--- /dev/null
+/* $Id$ */
+/* Copyright W. Bangerth, University of Heidelberg, 1998 */
+
+
+#include <grid/tria.h>
+#include <grid/mg_dof.h>
+#include <grid/tria_accessor.h>
+#include <grid/mg_dof_accessor.h>
+#include <grid/tria_iterator.h>
+#include <grid/tria_boundary.h>
+#include <grid/dof_constraints.h>
+#include <basic/function.h>
+#include <basic/data_io.h>
+#include <fe/fe_lib.lagrange.h>
+#include <fe/fe_lib.criss_cross.h>
+#include <fe/quadrature_lib.h>
+#include <numerics/assembler.h>
+#include <numerics/vectors.h>
+
+#include <map>
+#include <fstream>
+#include <cmath>
+#include <string>
+#include <cstdlib>
+
+
+
+
+
+template <int dim>
+class PoissonEquation : public Equation<dim> {
+ public:
+ PoissonEquation (const Function<dim> &rhs) :
+ Equation<dim>(1),
+ right_hand_side (rhs) {};
+
+ virtual void assemble (dFMatrix &cell_matrix,
+ dVector &rhs,
+ const FEValues<dim> &fe_values,
+ const Triangulation<dim>::cell_iterator &cell) const;
+ virtual void assemble (dFMatrix &cell_matrix,
+ const FEValues<dim> &fe_values,
+ const Triangulation<dim>::cell_iterator &cell) const;
+ virtual void assemble (dVector &rhs,
+ const FEValues<dim> &fe_values,
+ const Triangulation<dim>::cell_iterator &cell) const;
+ protected:
+ const Function<dim> &right_hand_side;
+};
+
+
+
+
+
+
+template <int dim>
+class PoissonProblem {
+ public:
+ PoissonProblem (unsigned int order);
+
+ void clear ();
+ void create_new ();
+ int run (unsigned int level);
+ void print_history (string filename) const;
+
+ protected:
+ Triangulation<dim> *tria;
+ MGDoFHandler<dim> *dof;
+
+ Function<dim> *rhs;
+ Function<dim> *boundary_values;
+
+ vector<double> l1_error, l2_error, linfty_error, h1_seminorm_error, h1_error;
+ vector<int> n_dofs;
+
+ unsigned int order;
+};
+
+
+
+
+
+/**
+ Right hand side constructed such that the exact solution is
+ $sin(2 pi x) + sin(2 pi y)$
+ */
+template <int dim>
+class RHSPoly : public Function<dim> {
+ public:
+ /**
+ * Return the value of the function
+ * at the given point.
+ */
+ virtual double operator () (const Point<dim> &p) const;
+};
+
+
+
+template <int dim>
+class Solution : public Function<dim> {
+ public:
+ /**
+ * Return the value of the function
+ * at the given point.
+ */
+ virtual double operator () (const Point<dim> &p) const;
+ /**
+ * Return the gradient of the function
+ * at the given point.
+ */
+ virtual Point<dim> gradient (const Point<dim> &p) const;
+};
+
+
+
+
+double RHSPoly<2>::operator () (const Point<2> &p) const {
+ const double x = p(0),
+ y = p(1);
+ const double pi= 3.1415926536;
+ return 4*pi*pi*(sin(2*pi*x)+sin(2*pi*y));
+};
+
+
+
+double Solution<2>::operator () (const Point<2> &p) const {
+ const double x = p(0),
+ y = p(1);
+ const double pi= 3.1415926536;
+ return sin(2*pi*x)+sin(2*pi*y);
+};
+
+
+Point<2> Solution<2>::gradient (const Point<2> &p) const {
+ const double x = p(0),
+ y = p(1);
+ const double pi= 3.1415926536;
+ return Point<2> (2*pi*cos(2*pi*x),
+ 2*pi*cos(2*pi*y));
+};
+
+
+
+
+
+
+void PoissonEquation<2>::assemble (dFMatrix &cell_matrix,
+ dVector &rhs,
+ const FEValues<2> &fe_values,
+ const Triangulation<2>::cell_iterator &) const {
+ for (unsigned int point=0; point<fe_values.n_quadrature_points; ++point)
+ for (unsigned int i=0; i<fe_values.total_dofs; ++i)
+ {
+ for (unsigned int j=0; j<fe_values.total_dofs; ++j)
+ cell_matrix(i,j) += (fe_values.shape_grad(i,point) *
+ fe_values.shape_grad(j,point)) *
+ fe_values.JxW(point);
+ rhs(i) += fe_values.shape_value(i,point) *
+ right_hand_side(fe_values.quadrature_point(point)) *
+ fe_values.JxW(point);
+ };
+};
+
+
+
+template <int dim>
+void PoissonEquation<dim>::assemble (dFMatrix &,
+ const FEValues<dim> &,
+ const Triangulation<dim>::cell_iterator &) const {
+ Assert (false, ExcPureVirtualFunctionCalled());
+};
+
+
+
+template <int dim>
+void PoissonEquation<dim>::assemble (dVector &,
+ const FEValues<dim> &,
+ const Triangulation<dim>::cell_iterator &) const {
+ Assert (false, ExcPureVirtualFunctionCalled());
+};
+
+
+
+
+
+
+
+
+
+template <int dim>
+PoissonProblem<dim>::PoissonProblem (unsigned int order) :
+ tria(0), dof(0), rhs(0),
+ boundary_values(0), order(order) {};
+
+
+
+
+template <int dim>
+void PoissonProblem<dim>::clear () {
+ if (tria != 0) {
+ delete tria;
+ tria = 0;
+ };
+
+ if (dof != 0) {
+ delete dof;
+ dof = 0;
+ };
+
+ if (rhs != 0)
+ {
+ delete rhs;
+ rhs = 0;
+ };
+
+ if (boundary_values != 0)
+ {
+ delete boundary_values;
+ boundary_values = 0;
+ };
+
+ ProblemBase<dim>::clear ();
+};
+
+
+
+
+template <int dim>
+void PoissonProblem<dim>::create_new () {
+ clear ();
+
+ tria = new Triangulation<dim>();
+ dof = new MGDoFHandler<dim> (tria);
+ set_tria_and_dof (tria, dof);
+};
+
+
+
+
+template <int dim>
+int PoissonProblem<dim>::run (const unsigned int level) {
+ create_new ();
+
+ cout << "Refinement level = " << level
+ << ", using elements of type <";
+ switch (order)
+ {
+ case 0:
+ cout << "criss-cross";
+ break;
+ default:
+ cout << "Lagrange-" << order;
+ break;
+ };
+ cout << ">" << endl;
+
+ cout << " Making grid... ";
+ tria->create_hyper_ball ();
+ HyperBallBoundary<dim> boundary_description;
+ tria->set_boundary (&boundary_description);
+ tria->begin_active()->set_refine_flag();
+ (++(++(tria->begin_active())))->set_refine_flag();
+ tria->execute_refinement ();
+ tria->refine_global (level);
+ cout << tria->n_active_cells() << " active cells." << endl;
+
+ rhs = new RHSPoly<dim>();
+ boundary_values = new Solution<dim> ();
+
+
+ FiniteElement<dim> *fe;
+ PoissonEquation<dim> equation (*rhs);
+ Quadrature<dim> *quadrature;
+ Quadrature<dim-1> *boundary_quadrature;
+ switch (order) {
+ case 0:
+ fe = new FECrissCross<dim>();
+ quadrature = new QCrissCross1<dim>();
+ boundary_quadrature = new QGauss2<dim-1>();
+ break;
+ case 1:
+ fe = new FELinear<dim>();
+ quadrature = new QGauss3<dim>();
+ boundary_quadrature = new QGauss2<dim-1>();
+ break;
+ case 2:
+ fe = new FEQuadraticSub<dim>();
+ quadrature = new QGauss4<dim>();
+ boundary_quadrature = new QGauss3<dim-1>();
+ break;
+ case 3:
+ fe = new FECubicSub<dim>();
+ quadrature = new QGauss5<dim>();
+ boundary_quadrature = new QGauss4<dim-1>();
+ break;
+ case 4:
+ fe = new FEQuarticSub<dim>();
+ quadrature = new QGauss6<dim>();
+ boundary_quadrature = new QGauss5<dim-1>();
+ break;
+ default:
+ return 100000;
+ };
+
+ cout << " Distributing dofs... ";
+ dof->distribute_dofs (*fe);
+ cout << dof->n_dofs() << " degrees of freedom." << endl;
+ n_dofs.push_back (dof->n_dofs());
+
+ cout << " Assembling matrices..." << endl;
+ UpdateFlags update_flags = UpdateFlags(update_q_points | update_gradients |
+ update_JxW_values);
+
+ ProblemBase<dim>::FunctionMap dirichlet_bc;
+ dirichlet_bc[0] = boundary_values;
+ assemble (equation, *quadrature, *fe, update_flags, dirichlet_bc);
+
+ cout << " Solving..." << endl;
+ solve ();
+
+ Solution<dim> sol;
+ dVector l1_error_per_cell, l2_error_per_cell, linfty_error_per_cell;
+ dVector h1_seminorm_error_per_cell, h1_error_per_cell;
+
+ cout << " Calculating L1 error... ";
+ VectorTools<dim>::integrate_difference (*dof_handler,
+ solution, sol,
+ l1_error_per_cell,
+ *quadrature, *fe, L1_norm);
+ cout << l1_error_per_cell.l1_norm() << endl;
+ l1_error.push_back (l1_error_per_cell.l1_norm());
+
+ cout << " Calculating L2 error... ";
+ VectorTools<dim>::integrate_difference (*dof_handler,
+ solution, sol,
+ l2_error_per_cell,
+ *quadrature, *fe, L2_norm);
+ cout << l2_error_per_cell.l2_norm() << endl;
+ l2_error.push_back (l2_error_per_cell.l2_norm());
+
+ cout << " Calculating L-infinity error... ";
+ VectorTools<dim>::integrate_difference (*dof_handler,
+ solution, sol,
+ linfty_error_per_cell,
+ *quadrature, *fe, Linfty_norm);
+ cout << linfty_error_per_cell.linfty_norm() << endl;
+ linfty_error.push_back (linfty_error_per_cell.linfty_norm());
+
+ cout << " Calculating H1-seminorm error... ";
+ VectorTools<dim>::integrate_difference (*dof_handler,
+ solution, sol,
+ h1_seminorm_error_per_cell,
+ *quadrature, *fe, H1_seminorm);
+ cout << h1_seminorm_error_per_cell.l2_norm() << endl;
+ h1_seminorm_error.push_back (h1_seminorm_error_per_cell.l2_norm());
+
+ cout << " Calculating H1 error... ";
+ VectorTools<dim>::integrate_difference (*dof_handler,
+ solution, sol,
+ h1_error_per_cell,
+ *quadrature, *fe, H1_norm);
+ cout << h1_error_per_cell.l2_norm() << endl;
+ h1_error.push_back (h1_error_per_cell.l2_norm());
+
+ if (dof->n_dofs()<=5000)
+ {
+ dVector l1_error_per_dof, l2_error_per_dof, linfty_error_per_dof;
+ dVector h1_seminorm_error_per_dof, h1_error_per_dof;
+ dof->distribute_cell_to_dof_vector (l1_error_per_cell, l1_error_per_dof);
+ dof->distribute_cell_to_dof_vector (l2_error_per_cell, l2_error_per_dof);
+ dof->distribute_cell_to_dof_vector (linfty_error_per_cell,
+ linfty_error_per_dof);
+ dof->distribute_cell_to_dof_vector (h1_seminorm_error_per_cell,
+ h1_seminorm_error_per_dof);
+ dof->distribute_cell_to_dof_vector (h1_error_per_cell, h1_error_per_dof);
+
+// dVector projected_solution;
+// ConstraintMatrix constraints;
+// constraints.close ();
+// VectorTools<dim>::project (*dof, constraints, *fe,
+// StraightBoundary<dim>(), *quadrature,
+// sol, projected_solution, false,
+// *boundary_quadrature);
+// cout << " Calculating L2 error of projected solution... ";
+// VectorTools<dim>::integrate_difference (*dof_handler,
+// projected_solution, sol,
+// l2_error_per_cell,
+// *quadrature, *fe, L2_norm);
+// cout << l2_error_per_cell.l2_norm() << endl;
+
+
+ string filename;
+ filename = ('0'+order);
+ filename += ".";
+ filename += ('0'+level);
+ filename += ".ucd";
+ cout << " Writing error plots to <" << filename << ">..." << endl;
+
+ DataOut<dim> out;
+ ofstream o(filename.c_str());
+ fill_data (out);
+ out.add_data_vector (l1_error_per_dof, "L1-Error");
+ out.add_data_vector (l2_error_per_dof, "L2-Error");
+ out.add_data_vector (linfty_error_per_dof, "Linfty-Error");
+ out.add_data_vector (h1_seminorm_error_per_dof, "H1-seminorm-Error");
+ out.add_data_vector (h1_error_per_dof, "H1-Error");
+ out.write_ucd (o);
+ o.close ();
+ }
+ else
+ cout << " Not writing error as grid." << endl;
+
+ cout << endl;
+
+ delete fe;
+ delete quadrature;
+ delete boundary_quadrature;
+
+ return dof->n_dofs();
+};
+
+
+template <int dim>
+void PoissonProblem<dim>::print_history (string filename) const {
+ ofstream out(filename.c_str());
+ out << "# n_dofs l1_error l2_error linfty_error h1_seminorm_error h1_error"
+ << endl;
+ for (unsigned int i=0; i<n_dofs.size(); ++i)
+ out << n_dofs[i]
+ << " "
+ << l1_error[i] << " "
+ << l2_error[i] << " "
+ << linfty_error[i] << " "
+ << h1_seminorm_error[i] << " "
+ << h1_error[i] << endl;
+
+ double average_l1=0,
+ average_l2=0,
+ average_linfty=0,
+ average_h1_semi=0,
+ average_h1=0;
+ for (unsigned int i=1; i<n_dofs.size(); ++i)
+ {
+ average_l1 += l1_error[i]/l1_error[i-1];
+ average_l2 += l2_error[i]/l2_error[i-1];
+ average_linfty += linfty_error[i]/linfty_error[i-1];
+ average_h1_semi += h1_seminorm_error[i]/h1_seminorm_error[i-1];
+ average_h1 += h1_error[i]/h1_error[i-1];
+ };
+
+ average_l1 /= (l1_error.size()-1);
+ average_l2 /= (l1_error.size()-1);
+ average_linfty /= (l1_error.size()-1);
+ average_h1_semi /= (l1_error.size()-1);
+ average_h1 /= (l1_error.size()-1);
+
+ cout << "==========================================================\n";
+ cout << "Average error reduction rates for h->h/2:" << endl;
+ cout << " L1 error : " << 1./average_l1 << endl
+ << " L2 error : " << 1./average_l2 << endl
+ << " Linfty error : " << 1./average_linfty << endl
+ << " H1 seminorm error: " << 1./average_h1_semi << endl
+ << " H1 error : " << 1./average_h1 << endl;
+ cout << "==========================================================\n";
+ cout << "==========================================================\n";
+};
+
+
+
+
+int main () {
+ for (unsigned int order=0; order<5; ++order)
+ {
+ PoissonProblem<2> problem (order);
+
+ unsigned int level=0;
+ unsigned int n_dofs;
+ do
+ n_dofs = problem.run (level++);
+ while (n_dofs<25000);
+
+ string filename;
+ switch (order)
+ {
+ case 0:
+ filename = "criss_cross";
+ break;
+ case 1:
+ filename = "linear";
+ break;
+ case 2:
+ filename = "quadratic";
+ break;
+ case 3:
+ filename = "cubic";
+ break;
+ case 4:
+ filename = "quartic";
+ break;
+ };
+ filename += ".history";
+
+ cout << endl << "Printing convergence history to <"
+ << filename << ">..." << endl;
+ problem.print_history (filename);
+ cout << endl << endl << endl;
+ };
+
+ return 0;
+};