sheet 4

sheet4/C/.vscode/c_cpp_properties.json

@@ -0,0 +1,16 @@
+{
+    "configurations": [
+        {
+            "name": "Linux",
+            "includePath": [
+                "${workspaceFolder}/**"
+            ],
+            "defines": [],
+            "compilerPath": "/usr/bin/gcc",
+            "cStandard": "c17",
+            "cppStandard": "gnu++17",
+            "intelliSenseMode": "linux-gcc-x64"
+        }
+    ],
+    "version": 4
+}

sheet4/C/.vscode/settings.json

@@ -0,0 +1,6 @@
+{
+    "files.associations": {
+        "ostream": "cpp",
+        "iostream": "cpp"
+    }
+}

sheet4/C/Makefile

@@ -0,0 +1,32 @@
+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+# use Intel compilers
+#COMPILER=ICC_
+
+# use PGI compilers
+# COMPILER=PGI_
+
+
+SOURCES = main.cpp 
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= main.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+LINKFLAGS += -g
+# do not use -pg with PGI compilers
+
+ifndef COMPILER
+  COMPILER=GCC_
+endif
+
+include ../${COMPILER}default.mk
+$(PROGRAM): $(OBJECTS)
+	$(CXX) $(CXXFLAGS) $(OBJECTS) -llapacke -lopenblas -o $(PROGRAM)

sheet4/C/main.cpp

@@ -0,0 +1,51 @@
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <cmath>
+#include <lapacke.h>
+using namespace std;
+
+
+int main()
+{   
+    unsigned int ns[5] = {10,20,30,40,70};
+    int p = 70;
+    int rhs = 1;
+    for(unsigned int i = 0; i< sizeof(ns)/sizeof(ns[0]); i++)
+    {
+        int n=ns[i];
+        unsigned int nodes = n+1;
+
+        vector<double> upperdiagonal(n,-n+p/2.0);
+        vector<double> lowerdiagonal(n,-n-p/2.0);
+        vector<double> diagonal(nodes,2*n);
+        vector<double> F(nodes,0.0);
+        upperdiagonal[0]=0.0;
+        lowerdiagonal[n-1]=0.0;
+        diagonal[0] = 1.0;
+        diagonal[n] = 1.0;
+        F[n] = 1.0;
+
+        //Tridiagonal
+        LAPACKE_dgtsv(LAPACK_COL_MAJOR,nodes,rhs,lowerdiagonal.data(),diagonal.data(),upperdiagonal.data(),F.data(),nodes);
+
+
+         cout << "Solution u_h at nodes x_0..x_" << n << ":\n";
+    
+        for (unsigned int j = 0; j < nodes; ++j) {
+
+            double xi = double(j) /double(n);
+            cout << "u_h(" << xi << ") = " << F[j] << "\n";
+            // F will be overwritten with sol
+        }
+    }
+
+    /*
+    From Methode  der finiten Elemente fuer Ingenieure:
+    small n approximates pu' not good espicially if n < p/2=35 therefor this oscillation (see plot) occurs.
+    */
+    return 0;
+
+    
+}  

sheet4/C/output.txt

@@ -0,0 +1,180 @@
+Solution u_h at nodes x_0..x_10:
+u_h(0) = -3.51571e-17
+u_h(0.1) = -0.00786414
+u_h(0.2) = 0.00629131
+u_h(0.3) = -0.0191885
+u_h(0.4) = 0.0266752
+u_h(0.5) = -0.0558794
+u_h(0.6) = 0.0927188
+u_h(0.7) = -0.174758
+u_h(0.8) = 0.3067
+u_h(0.9) = -0.559925
+u_h(1) = 1
+Solution u_h at nodes x_0..x_20:
+u_h(0) = -3.2746e-17
+u_h(0.05) = -2.41868e-11
+u_h(0.1) = 6.44981e-11
+u_h(0.15) = -2.6068e-10
+u_h(0.2) = 9.31639e-10
+u_h(0.25) = -3.4402e-09
+u_h(0.3) = 1.25899e-08
+u_h(0.35) = -4.6187e-08
+u_h(0.4) = 1.69328e-07
+u_h(0.45) = -6.20895e-07
+u_h(0.5) = 2.27659e-06
+u_h(0.55) = -8.34752e-06
+u_h(0.6) = 3.06075e-05
+u_h(0.65) = -0.000112228
+u_h(0.7) = 0.000411501
+u_h(0.75) = -0.00150884
+u_h(0.8) = 0.00553241
+u_h(0.85) = -0.0202855
+u_h(0.9) = 0.0743802
+u_h(0.95) = -0.272727
+u_h(1) = 1
+Solution u_h at nodes x_0..x_30:
+u_h(0) = -6.65912e-18
+u_h(0.0333333) = -6.65912e-18
+u_h(0.0666667) = -6.65912e-18
+u_h(0.1) = -6.65912e-18
+u_h(0.133333) = -6.65912e-18
+u_h(0.166667) = -6.65912e-18
+u_h(0.2) = -6.65912e-18
+u_h(0.233333) = -6.65912e-18
+u_h(0.266667) = -6.65912e-18
+u_h(0.3) = -6.65912e-18
+u_h(0.333333) = -6.65907e-18
+u_h(0.366667) = -6.6598e-18
+u_h(0.4) = -6.65023e-18
+u_h(0.433333) = -6.77472e-18
+u_h(0.466667) = -5.1563e-18
+u_h(0.5) = -2.61958e-17
+u_h(0.533333) = 2.47317e-16
+u_h(0.566667) = -3.30835e-15
+u_h(0.6) = 4.29153e-14
+u_h(0.633333) = -5.57992e-13
+u_h(0.666667) = 7.25381e-12
+u_h(0.7) = -9.42996e-11
+u_h(0.733333) = 1.22589e-09
+u_h(0.766667) = -1.59366e-08
+u_h(0.8) = 2.07176e-07
+u_h(0.833333) = -2.69329e-06
+u_h(0.866667) = 3.50128e-05
+u_h(0.9) = -0.000455166
+u_h(0.933333) = 0.00591716
+u_h(0.966667) = -0.0769231
+u_h(1) = 1
+Solution u_h at nodes x_0..x_40:
+u_h(0) = -4.79093e-18
+u_h(0.025) = -4.79093e-18
+u_h(0.05) = -4.79093e-18
+u_h(0.075) = -4.79093e-18
+u_h(0.1) = -4.79093e-18
+u_h(0.125) = -4.79093e-18
+u_h(0.15) = -4.79093e-18
+u_h(0.175) = -4.79093e-18
+u_h(0.2) = -4.79093e-18
+u_h(0.225) = -4.79093e-18
+u_h(0.25) = -4.79093e-18
+u_h(0.275) = -4.79093e-18
+u_h(0.3) = -4.79093e-18
+u_h(0.325) = -4.79093e-18
+u_h(0.35) = -4.79093e-18
+u_h(0.375) = -4.79093e-18
+u_h(0.4) = -4.79093e-18
+u_h(0.425) = -4.79093e-18
+u_h(0.45) = -4.79093e-18
+u_h(0.475) = -4.79093e-18
+u_h(0.5) = -4.79093e-18
+u_h(0.525) = -4.79089e-18
+u_h(0.55) = -4.79026e-18
+u_h(0.575) = -4.78078e-18
+u_h(0.6) = -4.63869e-18
+u_h(0.625) = -2.50728e-18
+u_h(0.65) = 2.94639e-17
+u_h(0.675) = 5.09032e-16
+u_h(0.7) = 7.70256e-15
+u_h(0.725) = 1.15605e-13
+u_h(0.75) = 1.73415e-12
+u_h(0.775) = 2.60123e-11
+u_h(0.8) = 3.90184e-10
+u_h(0.825) = 5.85277e-09
+u_h(0.85) = 8.77915e-08
+u_h(0.875) = 1.31687e-06
+u_h(0.9) = 1.97531e-05
+u_h(0.925) = 0.000296296
+u_h(0.95) = 0.00444444
+u_h(0.975) = 0.0666667
+u_h(1) = 1
+Solution u_h at nodes x_0..x_70:
+u_h(0) = -1.30667e-17
+u_h(0.0142857) = -1.30667e-17
+u_h(0.0285714) = -1.30667e-17
+u_h(0.0428571) = -1.30667e-17
+u_h(0.0571429) = -1.30667e-17
+u_h(0.0714286) = -1.30667e-17
+u_h(0.0857143) = -1.30667e-17
+u_h(0.1) = -1.30667e-17
+u_h(0.114286) = -1.30667e-17
+u_h(0.128571) = -1.30667e-17
+u_h(0.142857) = -1.30667e-17
+u_h(0.157143) = -1.30667e-17
+u_h(0.171429) = -1.30667e-17
+u_h(0.185714) = -1.30667e-17
+u_h(0.2) = -1.30667e-17
+u_h(0.214286) = -1.30667e-17
+u_h(0.228571) = -1.30667e-17
+u_h(0.242857) = -1.30667e-17
+u_h(0.257143) = -1.30667e-17
+u_h(0.271429) = -1.30667e-17
+u_h(0.285714) = -1.30667e-17
+u_h(0.3) = -1.30667e-17
+u_h(0.314286) = -1.30667e-17
+u_h(0.328571) = -1.30667e-17
+u_h(0.342857) = -1.30666e-17
+u_h(0.357143) = -1.30664e-17
+u_h(0.371429) = -1.30657e-17
+u_h(0.385714) = -1.30637e-17
+u_h(0.4) = -1.30576e-17
+u_h(0.414286) = -1.30393e-17
+u_h(0.428571) = -1.29845e-17
+u_h(0.442857) = -1.282e-17
+u_h(0.457143) = -1.23265e-17
+u_h(0.471429) = -1.08459e-17
+u_h(0.485714) = -6.40428e-18
+u_h(0.5) = 6.92065e-18
+u_h(0.514286) = 4.68954e-17
+u_h(0.528571) = 1.6682e-16
+u_h(0.542857) = 5.26593e-16
+u_h(0.557143) = 1.60591e-15
+u_h(0.571429) = 4.84387e-15
+u_h(0.585714) = 1.45577e-14
+u_h(0.6) = 4.36994e-14
+u_h(0.614286) = 1.31124e-13
+u_h(0.628571) = 3.93399e-13
+u_h(0.642857) = 1.18022e-12
+u_h(0.657143) = 3.54069e-12
+u_h(0.671429) = 1.06221e-11
+u_h(0.685714) = 3.18663e-11
+u_h(0.7) = 9.55991e-11
+u_h(0.714286) = 2.86797e-10
+u_h(0.728571) = 8.60392e-10
+u_h(0.742857) = 2.58117e-09
+u_h(0.757143) = 7.74352e-09
+u_h(0.771429) = 2.32306e-08
+u_h(0.785714) = 6.96917e-08
+u_h(0.8) = 2.09075e-07
+u_h(0.814286) = 6.27225e-07
+u_h(0.828571) = 1.88168e-06
+u_h(0.842857) = 5.64503e-06
+u_h(0.857143) = 1.69351e-05
+u_h(0.871429) = 5.08053e-05
+u_h(0.885714) = 0.000152416
+u_h(0.9) = 0.000457247
+u_h(0.914286) = 0.00137174
+u_h(0.928571) = 0.00411523
+u_h(0.942857) = 0.0123457
+u_h(0.957143) = 0.037037
+u_h(0.971429) = 0.111111
+u_h(0.985714) = 0.333333
+u_h(1) = 1