Sheet 7
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Markus Schmidt
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sheet7/jacobi.template/jacsolve.cpp
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235
sheet7/jacobi.template/jacsolve.cpp
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#include "vdop.h"
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#include "geom.h"
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#include "getmatrix.h"
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#include "jacsolve.h"
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#include "userset.h"
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#include <cassert>
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#include <cmath>
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#include <iostream>
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#include <vector>
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using namespace std;
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// #####################################################################
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// ParMesh const & mesh,
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void JacobiSolve(CRS_Matrix const &SK, vector<double> const &f, vector<double> &u)
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{
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const double omega = 1.0;
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const int maxiter = 1000;
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const double tol = 1e-6, // tolerance
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tol2 = tol * tol; // tolerance^2
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int nrows = SK.Nrows(); // number of rows == number of columns
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assert( nrows == static_cast<int>(f.size()) && f.size() == u.size() );
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cout << endl << " Start Jacobi solver for " << nrows << " d.o.f.s" << endl;
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// Choose initial guess
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for (int k = 0; k < nrows; ++k) {
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u[k] = 0.0; // u := 0
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}
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vector<double> dd(nrows); // matrix diagonal
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vector<double> r(nrows); // residual
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vector<double> w(nrows); // correction
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SK.GetDiag(dd); // dd := diag(K)
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////DebugVector(dd);{int ijk; cin >> ijk;}
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// Initial sweep
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SK.Defect(r, f, u); // r := f - K*u
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vddiv(w, r, dd); // w := D^{-1}*r
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const double sigma0 = dscapr(w, r); // s0 := <w,r>
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// Iteration sweeps
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int iter = 0;
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double sigma = sigma0;
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while ( sigma > tol2 * sigma0 && maxiter > iter) // relative error
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//while ( sigma > tol2 && maxiter > iter) // absolute error
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{
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++iter;
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vdaxpy(u, u, omega, w ); // u := u + om*w
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SK.Defect(r, f, u); // r := f - K*u
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vddiv(w, r, dd); // w := D^{-1}*r
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sigma = dscapr(w, r); // s0 := <w,r>
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// cout << "Iteration " << iter << " : " << sqrt(sigma/sigma0) << endl;
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}
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cout << "aver. Jacobi rate : " << exp(log(sqrt(sigma / sigma0)) / iter) << " (" << iter << " iter)" << endl;
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cout << "final error: " << sqrt(sigma / sigma0) << " (rel) " << sqrt(sigma) << " (abs)\n";
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return;
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}
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void JacobiSmoother(Matrix const &SK, std::vector<double> const &f, std::vector<double> &u,
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std::vector<double> &r, int nsmooth, double const omega, bool zero)
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{
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// ToDO: ensure compatible dimensions
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int const nnodes = static_cast<int>(u.size());
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if (zero) { // assumes initial solution is zero
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DiagPrecond(SK, f, u, omega);
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--nsmooth; // first smoothing sweep done
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}
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auto const &D = SK.GetDiag(); // accumulated diagonal of matrix @p SK.
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for (int ns = 1; ns <= nsmooth; ++ns) {
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SK.Defect(r, f, u); // r := f - K*u
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#pragma omp parallel for
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for (int k = 0; k < nnodes; ++k) {
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// u := u + om*D^{-1}*r
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u[k] = u[k] + omega * r[k] / D[k]; // MPI: distributed to accumulated vector needed
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}
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}
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return;
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}
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void DiagPrecond(Matrix const &SK, std::vector<double> const &r, std::vector<double> &w,
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double const omega)
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{
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// ToDO: ensure compatible dimensions
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auto const &D = SK.GetDiag(); // accumulated diagonal of matrix @p SK.
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int const nnodes = static_cast<int>(w.size());
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#pragma omp parallel for
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for (int k = 0; k < nnodes; ++k) {
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w[k] = omega * r[k] / D[k]; // MPI: distributed to accumulated vector needed
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}
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return;
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}
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Multigrid::Multigrid(Mesh const &cmesh, int const nlevel)
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: _meshes(cmesh, nlevel),
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_SK(), _u(_meshes.size()), _f(_meshes.size()), _d(_meshes.size()), _w(_meshes.size()),
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_Pc2f()
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{
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cout << "\n........................ in Multigrid::Multigrid ..................\n";
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// Allocate Memory for matrices/vectors on all levels
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for (size_t lev = 0; lev < Nlevels(); ++lev) {
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_SK.push_back( FEM_Matrix(_meshes[lev]) ); // CRS matrix
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const auto nn = _SK[lev].Nrows();
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_u[lev].resize(nn);
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_f[lev].resize(nn);
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_d[lev].resize(nn);
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_w[lev].resize(nn);
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auto vv = _meshes[lev].GetFathersOfVertices();
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cout << vv.size() << endl;
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}
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// Intergrid transfer operators
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//cout << "\n........................ in Multigrid::Multigrid Prolongation ..................\n";
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//_Pc2f.push_back( BisectInterpolation(vector<int>(0)) ); // no prolongation to coarsest grid
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_Pc2f.push_back( BisectIntDirichlet() ); // no prolongation to coarsest grid
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for (size_t lev = 1; lev < Nlevels(); ++lev) {
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//cout << lev << endl;
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//cout << _meshes[lev].GetFathersOfVertices () << endl;
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_Pc2f.push_back( BisectIntDirichlet( _meshes[lev].GetFathersOfVertices (), _meshes[lev-1].Index_DirichletNodes () ) );
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//cout << _Pc2f.back().Nrows() << " " << _Pc2f.back().Ncols() << endl;
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}
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cout << "\n..........................................\n";
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}
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Multigrid::~Multigrid()
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{}
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void Multigrid::DefineOperators()
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{
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for (size_t lev = 0; lev < Nlevels(); ++lev) {
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DefineOperator(lev);
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}
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return;
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}
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// GH: Hack
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void Multigrid::DefineOperator(size_t lev)
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{
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_SK[lev].CalculateLaplace(_f[lev]); // fNice() in userset.h
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if (lev == Nlevels() - 1) { // fine mesh
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_meshes[lev].SetValues(_u[lev], [](double x, double y) -> double
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{ return x *x * std::sin(2.5 * M_PI * y); }
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);
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}
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else {
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_meshes[lev].SetValues(_u[lev], f_zero);
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}
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_SK[lev].ApplyDirichletBC(_u[lev], _f[lev]);
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return;
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}
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void Multigrid::JacobiSolve(size_t lev)
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{
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assert(lev < Nlevels());
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::JacobiSolve(_SK[lev], _f[lev], _u[lev]);
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}
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void Multigrid::MG_Step(size_t lev, int const pre_smooth, bool const bzero, int nu)
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{
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assert(lev < Nlevels());
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int const post_smooth = pre_smooth;
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if (lev == 0) { // coarse level
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JacobiSmoother(_SK[lev], _f[lev], _u[lev], _d[lev], 100, 1.0, false);
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}
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else {
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JacobiSmoother(_SK[lev], _f[lev], _u[lev], _d[lev], pre_smooth, 0.85, bzero);
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if (nu > 0) {
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_SK[lev].Defect(_d[lev], _f[lev], _u[lev]); // d := f - K*u
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_Pc2f[lev].MultT(_d[lev], _f[lev - 1]); // f_H := R*d
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//DefectRestrict(_SK[lev], _Pc2f[lev], _f[lev - 1], _f[lev], _u[lev]); // f_H := R*(f - K*u)
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//_meshes[lev-1].Visualize(_f[lev - 1]); // GH: Visualize: f_H should be 0 on Dirichlet B.C.
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MG_Step(lev - 1, pre_smooth, true, nu); // solve K_H * u_H =f_H with u_H:=0
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for (int k = 1; k < nu; ++k) {
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// W-cycle
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MG_Step(lev - 1, pre_smooth, false, nu); // solve K_H * u_H =f_H
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}
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_Pc2f[lev].Mult(_w[lev], _u[lev - 1]); // w := P*u_H
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vdaxpy(_u[lev], _u[lev], 1.0, _w[lev] ); // u := u + tau*w
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}
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JacobiSmoother(_SK[lev], _f[lev], _u[lev], _d[lev], post_smooth, 0.85, false);
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}
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return;
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}
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void Multigrid::MG_Solve(int pre_smooth, double eps, int nu)
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{
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size_t lev=Nlevels()-1; // fine level
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// start with zero guess
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DiagPrecond(_SK[lev], _f[lev], _w[lev], 1.0); // w := D^{-1]*f
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//double s0 = L2_scapr(_f[lev],_w[lev]); // s_0 := <f,w>
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double s0 = dscapr(_f[lev],_w[lev]); // s_0 := <f,w>
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double si;
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bool bzero = true; // start with zero guess
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int iter = 0;
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do
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{
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MG_Step(lev, pre_smooth, bzero, nu);
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bzero=false;
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_SK[lev].Defect(_d[lev], _f[lev], _u[lev]); // d := f - K*u
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DiagPrecond(_SK[lev], _d[lev], _w[lev], 1.0); // w := D^{-1]*d
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//si = L2_scapr(_d[lev],_w[lev]); // s_i := <d,w>
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si = dscapr(_d[lev],_w[lev]); // s_i := <d,w>
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++iter;
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} while (si>s0*eps*eps);
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cout << "\nrel. error: " << sqrt(si/s0) << " ( " << iter << " iter.)" << endl;
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return;
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}
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