-void create_parallelogram(Triangulation<2> &tria)
-{
- const int dim = 2;
- std::vector<Point<dim> > points (4);
- points[0] = Point<dim> (0, 0);
- points[1] = Point<dim> (0, 1);
- points[2] = Point<dim> (1 ,0.5);
- points[3] = Point<dim> (1 ,1.5);
-
- std::vector<CellData<dim> > cells(1);
- cells[0].vertices[0] = 0;
- cells[0].vertices[1] = 2;
- cells[0].vertices[2] = 1;
- cells[0].vertices[3] = 3;
- cells[0].material_id = 0;
-
- tria.create_triangulation (points, cells, SubCellData());
-}
-
-
-
-void create_parallelogram(Triangulation<3> &tria)
-{
- const int dim = 3;
- std::vector<Point<dim> > points (8);
- points[0] = Point<dim> (0,0,0);
- points[1] = Point<dim> (0,1.,0.5);
- points[2] = Point<dim> (0,0,1);
- points[3] = Point<dim> (0,1.,1.5);
- points[4] = Point<dim> (1.,0,1.);
- points[5] = Point<dim> (1.,1.,1.5);
- points[6] = Point<dim> (1.,0,2);
- points[7] = Point<dim> (1.,1.,2.5);
-
- std::vector<CellData<dim> > cells(1);
- cells[0].vertices[0] = 0;
- cells[0].vertices[1] = 4;
- cells[0].vertices[2] = 1;
- cells[0].vertices[3] = 5;
- cells[0].vertices[4] = 2;
- cells[0].vertices[5] = 6;
- cells[0].vertices[6] = 3;
- cells[0].vertices[7] = 7;
- cells[0].material_id = 0;
-
- tria.create_triangulation (points, cells, SubCellData());
-}
-
-
-
template <int dim>
void test_parallelogram ()
{
deallog << "Parallelogram" << std::endl;
Triangulation<dim> tria;
- create_parallelogram(tria);
+ Point<dim> corners[dim];
+ for (unsigned int d=0; d<dim; ++d)
+ {
+ corners[d][d] = 1.;
+ if (d>0)
+ corners[d][0] = 0.5+0.5*d;
+ }
+ GridGenerator::parallelepiped(tria, corners);
tria.refine_global(5-dim);
FE_Q<dim> fe (1);
--- /dev/null
+//------------------ estimate_condition_number_mass.cc ---------------------
+// $Id$
+// Version: $Name$
+//
+//------------------ estimate_condition_number_mass.cc ---------------------
+
+
+// this function computes condition number estimates for the mass matrix at
+// different polynomial degrees. The mesh uses a hypercube mesh with no
+// hanging nodes and no other constraints
+
+#include "../tests.h"
+
+std::ofstream logfile("estimate_condition_number_mass/output");
+
+#include <deal.II/matrix_free/matrix_free.h>
+#include <deal.II/matrix_free/fe_evaluation.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q_hierarchical.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/base/function_lib.h>
+
+
+template <int dim, int fe_degree, typename Number>
+void
+mass_operator (const MatrixFree<dim,Number> &data,
+ Vector<Number> &dst,
+ const Vector<Number> &src,
+ const std::pair<unsigned int,unsigned int> &cell_range)
+{
+ FEEvaluationGeneral<dim,fe_degree,fe_degree+1,1,Number> fe_eval (data);
+ const unsigned int n_q_points = fe_eval.n_q_points;
+
+ for(unsigned int cell=cell_range.first;cell<cell_range.second;++cell)
+ {
+ fe_eval.reinit (cell);
+ fe_eval.read_dof_values (src);
+ fe_eval.template evaluate (true, false, false);
+ for (unsigned int q=0; q<n_q_points; ++q)
+ {
+ fe_eval.submit_value (fe_eval.get_value(q),q);
+ }
+ fe_eval.template integrate (true,false);
+ fe_eval.distribute_local_to_global (dst);
+ }
+}
+
+
+
+template <int dim, int fe_degree, typename Number>
+class MatrixFreeTest
+{
+ public:
+ typedef VectorizedArray<Number> vector_t;
+
+ MatrixFreeTest(const MatrixFree<dim,Number> &data_in):
+ data (data_in)
+ {};
+
+ void vmult (Vector<Number> &dst,
+ const Vector<Number> &src) const
+ {
+ dst = 0;
+ const std_cxx1x::function<void(const MatrixFree<dim,Number> &,
+ Vector<Number> &,
+ const Vector<Number> &,
+ const std::pair<unsigned int,unsigned int>&)>
+ wrap = mass_operator<dim,fe_degree,Number>;
+ data.cell_loop (wrap, dst, src);
+ };
+
+private:
+ const MatrixFree<dim,Number> &data;
+};
+
+
+
+template <int dim, int fe_degree>
+void test (const FiniteElement<dim> &fe)
+{
+ typedef double number;
+
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube (tria);
+ tria.refine_global(2);
+
+ DoFHandler<dim> dof(tria);
+ dof.distribute_dofs(fe);
+ ConstraintMatrix constraints;
+ constraints.close();
+
+ deallog << "Testing " << dof.get_fe().get_name() << std::endl;
+
+ MatrixFree<dim,number> mf_data;
+ {
+ const QGauss<1> quad (fe_degree+1);
+ mf_data.reinit (dof, constraints, quad);
+ }
+
+ MatrixFreeTest<dim,fe_degree,number> mf (mf_data);
+ Vector<number> in (dof.n_dofs()), out (dof.n_dofs());
+
+ VectorTools::create_right_hand_side(dof, QGauss<dim>(fe_degree+1),
+ Functions::CosineFunction<dim>(), in);
+
+ SolverControl control(10000, 1e-9*in.l2_norm());
+ typename SolverCG<>::AdditionalData data;
+ data.compute_condition_number = true;
+ SolverCG<> solver(control,data);
+ solver.solve(mf, out, in, PreconditionIdentity());
+ deallog << std::endl;
+}
+
+
+int main ()
+{
+ deallog.attach(logfile);
+ deallog.depth_console(0);
+
+ deallog << std::setprecision (2);
+
+ {
+ deallog.threshold_double(1.e-9);
+ deallog.push("2d");
+ test<2,1>(FE_Q<2>(1));
+ test<2,1>(FE_DGQ<2>(1));
+ test<2,2>(FE_Q<2>(2));
+ test<2,2>(FE_DGQ<2>(2));
+ test<2,4>(FE_Q<2>(4));
+ test<2,4>(FE_Q<2>(QGaussLobatto<1>(5)));
+ test<2,4>(FE_DGQ<2>(4));
+ test<2,4>(FE_Q_Hierarchical<2>(4));
+ test<2,6>(FE_Q<2>(6));
+ test<2,6>(FE_Q<2>(QGaussLobatto<1>(7)));
+ test<2,6>(FE_DGQ<2>(6));
+ test<2,6>(FE_DGQArbitraryNodes<2>(QGaussLobatto<1>(7)));
+ test<2,10>(FE_Q<2>(10));
+ test<2,10>(FE_Q<2>(QGaussLobatto<1>(11)));
+ test<2,16>(FE_Q<2>(QGaussLobatto<1>(17)));
+ deallog.pop();
+ deallog.push("3d");
+ test<3,1>(FE_Q<3>(1));
+ test<3,2>(FE_Q<3>(2));
+ test<3,5>(FE_Q<3>(5));
+ test<3,5>(FE_Q<3>(QGaussLobatto<1>(6)));
+ deallog.pop();
+ }
+}
+
+
--- /dev/null
+
+DEAL:2d::Testing FE_Q<2>(1)
+DEAL:2d:cg::Starting value 0.117
+DEAL:2d:cg::Convergence step 16 value 0
+DEAL:2d:cg::Condition number estimate: 15.4
+DEAL:2d::
+DEAL:2d::Testing FE_DGQ<2>(1)
+DEAL:2d:cg::Starting value 0.0625
+DEAL:2d:cg::Convergence step 1 value 0
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(2)
+DEAL:2d:cg::Starting value 0.0686
+DEAL:2d:cg::Convergence step 38 value 0
+DEAL:2d:cg::Condition number estimate: 29.1
+DEAL:2d::
+DEAL:2d::Testing FE_DGQ<2>(2)
+DEAL:2d:cg::Starting value 0.0625
+DEAL:2d:cg::Convergence step 3 value 0
+DEAL:2d:cg::Condition number estimate: 6.95
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(4)
+DEAL:2d:cg::Starting value 0.0367
+DEAL:2d:cg::Convergence step 92 value 0
+DEAL:2d:cg::Condition number estimate: 148.
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(QGaussLobatto(5))
+DEAL:2d:cg::Starting value 0.0355
+DEAL:2d:cg::Convergence step 62 value 0
+DEAL:2d:cg::Condition number estimate: 74.3
+DEAL:2d::
+DEAL:2d::Testing FE_DGQ<2>(4)
+DEAL:2d:cg::Starting value 0.0353
+DEAL:2d:cg::Convergence step 7 value 0
+DEAL:2d:cg::Condition number estimate: 200.
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(6)
+DEAL:2d:cg::Starting value 0.0310
+DEAL:2d:cg::Convergence step 209 value 0
+DEAL:2d:cg::Condition number estimate: 1.56e+03
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(QGaussLobatto(7))
+DEAL:2d:cg::Starting value 0.0241
+DEAL:2d:cg::Convergence step 86 value 0
+DEAL:2d:cg::Condition number estimate: 140.
+DEAL:2d::
+DEAL:2d::Testing FE_DGQ<2>(6)
+DEAL:2d:cg::Starting value 0.0305
+DEAL:2d:cg::Convergence step 15 value 0
+DEAL:2d:cg::Condition number estimate: 1.95e+03
+DEAL:2d::
+DEAL:2d::Testing FE_DGQArbitraryNodes<2>(QGaussLobatto(7))
+DEAL:2d:cg::Starting value 0.0240
+DEAL:2d:cg::Convergence step 12 value 0
+DEAL:2d:cg::Condition number estimate: 185.
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(10)
+DEAL:2d:cg::Starting value 0.173
+DEAL:2d:cg::Convergence step 1305 value 0
+DEAL:2d:cg::Condition number estimate: 2.21e+06
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(QGaussLobatto(11))
+DEAL:2d:cg::Starting value 0.0148
+DEAL:2d:cg::Convergence step 132 value 0
+DEAL:2d:cg::Condition number estimate: 328.
+DEAL:2d::
+DEAL:2d::Testing FE_Q<2>(QGaussLobatto(17))
+DEAL:2d:cg::Starting value 0.00937
+DEAL:2d:cg::Convergence step 200 value 0
+DEAL:2d:cg::Condition number estimate: 759.
+DEAL:2d::
+DEAL:3d::Testing FE_Q<3>(1)
+DEAL:3d:cg::Starting value 0.102
+DEAL:3d:cg::Convergence step 12 value 0
+DEAL:3d:cg::Condition number estimate: 57.8
+DEAL:3d::
+DEAL:3d::Testing FE_Q<3>(2)
+DEAL:3d:cg::Starting value 0.0498
+DEAL:3d:cg::Convergence step 51 value 0
+DEAL:3d:cg::Condition number estimate: 161.
+DEAL:3d::
+DEAL:3d::Testing FE_Q<3>(5)
+DEAL:3d:cg::Starting value 0.0121
+DEAL:3d:cg::Convergence step 475 value 0
+DEAL:3d:cg::Condition number estimate: 8.96e+03
+DEAL:3d::
+DEAL:3d::Testing FE_Q<3>(QGaussLobatto(6))
+DEAL:3d:cg::Starting value 0.0137
+DEAL:3d:cg::Convergence step 167 value 0
+DEAL:3d:cg::Condition number estimate: 1.06e+03
+DEAL:3d::
template <int dim, int fe_degree>
void test ()
{
- if (dim == 3)
- return;
Triangulation<dim> tria;
- Tensor<2,dim> points;
+ Point<dim> points[dim];
points[0][0] = 0.25;
points[0][1] = 0.123;
points[1][0] = 0.09983712334;
points[1][1] = 0.314159265358979;
- GridGenerator::parallelogram (tria, points);
+ if (dim == 3)
+ {
+ //points[2][0] = 0.21;
+ //points[2][2] = 0.4123;
+ }
+ GridGenerator::parallelepiped (tria, points);
typename Triangulation<dim>::active_cell_iterator
cell = tria.begin_active (),
endc = tria.end();
if (cell->center().norm()<0.2)
cell->set_refine_flag();
tria.execute_coarsening_and_refinement();
- if (dim < 3 || fe_degree < 2)
+ if (dim < 3)
tria.refine_global(2);
tria.begin(tria.n_levels()-1)->set_refine_flag();
tria.last()->set_refine_flag();
tria.execute_coarsening_and_refinement();
- cell = tria.begin_active ();
- for (unsigned int i=0; i<5; ++i)
+ for (int i=0; i<7-2*fe_degree; ++i)
{
cell = tria.begin_active ();
unsigned int counter = 0;
cell->set_refine_flag();
tria.execute_coarsening_and_refinement();
}
+ std::cout << dim << " " << tria.n_active_cells() << std::endl;
FE_Q<dim> fe (fe_degree);
DoFHandler<dim> dof (tria);
DEAL:2d::Testing FE_Q<2>(2)
DEAL:2d::Norm of difference: 0
DEAL:2d::
+DEAL:3d::Testing FE_Q<3>(1)
+DEAL:3d::Norm of difference: 0
+DEAL:3d::
+DEAL:3d::Testing FE_Q<3>(2)
+DEAL:3d::Norm of difference: 0
+DEAL:3d::
for(unsigned int cell=cell_range.first;cell<cell_range.second;++cell)
{
fe_eval.reinit (cell);
-
- // compare values with the ones the FEValues
- // gives us. Those are seen as reference
fe_eval.read_dof_values (src);
fe_eval.template evaluate (true, true, false);
for (unsigned int q=0; q<n_q_points; ++q)