Target>
|
||||||
|
<Target title="Release">
|
||||||
|
<Option output="bin/Release/jacobi" prefix_auto="1" extension_auto="1" />
|
||||||
|
<Option object_output="obj/Release/" />
|
||||||
|
<Option type="1" />
|
||||||
|
<Option compiler="gcc" />
|
||||||
|
<Compiler>
|
||||||
|
<Add option="-O2" />
|
||||||
|
</Compiler>
|
||||||
|
<Linker>
|
||||||
|
<Add option="-s" />
|
||||||
|
</Linker>
|
||||||
|
</Target>
|
||||||
|
</Build>
|
||||||
|
<Compiler>
|
||||||
|
<Add option="-Wshadow" />
|
||||||
|
<Add option="-Winit-self" />
|
||||||
|
<Add option="-Wredundant-decls" />
|
||||||
|
<Add option="-Wcast-align" />
|
||||||
|
<Add option="-Wundef" />
|
||||||
|
<Add option="-Wfloat-equal" />
|
||||||
|
<Add option="-Wunreachable-code" />
|
||||||
|
<Add option="-Wmissing-declarations" />
|
||||||
|
<Add option="-Wswitch-default" />
|
||||||
|
<Add option="-Weffc++" />
|
||||||
|
<Add option="-Wmain" />
|
||||||
|
<Add option="-pedantic" />
|
||||||
|
<Add option="-Wextra" />
|
||||||
|
<Add option="-Wall" />
|
||||||
|
<Add option="-fexceptions" />
|
||||||
|
</Compiler>
|
||||||
|
<Unit filename="geom.cpp" />
|
||||||
|
<Unit filename="geom.h" />
|
||||||
|
<Unit filename="getmatrix.cpp" />
|
||||||
|
<Unit filename="getmatrix.h" />
|
||||||
|
<Unit filename="jacsolve.cpp" />
|
||||||
|
<Unit filename="jacsolve.h" />
|
||||||
|
<Unit filename="main.cpp" />
|
||||||
|
<Unit filename="userset.cpp" />
|
||||||
|
<Unit filename="userset.h" />
|
||||||
|
<Unit filename="vdop.cpp" />
|
||||||
|
<Unit filename="vdop.h" />
|
||||||
|
<Extensions>
|
||||||
|
<code_completion />
|
||||||
|
<envvars />
|
||||||
|
<lib_finder disable_auto="1" />
|
||||||
|
<debugger />
|
||||||
|
<DoxyBlocks>
|
||||||
|
<comment_style block="0" line="0" />
|
||||||
|
<doxyfile_project />
|
||||||
|
<doxyfile_build extract_all="1" />
|
||||||
|
<doxyfile_warnings />
|
||||||
|
<doxyfile_output />
|
||||||
|
<doxyfile_dot class_diagrams="1" have_dot="1" />
|
||||||
|
<general use_at_in_tags="1" />
|
||||||
|
</DoxyBlocks>
|
||||||
|
</Extensions>
|
||||||
|
</Project>
|
||||||
|
</CodeBlocks_project_file>
|
||||||
4
sheet3/8/jacobi.layout
Normal file
4
sheet3/8/jacobi.layout
Normal file
|
|
@ -0,0 +1,4 @@
|
||||||
|
<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
|
||||||
|
<CodeBlocks_layout_file>
|
||||||
|
<ActiveTarget name="Debug" />
|
||||||
|
</CodeBlocks_layout_file>
|
||||||
61
sheet3/8/jacsolve.cpp
Normal file
61
sheet3/8/jacsolve.cpp
Normal file
|
|
@ -0,0 +1,61 @@
|
||||||
|
#include "vdop.h"
|
||||||
|
#include "getmatrix.h"
|
||||||
|
#include "jacsolve.h"
|
||||||
|
|
||||||
|
#include <cassert>
|
||||||
|
#include <cmath>
|
||||||
|
#include <iostream>
|
||||||
|
#include <vector>
|
||||||
|
using namespace std;
|
||||||
|
|
||||||
|
// #####################################################################
|
||||||
|
// const int neigh[], const int color,
|
||||||
|
// const MPI::Intracomm& icomm,
|
||||||
|
void JacobiSolve(CRS_Matrix const &SK, vector<double> const &f, vector<double> &u)
|
||||||
|
{
|
||||||
|
const double omega = 1.0;
|
||||||
|
const int maxiter = 1000;
|
||||||
|
const double tol = 1e-5, // tolerance
|
||||||
|
tol2 = tol * tol; // tolerance^2
|
||||||
|
|
||||||
|
int nrows = SK.Nrows(); // number of rows == number of columns
|
||||||
|
assert( nrows == static_cast<int>(f.size()) && f.size() == u.size() );
|
||||||
|
|
||||||
|
cout << endl << " Start Jacobi solver for " << nrows << " d.o.f.s" << endl;
|
||||||
|
// Choose initial guess
|
||||||
|
for (int k = 0; k < nrows; ++k)
|
||||||
|
{
|
||||||
|
u[k] = 0.0; // u := 0
|
||||||
|
}
|
||||||
|
|
||||||
|
vector<double> dd(nrows); // matrix diagonal
|
||||||
|
vector<double> r(nrows); // residual
|
||||||
|
vector<double> w(nrows); // correction
|
||||||
|
|
||||||
|
SK.GetDiag(dd); // dd := diag(K)
|
||||||
|
////DebugVector(dd);{int ijk; cin >> ijk;}
|
||||||
|
|
||||||
|
// Initial sweep
|
||||||
|
SK.Defect(r, f, u); // r := f - K*u
|
||||||
|
|
||||||
|
vddiv(w, r, dd); // w := D^{-1}*r
|
||||||
|
double sigma0 = dscapr(w, r); // s0 := <w,r>
|
||||||
|
|
||||||
|
// Iteration sweeps
|
||||||
|
int iter = 0;
|
||||||
|
double sigma = sigma0;
|
||||||
|
while ( sigma > tol2 * sigma0 && maxiter > iter)
|
||||||
|
{
|
||||||
|
++iter;
|
||||||
|
vdaxpy(u, u, omega, w ); // u := u + om*w
|
||||||
|
SK.Defect(r, f, u); // r := f - K*u
|
||||||
|
vddiv(w, r, dd); // w := D^{-1}*r
|
||||||
|
sigma = dscapr(w, r); // s0 := <w,r>
|
||||||
|
// cout << "Iteration " << iter << " : " << sqrt(sigma/sigma0) << endl;
|
||||||
|
}
|
||||||
|
cout << "aver. Jacobi rate : " << exp(log(sqrt(sigma / sigma0)) / iter) << " (" << iter << " iter)" << endl;
|
||||||
|
cout << "final error: " << sqrt(sigma / sigma0) << " (rel) " << sqrt(sigma) << " (abs)\n";
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
18
sheet3/8/jacsolve.h
Normal file
18
sheet3/8/jacsolve.h
Normal file
|
|
@ -0,0 +1,18 @@
|
||||||
|
#ifndef JACSOLVE_FILE
|
||||||
|
#define JACSOLVE_FILE
|
||||||
|
#include "getmatrix.h"
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Solves linear system of equations K @p u = @p f via the Jacobi iteration.
|
||||||
|
* We use a distributed symmetric CSR matrix @p SK and initial guess of the
|
||||||
|
* solution is set to 0.
|
||||||
|
* @param[in] SK CSR matrix
|
||||||
|
* @param[in] f distributed local vector storing the right hand side
|
||||||
|
* @param[out] u accumulated local vector storing the solution.
|
||||||
|
*/
|
||||||
|
void JacobiSolve(CRS_Matrix const &SK, std::vector<double> const &f, std::vector<double> &u);
|
||||||
|
|
||||||
|
|
||||||
|
#endif
|
||||||
129
sheet3/8/main.cpp
Normal file
129
sheet3/8/main.cpp
Normal file
|
|
@ -0,0 +1,129 @@
|
||||||
|
// MPI code in C++.
|
||||||
|
// See [Gropp/Lusk/Skjellum, "Using MPI", p.33/41 etc.]
|
||||||
|
// and /opt/mpich/include/mpi2c++/comm.h for details
|
||||||
|
|
||||||
|
#include "geom.h"
|
||||||
|
#include "getmatrix.h"
|
||||||
|
#include "jacsolve.h"
|
||||||
|
#include "userset.h"
|
||||||
|
#include "vdop.h"
|
||||||
|
|
||||||
|
#include <chrono> // timing
|
||||||
|
#include <cmath>
|
||||||
|
#include <iostream>
|
||||||
|
using namespace std;
|
||||||
|
using namespace std::chrono; // timing
|
||||||
|
|
||||||
|
|
||||||
|
int main(int, char ** )
|
||||||
|
{
|
||||||
|
const int numprocs = 1;
|
||||||
|
const int myrank = 0;
|
||||||
|
|
||||||
|
if (myrank == 0)
|
||||||
|
{
|
||||||
|
cout << "\n There are " << numprocs << " processes running.\n \n";
|
||||||
|
}
|
||||||
|
|
||||||
|
const auto procx = static_cast<int>(sqrt(numprocs + 0.0));
|
||||||
|
const int procy = procx;
|
||||||
|
|
||||||
|
if (procy * procx != numprocs)
|
||||||
|
{
|
||||||
|
cout << "\n Wrong number of processors !\n \n";
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
// #####################################################################
|
||||||
|
// Here starts the real code
|
||||||
|
// #####################################################################
|
||||||
|
//bool ScaleUp = !true;
|
||||||
|
int nx, ny, NXglob, NYglob; /* number of local intervals on (xl,xr)=:nx, (yb,yt)=:ny */
|
||||||
|
//nx = 1024;
|
||||||
|
//ny = 1024;
|
||||||
|
nx = 100;
|
||||||
|
ny = 100;
|
||||||
|
NXglob = nx * procx;
|
||||||
|
NYglob = ny * procy;
|
||||||
|
cout << "Intervalls: " << NXglob << " x " << NYglob << endl;
|
||||||
|
|
||||||
|
// ##################### STL ###########################################
|
||||||
|
{
|
||||||
|
Mesh_2d_3_square const mesh(nx, ny);
|
||||||
|
//mesh.Debug();
|
||||||
|
|
||||||
|
CRS_Matrix SK(mesh); // CRS matrix
|
||||||
|
//SK.Debug();
|
||||||
|
vector<double> uv(SK.Nrows(), 0.0); // temperature
|
||||||
|
vector<double> fv(SK.Nrows(), 0.0); // r.h.s.
|
||||||
|
|
||||||
|
SK.CalculateLaplace(fv);
|
||||||
|
//SK.Debug();
|
||||||
|
|
||||||
|
//mesh.SetU(uv); // deprecated
|
||||||
|
//mesh.SetF(fv); // deprecated
|
||||||
|
// Two ways to initialize the vector
|
||||||
|
//mesh.SetValues(uv,f_zero); // functional
|
||||||
|
mesh.SetValues(uv, [](double x, double y) -> double {return 0.0 * x *y;} ); // lambda function
|
||||||
|
|
||||||
|
SK.ApplyDirichletBC(uv, fv);
|
||||||
|
//SK.Compare2Old(nnode, id, ik, sk);
|
||||||
|
//SK.Debug();
|
||||||
|
|
||||||
|
auto tstart = system_clock::now(); // start timer
|
||||||
|
|
||||||
|
JacobiSolve(SK, fv, uv ); // solve the system of equations
|
||||||
|
|
||||||
|
auto tend = system_clock::now(); // end timer
|
||||||
|
auto duration = duration_cast<microseconds>(tend - tstart);
|
||||||
|
auto t1 = static_cast<double>(duration.count()) / 1e6 ; // t1 in seconds
|
||||||
|
cout << "JacobiSolve: timing in sec. : " << t1 << endl;
|
||||||
|
|
||||||
|
//CompareVectors(uv, nnode, u, 1e-6); // Check correctness
|
||||||
|
|
||||||
|
//mesh.SaveVectorP("t.dat", uv);
|
||||||
|
//mesh.Visualize(uv);
|
||||||
|
|
||||||
|
}
|
||||||
|
// ##################### STL ###########################################
|
||||||
|
{
|
||||||
|
//Mesh_2d_3_matlab const mesh("square_tiny.txt");
|
||||||
|
Mesh_2d_3_matlab const mesh("square_100.txt");
|
||||||
|
//Mesh_2d_3_matlab const mesh("L_shape.txt");
|
||||||
|
//mesh.Debug();
|
||||||
|
|
||||||
|
CRS_Matrix SK(mesh); // CRS matrix
|
||||||
|
//SK.Debug();
|
||||||
|
|
||||||
|
vector<double> uv(SK.Nrows(), 0.0); // temperature
|
||||||
|
vector<double> fv(SK.Nrows(), 0.0); // r.h.s.
|
||||||
|
|
||||||
|
SK.CalculateLaplace(fv);
|
||||||
|
//SK.Debug();
|
||||||
|
|
||||||
|
//mesh.SetU(uv); // deprecated
|
||||||
|
// Two ways to initialize the vector
|
||||||
|
//mesh.SetValues(uv,f_zero); // user function
|
||||||
|
mesh.SetValues(uv, [](double x, double y) -> double {return 0.0 * x *y;} ); // lambda function
|
||||||
|
|
||||||
|
SK.ApplyDirichletBC(uv, fv);
|
||||||
|
//SK.Compare2Old(nnode, id, ik, sk);
|
||||||
|
//SK.Debug();
|
||||||
|
|
||||||
|
auto tstart = system_clock::now(); // start timer
|
||||||
|
|
||||||
|
JacobiSolve(SK, fv, uv ); // solve the system of equations
|
||||||
|
|
||||||
|
auto tend = system_clock::now(); // end timer
|
||||||
|
auto duration = duration_cast<microseconds>(tend - tstart);
|
||||||
|
auto t1 = static_cast<double>(duration.count()) / 1e6 ; // t1 in seconds
|
||||||
|
cout << "JacobiSolve: timing in sec. : " << t1 << endl;
|
||||||
|
|
||||||
|
//mesh.Write_ascii_matlab("uv.txt", uv);
|
||||||
|
//mesh.Visualize(uv);
|
||||||
|
}
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
20
sheet3/8/nl.awk
Normal file
20
sheet3/8/nl.awk
Normal file
|
|
@ -0,0 +1,20 @@
|
||||||
|
#
|
||||||
|
# Have to add a newline for a new row of coordinates
|
||||||
|
#
|
||||||
|
BEGIN { OFS=" "; YO=-1.23456789; X=YO; Y=YO; Z=YO }
|
||||||
|
{
|
||||||
|
if ($1!="")
|
||||||
|
{
|
||||||
|
if ($1!=YO) { print " "; YO=$1 }
|
||||||
|
if ($1==X && $2==Y)
|
||||||
|
{
|
||||||
|
# print $1,$2,($3+Z)/2
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
print $1,$2,$3
|
||||||
|
}
|
||||||
|
X=$1; Y=$2; Z=$3;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
END {}
|
||||||
9
sheet3/8/out_100_GCC.txt
Normal file
9
sheet3/8/out_100_GCC.txt
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
|
||||||
|
There are 1 processes running.
|
||||||
|
|
||||||
|
Intervalls: 100 x 100
|
||||||
|
|
||||||
|
Start Jacobi solver for 10201 d.o.f.s
|
||||||
|
aver. Jacobi rate : 0.997922 (1000 iter)
|
||||||
|
final error: 0.124971 (rel) 0.000194029 (abs)
|
||||||
|
JacobiSolve: timing in sec. : 0.155127
|
||||||
24
sheet3/8/output.txt
Normal file
24
sheet3/8/output.txt
Normal file
|
|
@ -0,0 +1,24 @@
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o main.o main.cpp
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o vdop.o vdop.cpp
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o geom.o geom.cpp
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o getmatrix.o getmatrix.cpp
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o jacsolve.o jacsolve.cpp
|
||||||
|
g++ -c -g -O0 -funroll-all-loops -std=c++17 -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -Wredundant-decls -Winline -fmax-errors=1 -flto -o userset.o userset.cpp
|
||||||
|
g++ main.o vdop.o geom.o getmatrix.o jacsolve.o userset.o -O0 -llapack -lblas -flto -o main.GCC_
|
||||||
|
./main.GCC_
|
||||||
|
|
||||||
|
There are 1 processes running.
|
||||||
|
|
||||||
|
Intervalls: 100 x 100
|
||||||
|
|
||||||
|
Start Jacobi solver for 10201 d.o.f.s
|
||||||
|
aver. Jacobi rate : 0.997922 (1000 iter)
|
||||||
|
final error: 0.124971 (rel) 0.000194029 (abs)
|
||||||
|
JacobiSolve: timing in sec. : 0.799123
|
||||||
|
ASCI file square_100.txt opened
|
||||||
|
17361 2 34320 3
|
||||||
|
|
||||||
|
Start Jacobi solver for 17361 d.o.f.s
|
||||||
|
aver. Jacobi rate : 0.998401 (1000 iter)
|
||||||
|
final error: 0.201744 (rel) 0.000265133 (abs)
|
||||||
|
JacobiSolve: timing in sec. : 1.54385
|
||||||
1826
sheet3/8/small_Doxyfile
Normal file
1826
sheet3/8/small_Doxyfile
Normal file
File diff suppressed because it is too large
Load diff
41
sheet3/8/square.m
Normal file
41
sheet3/8/square.m
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
% Square:
|
||||||
|
% flatpak run org.octave.Octave <filename>
|
||||||
|
% or
|
||||||
|
% octave --no-window-system --no-gui -qf <filename>
|
||||||
|
|
||||||
|
clear all
|
||||||
|
clc
|
||||||
|
% %% L-shape
|
||||||
|
% g=[2 0 2 0 0 1 0; % #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
|
||||||
|
% 2 2 2 0 1 1 0;
|
||||||
|
% 2 2 1 1 0.5 1 0;
|
||||||
|
% 2 1 1 0.5 2 1 0;
|
||||||
|
% 2 1 0 2 2 1 0;
|
||||||
|
% 2 0 0 2 0 1 0]';
|
||||||
|
|
||||||
|
%% square
|
||||||
|
g=[2 0 1 0 0 1 0; % #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
|
||||||
|
2 1 1 0 1 1 0;
|
||||||
|
2 1 0 1 1 1 0;
|
||||||
|
2 0 0 1 0 1 0]';
|
||||||
|
|
||||||
|
[p,e,t] = initmesh(g,'hmax',0.01);
|
||||||
|
pdemesh(p,e,t)
|
||||||
|
|
||||||
|
%% GH
|
||||||
|
% output from <https://de.mathworks.com/help/pde/ug/initmesh.html initmesh>
|
||||||
|
%
|
||||||
|
% coordinates p: [2][nnode]
|
||||||
|
% connectivity t: [4][nelem] with t(4,:) are the subdomain numbers
|
||||||
|
% edges e: [7][nedges] boundary edges
|
||||||
|
% e([1,2],:) - start/end vertex of edge
|
||||||
|
% e([3,4],:) - start/end values
|
||||||
|
% e(5,:) - segment number
|
||||||
|
% e([6,7],:) - left/right subdomain
|
||||||
|
|
||||||
|
ascii_write_mesh( p, t, e, mfilename);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% tmp=t(1:3,:)
|
||||||
|
|
||||||
138487
sheet3/8/square_100.txt
Normal file
138487
sheet3/8/square_100.txt
Normal file
File diff suppressed because it is too large
Load diff
95
sheet3/8/square_tiny.txt
Normal file
95
sheet3/8/square_tiny.txt
Normal file
|
|
@ -0,0 +1,95 @@
|
||||||
|
13
|
||||||
|
2
|
||||||
|
16
|
||||||
|
3
|
||||||
|
0
|
||||||
|
0
|
||||||
|
1
|
||||||
|
0
|
||||||
|
1
|
||||||
|
1
|
||||||
|
0
|
||||||
|
1
|
||||||
|
0.5
|
||||||
|
0
|
||||||
|
1
|
||||||
|
0.5
|
||||||
|
0.5
|
||||||
|
1
|
||||||
|
0
|
||||||
|
0.5
|
||||||
|
0.4999999999999999
|
||||||
|
0.4999999999999999
|
||||||
|
0.3333333333333333
|
||||||
|
0.6666666666666666
|
||||||
|
0.6666666666666666
|
||||||
|
0.6666666666666666
|
||||||
|
0.6666666666666666
|
||||||
|
0.3333333333333333
|
||||||
|
0.3333333333333333
|
||||||
|
0.3333333333333333
|
||||||
|
8
|
||||||
|
1
|
||||||
|
13
|
||||||
|
5
|
||||||
|
2
|
||||||
|
12
|
||||||
|
6
|
||||||
|
3
|
||||||
|
11
|
||||||
|
7
|
||||||
|
4
|
||||||
|
10
|
||||||
|
1
|
||||||
|
5
|
||||||
|
13
|
||||||
|
10
|
||||||
|
8
|
||||||
|
13
|
||||||
|
2
|
||||||
|
6
|
||||||
|
12
|
||||||
|
3
|
||||||
|
7
|
||||||
|
11
|
||||||
|
4
|
||||||
|
8
|
||||||
|
10
|
||||||
|
12
|
||||||
|
9
|
||||||
|
13
|
||||||
|
10
|
||||||
|
9
|
||||||
|
11
|
||||||
|
7
|
||||||
|
10
|
||||||
|
11
|
||||||
|
11
|
||||||
|
9
|
||||||
|
12
|
||||||
|
6
|
||||||
|
11
|
||||||
|
12
|
||||||
|
9
|
||||||
|
10
|
||||||
|
13
|
||||||
|
5
|
||||||
|
12
|
||||||
|
13
|
||||||
|
8
|
||||||
|
1
|
||||||
|
5
|
||||||
|
5
|
||||||
|
2
|
||||||
|
2
|
||||||
|
6
|
||||||
|
6
|
||||||
|
3
|
||||||
|
3
|
||||||
|
7
|
||||||
|
7
|
||||||
|
4
|
||||||
|
4
|
||||||
|
8
|
||||||
|
8
|
||||||
|
1
|
||||||
16
sheet3/8/userset.cpp
Normal file
16
sheet3/8/userset.cpp
Normal file
|
|
@ -0,0 +1,16 @@
|
||||||
|
#include "userset.h"
|
||||||
|
#include <cmath>
|
||||||
|
|
||||||
|
|
||||||
|
double FunctF(double const x, double const y)
|
||||||
|
{
|
||||||
|
// return std::sin(3.14159*1*x)*std::sin(3.14159*1*y);
|
||||||
|
// return 16.0*1024. ;
|
||||||
|
// return (double)1.0 ;
|
||||||
|
return x * x * std::sin(2.5 * 3.14159 * y);
|
||||||
|
}
|
||||||
|
|
||||||
|
double FunctU(const double /* x */, double const /* y */)
|
||||||
|
{
|
||||||
|
return 1.0 ;
|
||||||
|
}
|
||||||
44
sheet3/8/userset.h
Normal file
44
sheet3/8/userset.h
Normal file
|
|
@ -0,0 +1,44 @@
|
||||||
|
#ifndef USERSET_FILE
|
||||||
|
#define USERSET_FILE
|
||||||
|
#include <cmath>
|
||||||
|
/**
|
||||||
|
* User function: f(@p x,@p y)
|
||||||
|
* @param[in] x x-coordinate of discretization point
|
||||||
|
* @param[in] y y-coordinate of discretization point
|
||||||
|
* @return value for right hand side f(@p x,@p y)
|
||||||
|
*/
|
||||||
|
double FunctF(double const x, double const y);
|
||||||
|
|
||||||
|
/**
|
||||||
|
* User function: u(@p x,@p y)
|
||||||
|
* @param[in] x x-coordinate of discretization point
|
||||||
|
* @param[in] y y-coordinate of discretization point
|
||||||
|
* @return value for solution vector u(@p x,@p y)
|
||||||
|
*/
|
||||||
|
double FunctU(double const x, double const y);
|
||||||
|
|
||||||
|
|
||||||
|
/**
|
||||||
|
* User function: f(@p x,@p y) = @f$ x^2 \sin(2.5\pi y)@f$.
|
||||||
|
* @param[in] x x-coordinate of discretization point
|
||||||
|
* @param[in] y y-coordinate of discretization point
|
||||||
|
* @return value f(@p x,@p y)
|
||||||
|
*/
|
||||||
|
inline double fNice(double const x, double const y)
|
||||||
|
{
|
||||||
|
return x * x * std::sin(2.5 * 3.14159 * y);
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* User function: f(@p x,@p y) = 0$.
|
||||||
|
* @param[in] x x-coordinate of discretization point
|
||||||
|
* @param[in] y y-coordinate of discretization point
|
||||||
|
* @return value 0
|
||||||
|
*/
|
||||||
|
inline double f_zero(double const x, double const y)
|
||||||
|
//double f_zero(double const /*x*/, double const /*y*/)
|
||||||
|
{
|
||||||
|
return 0.0 + 0.0*(x+y);
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif
|
||||||
69043
sheet3/8/uv.txt
Normal file
69043
sheet3/8/uv.txt
Normal file
File diff suppressed because it is too large
Load diff
84
sheet3/8/vdop.cpp
Normal file
84
sheet3/8/vdop.cpp
Normal file
|
|
@ -0,0 +1,84 @@
|
||||||
|
#include "vdop.h"
|
||||||
|
#include <cassert> // assert()
|
||||||
|
#include <cmath>
|
||||||
|
#include <iostream>
|
||||||
|
#include <vector>
|
||||||
|
using namespace std;
|
||||||
|
|
||||||
|
|
||||||
|
void vddiv(vector<double> &x, vector<double> const &y,
|
||||||
|
vector<double> const &z)
|
||||||
|
{
|
||||||
|
assert( x.size() == y.size() && y.size() == z.size() );
|
||||||
|
size_t n = x.size();
|
||||||
|
|
||||||
|
for (size_t k = 0; k < n; ++k)
|
||||||
|
{
|
||||||
|
x[k] = y[k] / z[k];
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
//******************************************************************************
|
||||||
|
|
||||||
|
void vdaxpy(std::vector<double> &x, std::vector<double> const &y,
|
||||||
|
double alpha, std::vector<double> const &z )
|
||||||
|
{
|
||||||
|
assert( x.size() == y.size() && y.size() == z.size() );
|
||||||
|
size_t n = x.size();
|
||||||
|
|
||||||
|
for (size_t k = 0; k < n; ++k)
|
||||||
|
{
|
||||||
|
x[k] = y[k] + alpha * z[k];
|
||||||
|
}
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
//******************************************************************************
|
||||||
|
|
||||||
|
double dscapr(std::vector<double> const &x, std::vector<double> const &y)
|
||||||
|
{
|
||||||
|
assert( x.size() == y.size());
|
||||||
|
size_t n = x.size();
|
||||||
|
|
||||||
|
double s = 0.0;
|
||||||
|
for (size_t k = 0; k < n; ++k)
|
||||||
|
{
|
||||||
|
s += x[k] * y[k];
|
||||||
|
}
|
||||||
|
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
//******************************************************************************
|
||||||
|
void DebugVector(vector<double> const &v)
|
||||||
|
{
|
||||||
|
cout << "\nVector (nnode = " << v.size() << ")\n";
|
||||||
|
for (size_t j = 0; j < v.size(); ++j)
|
||||||
|
{
|
||||||
|
cout.setf(ios::right, ios::adjustfield);
|
||||||
|
cout << v[j] << " ";
|
||||||
|
}
|
||||||
|
cout << endl;
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
//******************************************************************************
|
||||||
|
bool CompareVectors(std::vector<double> const &x, int const n, double const y[], double const eps)
|
||||||
|
{
|
||||||
|
bool bn = (static_cast<int>(x.size()) == n);
|
||||||
|
if (!bn)
|
||||||
|
{
|
||||||
|
cout << "######### Error: " << "number of elements" << endl;
|
||||||
|
}
|
||||||
|
//bool bv = equal(x.cbegin(),x.cend(),y);
|
||||||
|
bool bv = equal(x.cbegin(), x.cend(), y,
|
||||||
|
[eps](double a, double b) -> bool
|
||||||
|
{ return std::abs(a - b) < eps * (1.0 + 0.5 * (std::abs(a) + std::abs(a))); }
|
||||||
|
);
|
||||||
|
if (!bv)
|
||||||
|
{
|
||||||
|
assert(static_cast<int>(x.size()) == n);
|
||||||
|
cout << "######### Error: " << "values" << endl;
|
||||||
|
}
|
||||||
|
return bn && bv;
|
||||||
|
}
|
||||||
58
sheet3/8/vdop.h
Normal file
58
sheet3/8/vdop.h
Normal file
|
|
@ -0,0 +1,58 @@
|
||||||
|
#ifndef VDOP_FILE
|
||||||
|
#define VDOP_FILE
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
/** @brief Element-wise vector divison x_k = y_k/z_k.
|
||||||
|
*
|
||||||
|
* @param[out] x target vector
|
||||||
|
* @param[in] y source vector
|
||||||
|
* @param[in] z source vector
|
||||||
|
*
|
||||||
|
*/
|
||||||
|
void vddiv(std::vector<double> & x, std::vector<double> const& y,
|
||||||
|
std::vector<double> const& z);
|
||||||
|
|
||||||
|
/** @brief Element-wise daxpy operation x(k) = y(k) + alpha*z(k).
|
||||||
|
*
|
||||||
|
* @param[out] x target vector
|
||||||
|
* @param[in] y source vector
|
||||||
|
* @param[in] alpha scalar
|
||||||
|
* @param[in] z source vector
|
||||||
|
*
|
||||||
|
*/
|
||||||
|
void vdaxpy(std::vector<double> & x, std::vector<double> const& y,
|
||||||
|
double alpha, std::vector<double> const& z );
|
||||||
|
|
||||||
|
|
||||||
|
/** @brief Calculates the Euclidian inner product of two vectors.
|
||||||
|
*
|
||||||
|
* @param[in] x vector
|
||||||
|
* @param[in] y vector
|
||||||
|
* @return Euclidian inner product @f$\langle x,y \rangle@f$
|
||||||
|
*
|
||||||
|
*/
|
||||||
|
double dscapr(std::vector<double> const& x, std::vector<double> const& y);
|
||||||
|
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Print entries of a vector.
|
||||||
|
* @param[in] v vector values
|
||||||
|
*/
|
||||||
|
void DebugVector(std::vector<double> const &v);
|
||||||
|
|
||||||
|
/** @brief Compares an STL vector with POD vector.
|
||||||
|
*
|
||||||
|
* The accuracy criteria @f$ |x_k-y_k| < \varepsilon \left({1+0.5(|x_k|+|y_k|)}\right) @f$
|
||||||
|
* follows the book by
|
||||||
|
* <a href="https://www.springer.com/la/book/9783319446592">Stoyan/Baran</a>, p.8.
|
||||||
|
*
|
||||||
|
* @param[in] x STL vector
|
||||||
|
* @param[in] n length of POD vector
|
||||||
|
* @param[in] y POD vector
|
||||||
|
* @param[in] eps relative accuracy criteria (default := 0.0).
|
||||||
|
* @return true iff pairwise vector elements are relatively close to each other.
|
||||||
|
*
|
||||||
|
*/
|
||||||
|
bool CompareVectors(std::vector<double> const& x, int n, double const y[], double const eps=0.0);
|
||||||
|
|
||||||
|
#endif
|
||||||
20
sheet3/8/visualize_results.m
Normal file
20
sheet3/8/visualize_results.m
Normal file
|
|
@ -0,0 +1,20 @@
|
||||||
|
%% Visualize results
|
||||||
|
%
|
||||||
|
% flatpak run org.octave.Octave <filename>
|
||||||
|
% or
|
||||||
|
% octave --no-window-system --no-gui -qf <filename>
|
||||||
|
%
|
||||||
|
% or
|
||||||
|
% matlab -nosplash < <filename>
|
||||||
|
|
||||||
|
clear all
|
||||||
|
clc
|
||||||
|
|
||||||
|
%%
|
||||||
|
fname = 'uv.txt';
|
||||||
|
|
||||||
|
[xc,ia,v] = ascii_read_meshvector(fname);
|
||||||
|
|
||||||
|
h = trisurf(ia, xc(:,1), xc(:,2), v);
|
||||||
|
|
||||||
|
waitfor(h) % wait for closing the figure
|
||||||
Loading…
Add table
Add a link
Reference in a new issue