From: Martin Kronbichler Date: Thu, 7 Sep 2023 18:53:25 +0000 (+0200) Subject: Matrix-free for Raviart-Thomas: Test correct interpolation (non-affine) X-Git-Tag: relicensing~518^2~1 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=400f15bea7ea3ba5402faf50c7434ff4dd22d8ce;p=dealii.git Matrix-free for Raviart-Thomas: Test correct interpolation (non-affine) --- diff --git a/tests/matrix_free/interpolate_rt_deformed.cc b/tests/matrix_free/interpolate_rt_deformed.cc new file mode 100644 index 0000000000..8b0374c8da --- /dev/null +++ b/tests/matrix_free/interpolate_rt_deformed.cc @@ -0,0 +1,529 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +// --------------------------------------------------------------------- + + + +// this function tests the correctness of the implementation of matrix-free +// operations in getting the function values, the function gradients, and the +// function Laplacians on a cartesian mesh (hyper cube) with deformed +// elements. This tests whether non-affine geometries with more complicated +// terms for the Jacobian are treated correctly. The test case is without any +// constraints + +#include +#include +#include + +#include +#include + +#include +#include + +#include +#include +#include + +#include +#include + +#include +#include + +#include + +#include +#include + +#include "../tests.h" + + +template +class CompareFunction : public Function +{ +public: + CompareFunction() + : Function(dim) + {} + + virtual double + value(const Point &p, const unsigned int component) const + { + double value = (1.2 - 0.5 * component) * p[0] * p[0] + 0.4 + component; + for (unsigned int d = 1; d < dim; ++d) + value -= (2.7 - 0.6 * component) * d * p[d] * p[d]; + return value; + } + + virtual Tensor<1, dim> + gradient(const Point &p, const unsigned int component) const + { + Tensor<1, dim> grad; + grad[0] = (1.2 - 0.5 * component) * p[0] * 2; + for (unsigned int d = 1; d < dim; ++d) + grad[d] = -(2.7 - 0.6 * component) * d * p[d] * 2; + return grad; + } +}; + + + +template +class MatrixFreeTest +{ +public: + MatrixFreeTest(const MatrixFree &data_in) + : data(data_in){}; + + MatrixFreeTest(const MatrixFree &data_in, + const Mapping &mapping) + : data(data_in){}; + + virtual ~MatrixFreeTest() + {} + + // make function virtual to allow derived classes to define a different + // function + virtual void + cell(const MatrixFree &data, + Vector &, + const Vector &src, + const std::pair &cell_range) const + { + FEEvaluation fe_eval(data); + + CompareFunction function; + + for (unsigned int cell = cell_range.first; cell < cell_range.second; ++cell) + { + fe_eval.reinit(cell); + fe_eval.read_dof_values(src); + fe_eval.evaluate(EvaluationFlags::values | EvaluationFlags::gradients); + + for (unsigned int j = 0; j < data.n_active_entries_per_cell_batch(cell); + ++j) + for (unsigned int q = 0; q < fe_eval.n_q_points; ++q) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = fe_eval.quadrature_point(q)[d][j]; + for (unsigned int d = 0; d < dim; ++d) + { + cell_errors[0][d] += std::abs(fe_eval.get_value(q)[d][j] - + function.value(p, d)) * + fe_eval.JxW(q)[j]; + for (unsigned int e = 0; e < dim; ++e) + cell_errors[1][d] += + std::abs(fe_eval.get_gradient(q)[d][e][j] - + function.gradient(p, d)[e]) * + fe_eval.JxW(q)[j]; + } + double divergence = 0; + for (unsigned int d = 0; d < dim; ++d) + divergence += function.gradient(p, d)[d]; + cell_errors[2][0] += + std::abs(fe_eval.get_divergence(q)[j] - divergence) * + fe_eval.JxW(q)[j]; + } + } + } + + virtual void + face(const MatrixFree &data, + Vector &, + const Vector &src, + const std::pair &face_range) const + { + FEFaceEvaluation fe_evalm(data, + true); + FEFaceEvaluation fe_evalp( + data, false); + + CompareFunction function; + + for (unsigned int face = face_range.first; face < face_range.second; ++face) + { + fe_evalm.reinit(face); + fe_evalm.read_dof_values(src); + fe_evalm.evaluate(EvaluationFlags::values | EvaluationFlags::gradients | + EvaluationFlags::hessians); + fe_evalp.reinit(face); + fe_evalp.read_dof_values(src); + fe_evalp.evaluate(EvaluationFlags::values | EvaluationFlags::gradients | + EvaluationFlags::hessians); + + for (unsigned int j = 0; j < VectorizedArray::size(); ++j) + { + // skip empty components in VectorizedArray + if (data.get_face_info(face).cells_interior[j] == + numbers::invalid_unsigned_int) + break; + for (unsigned int q = 0; q < fe_evalm.n_q_points; ++q) + { + Point p; + + // interior face + for (unsigned int d = 0; d < dim; ++d) + p[d] = fe_evalm.quadrature_point(q)[d][j]; + for (unsigned int d = 0; d < dim; ++d) + { + facem_errors[0][d] += std::abs(fe_evalm.get_value(q)[d][j] - + function.value(p, d)) * + fe_evalm.JxW(q)[j]; + for (unsigned int e = 0; e < dim; ++e) + { + facem_errors[1][d] += + std::abs(fe_evalm.get_gradient(q)[d][e][j] - + function.gradient(p, d)[e]) * + fe_evalm.JxW(q)[j]; + } + } + double divergence = 0; + for (unsigned int d = 0; d < dim; ++d) + divergence += function.gradient(p, d)[d]; + facem_errors[2][0] += + std::abs(fe_evalm.get_divergence(q)[j] - divergence) * + fe_evalm.JxW(q)[j]; + + // exterior face + for (unsigned int d = 0; d < dim; ++d) + { + facep_errors[0][d] += std::abs(fe_evalp.get_value(q)[d][j] - + function.value(p, d)) * + fe_evalm.JxW(q)[j]; + for (unsigned int e = 0; e < dim; ++e) + facep_errors[1][d] += + std::abs(fe_evalp.get_gradient(q)[d][e][j] - + function.gradient(p, d)[e]) * + fe_evalm.JxW(q)[j]; + } + facep_errors[2][0] += + std::abs(fe_evalp.get_divergence(q)[j] - divergence) * + fe_evalm.JxW(q)[j]; + } + } + } + } + + virtual void + boundary(const MatrixFree &data, + Vector &, + const Vector &src, + const std::pair &face_range) const + { + FEFaceEvaluation fe_evalm(data, + true); + + CompareFunction function; + + for (unsigned int face = face_range.first; face < face_range.second; ++face) + { + fe_evalm.reinit(face); + fe_evalm.read_dof_values(src); + fe_evalm.evaluate(EvaluationFlags::values | EvaluationFlags::gradients | + EvaluationFlags::hessians); + + for (unsigned int j = 0; j < VectorizedArray::size(); ++j) + { + // skip empty components in VectorizedArray + if (data.get_face_info(face).cells_interior[j] == + numbers::invalid_unsigned_int) + break; + for (unsigned int q = 0; q < fe_evalm.n_q_points; ++q) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = fe_evalm.quadrature_point(q)[d][j]; + for (unsigned int d = 0; d < dim; ++d) + { + boundary_errors[0][d] += + std::abs(fe_evalm.get_value(q)[d][j] - + function.value(p, d)) * + fe_evalm.JxW(q)[j]; + for (unsigned int e = 0; e < dim; ++e) + boundary_errors[1][d] += + std::abs(fe_evalm.get_gradient(q)[d][e][j] - + function.gradient(p, d)[e]) * + fe_evalm.JxW(q)[j]; + } + double divergence = 0; + for (unsigned int d = 0; d < dim; ++d) + divergence += function.gradient(p, d)[d]; + boundary_errors[2][0] += + std::abs(fe_evalm.get_divergence(q)[j] - divergence) * + fe_evalm.JxW(q)[j]; + } + } + } + } + + + + static void + print_error(const std::string &text, + const dealii::ndarray &array) + { + deallog << "Error " << std::left << std::setw(6) << text << " values: "; + for (unsigned int d = 0; d < dim; ++d) + deallog << array[0][d] << " "; + deallog << std::endl; + deallog << "Error " << std::left << std::setw(6) << text << " gradients: "; + for (unsigned int d = 0; d < dim; ++d) + deallog << array[1][d] << " "; + deallog << std::endl; + deallog << "Error " << std::left << std::setw(6) << text << " divergence: "; + deallog << array[2][0] << " "; + deallog << std::endl; + } + + void + test_functions(const Vector &src) const + { + for (unsigned int d = 0; d < dim; ++d) + for (unsigned int i = 0; i < 3; ++i) + { + cell_errors[i][d] = 0; + facem_errors[i][d] = 0; + facep_errors[i][d] = 0; + boundary_errors[i][d] = 0; + } + + Vector dst_dummy; + data.loop(&MatrixFreeTest::cell, + &MatrixFreeTest::face, + &MatrixFreeTest::boundary, + this, + dst_dummy, + src); + + print_error("cell", cell_errors); + print_error("face-", facem_errors); + print_error("face+", facep_errors); + print_error("face b", boundary_errors); + deallog << std::endl; + }; + +protected: + const MatrixFree &data; + mutable dealii::ndarray cell_errors, facem_errors, + facep_errors, boundary_errors; +}; + + + +template +void +do_test(const DoFHandler &dof, + const AffineConstraints &constraints) +{ + deallog << "Testing " << dof.get_fe().get_name() << std::endl; + // use this for info on problem + // std::cout << "Number of cells: " << + // dof.get_triangulation().n_active_cells() + // << std::endl; + // std::cout << "Number of degrees of freedom: " << dof.n_dofs() << std::endl; + // std::cout << "Number of constraints: " << constraints.n_constraints() << + // std::endl; + + MappingQ mapping(dof.get_fe().degree); + Vector interpolated(dof.n_dofs()); + VectorTools::interpolate(mapping, dof, CompareFunction(), interpolated); + + constraints.distribute(interpolated); + MatrixFree mf_data; + { + const QGauss<1> quad(dof.get_fe().degree + 1); + typename MatrixFree::AdditionalData data; + data.tasks_parallel_scheme = MatrixFree::AdditionalData::none; + data.mapping_update_flags = update_gradients | update_quadrature_points; + data.mapping_update_flags_boundary_faces = + update_gradients | update_quadrature_points; + data.mapping_update_flags_inner_faces = + update_gradients | update_quadrature_points; + mf_data.reinit(mapping, dof, constraints, quad, data); + } + + MatrixFreeTest mf(mf_data); + mf.test_functions(interpolated); +} + + + +template +class DeformedCubeManifold : public dealii::ChartManifold +{ +public: + DeformedCubeManifold(const double left, + const double right, + const double deformation, + const unsigned int frequency = 1) + : left(left) + , right(right) + , deformation(deformation) + , frequency(frequency) + {} + + dealii::Point + push_forward(const dealii::Point &chart_point) const override + { + double sinval = deformation; + for (unsigned int d = 0; d < dim; ++d) + sinval *= std::sin(frequency * dealii::numbers::PI * + (chart_point(d) - left) / (right - left)); + dealii::Point space_point; + for (unsigned int d = 0; d < dim; ++d) + space_point(d) = chart_point(d) + sinval; + return space_point; + } + + dealii::Point + pull_back(const dealii::Point &space_point) const override + { + dealii::Point x = space_point; + dealii::Point one; + for (unsigned int d = 0; d < dim; ++d) + one(d) = 1.; + + // Newton iteration to solve the nonlinear equation given by the point + dealii::Tensor<1, dim> sinvals; + for (unsigned int d = 0; d < dim; ++d) + sinvals[d] = std::sin(frequency * dealii::numbers::PI * (x(d) - left) / + (right - left)); + + double sinval = deformation; + for (unsigned int d = 0; d < dim; ++d) + sinval *= sinvals[d]; + dealii::Tensor<1, dim> residual = space_point - x - sinval * one; + unsigned int its = 0; + while (residual.norm() > 1e-12 && its < 100) + { + dealii::Tensor<2, dim> jacobian; + for (unsigned int d = 0; d < dim; ++d) + jacobian[d][d] = 1.; + for (unsigned int d = 0; d < dim; ++d) + { + double sinval_der = deformation * frequency / (right - left) * + dealii::numbers::PI * + std::cos(frequency * dealii::numbers::PI * + (x(d) - left) / (right - left)); + for (unsigned int e = 0; e < dim; ++e) + if (e != d) + sinval_der *= sinvals[e]; + for (unsigned int e = 0; e < dim; ++e) + jacobian[e][d] += sinval_der; + } + + x += invert(jacobian) * residual; + + for (unsigned int d = 0; d < dim; ++d) + sinvals[d] = std::sin(frequency * dealii::numbers::PI * + (x(d) - left) / (right - left)); + + sinval = deformation; + for (unsigned int d = 0; d < dim; ++d) + sinval *= sinvals[d]; + residual = space_point - x - sinval * one; + ++its; + } + AssertThrow(residual.norm() < 1e-12, + dealii::ExcMessage("Newton for point did not converge.")); + return x; + } + + std::unique_ptr> + clone() const override + { + return std::make_unique>(left, + right, + deformation, + frequency); + } + +private: + const double left; + const double right; + const double deformation; + const unsigned int frequency; +}; + + + +template +void +test() +{ + Triangulation tria; + Point left; + Point right; + right[0] = 2.; + right[1] = 1.; + if (dim > 2) + right[2] = 1.; + GridGenerator::hyper_rectangle(tria, left, right); + DeformedCubeManifold manifold(0, 1.0, 0.05, 1.); + tria.set_all_manifold_ids(1); + tria.set_manifold(1, manifold); + tria.refine_global(1); + + { + FE_RaviartThomasNodal fe(fe_degree - 1); + DoFHandler dof(tria); + dof.distribute_dofs(fe); + + AffineConstraints constraints; + constraints.close(); + deallog.push("L1"); + if (fe_degree > 2) + do_test(dof, constraints); + else + do_test(dof, constraints); + deallog.pop(); + + tria.refine_global(1); + dof.distribute_dofs(fe); + deallog.push("L2"); + if (fe_degree > 2) + do_test(dof, constraints); + else + do_test(dof, constraints); + deallog.pop(); + } +} + + + +int +main() +{ + initlog(); + + deallog << std::setprecision(5); + { + deallog.push("2d"); + test<2, 1>(); + test<2, 2>(); + test<2, 3>(); + test<2, 4>(); + deallog.pop(); + deallog.push("3d"); + test<3, 1>(); + test<3, 2>(); + test<3, 3>(); + deallog.pop(); + } +} diff --git a/tests/matrix_free/interpolate_rt_deformed.output b/tests/matrix_free/interpolate_rt_deformed.output new file mode 100644 index 0000000000..6f4753540f --- /dev/null +++ b/tests/matrix_free/interpolate_rt_deformed.output @@ -0,0 +1,197 @@ + +DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(0) +DEAL:2d:L1::Error cell values: 0.84082 0.80829 +DEAL:2d:L1::Error cell gradients: 6.7856 4.0124 +DEAL:2d:L1::Error cell divergence: 1.3856 +DEAL:2d:L1::Error face- values: 1.6772 1.5958 +DEAL:2d:L1::Error face- gradients: 10.686 6.9062 +DEAL:2d:L1::Error face- divergence: 3.3000 +DEAL:2d:L1::Error face+ values: 1.8022 1.4208 +DEAL:2d:L1::Error face+ gradients: 10.686 6.9062 +DEAL:2d:L1::Error face+ divergence: 3.3000 +DEAL:2d:L1::Error face b values: 3.6044 3.0166 +DEAL:2d:L1::Error face b gradients: 21.371 13.812 +DEAL:2d:L1::Error face b divergence: 6.6000 +DEAL:2d:L1:: +DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(0) +DEAL:2d:L2::Error cell values: 0.39688 0.40699 +DEAL:2d:L2::Error cell gradients: 6.1965 3.5312 +DEAL:2d:L2::Error cell divergence: 0.72001 +DEAL:2d:L2::Error face- values: 2.5592 2.4054 +DEAL:2d:L2::Error face- gradients: 29.152 17.800 +DEAL:2d:L2::Error face- divergence: 4.9440 +DEAL:2d:L2::Error face+ values: 2.6998 2.2721 +DEAL:2d:L2::Error face+ gradients: 28.810 17.584 +DEAL:2d:L2::Error face+ divergence: 4.9697 +DEAL:2d:L2::Error face b values: 1.7815 1.4453 +DEAL:2d:L2::Error face b gradients: 19.336 11.084 +DEAL:2d:L2::Error face b divergence: 3.4879 +DEAL:2d:L2:: +DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(1) +DEAL:2d:L1::Error cell values: 0.21645 0.22161 +DEAL:2d:L1::Error cell gradients: 1.4387 1.0370 +DEAL:2d:L1::Error cell divergence: 0.42416 +DEAL:2d:L1::Error face- values: 0.13278 0.23717 +DEAL:2d:L1::Error face- gradients: 3.8120 1.3753 +DEAL:2d:L1::Error face- divergence: 0.47783 +DEAL:2d:L1::Error face+ values: 0.13874 0.23808 +DEAL:2d:L1::Error face+ gradients: 3.8007 2.4672 +DEAL:2d:L1::Error face+ divergence: 0.70132 +DEAL:2d:L1::Error face b values: 0.34714 0.49328 +DEAL:2d:L1::Error face b gradients: 7.5692 3.9064 +DEAL:2d:L1::Error face b divergence: 2.1365 +DEAL:2d:L1:: +DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(1) +DEAL:2d:L2::Error cell values: 0.054207 0.054789 +DEAL:2d:L2::Error cell gradients: 0.63920 0.39444 +DEAL:2d:L2::Error cell divergence: 0.090741 +DEAL:2d:L2::Error face- values: 0.095632 0.16809 +DEAL:2d:L2::Error face- gradients: 5.2642 2.1852 +DEAL:2d:L2::Error face- divergence: 0.39297 +DEAL:2d:L2::Error face+ values: 0.095714 0.16806 +DEAL:2d:L2::Error face+ gradients: 5.1413 2.6374 +DEAL:2d:L2::Error face+ divergence: 0.39710 +DEAL:2d:L2::Error face b values: 0.072933 0.12250 +DEAL:2d:L2::Error face b gradients: 3.5245 1.5231 +DEAL:2d:L2::Error face b divergence: 0.46954 +DEAL:2d:L2:: +DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(2) +DEAL:2d:L1::Error cell values: 0.0047119 0.0023984 +DEAL:2d:L1::Error cell gradients: 0.085717 0.029296 +DEAL:2d:L1::Error cell divergence: 0.037673 +DEAL:2d:L1::Error face- values: 0.00065558 0.0035632 +DEAL:2d:L1::Error face- gradients: 0.16207 0.086326 +DEAL:2d:L1::Error face- divergence: 0.072374 +DEAL:2d:L1::Error face+ values: 0.00068398 0.0035694 +DEAL:2d:L1::Error face+ gradients: 0.27606 0.11372 +DEAL:2d:L1::Error face+ divergence: 0.070448 +DEAL:2d:L1::Error face b values: 0.0075049 0.00027532 +DEAL:2d:L1::Error face b gradients: 0.33903 0.075394 +DEAL:2d:L1::Error face b divergence: 0.19221 +DEAL:2d:L1:: +DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(2) +DEAL:2d:L2::Error cell values: 0.00078526 0.0035443 +DEAL:2d:L2::Error cell gradients: 0.025118 0.056502 +DEAL:2d:L2::Error cell divergence: 0.010753 +DEAL:2d:L2::Error face- values: 0.0022416 0.013546 +DEAL:2d:L2::Error face- gradients: 0.21582 0.39209 +DEAL:2d:L2::Error face- divergence: 0.063865 +DEAL:2d:L2::Error face+ values: 0.0022387 0.013547 +DEAL:2d:L2::Error face+ gradients: 0.21748 0.36902 +DEAL:2d:L2::Error face+ divergence: 0.064165 +DEAL:2d:L2::Error face b values: 0.00085314 1.8183e-05 +DEAL:2d:L2::Error face b gradients: 0.089290 0.12059 +DEAL:2d:L2::Error face b divergence: 0.052536 +DEAL:2d:L2:: +DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(3) +DEAL:2d:L1::Error cell values: 0.0017407 0.0076702 +DEAL:2d:L1::Error cell gradients: 0.039706 0.095855 +DEAL:2d:L1::Error cell divergence: 0.022800 +DEAL:2d:L1::Error face- values: 0.0010959 0.012127 +DEAL:2d:L1::Error face- gradients: 0.11291 0.26940 +DEAL:2d:L1::Error face- divergence: 0.055434 +DEAL:2d:L1::Error face+ values: 0.0010897 0.012127 +DEAL:2d:L1::Error face+ gradients: 0.081715 0.25146 +DEAL:2d:L1::Error face+ divergence: 0.048271 +DEAL:2d:L1::Error face b values: 0.0028746 3.3089e-05 +DEAL:2d:L1::Error face b gradients: 0.23518 0.25632 +DEAL:2d:L1::Error face b divergence: 0.12323 +DEAL:2d:L1:: +DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(3) +DEAL:2d:L2::Error cell values: 7.0146e-05 0.00037059 +DEAL:2d:L2::Error cell gradients: 0.0032332 0.0080000 +DEAL:2d:L2::Error cell divergence: 0.0012671 +DEAL:2d:L2::Error face- values: 0.00021264 0.0014135 +DEAL:2d:L2::Error face- gradients: 0.028685 0.071013 +DEAL:2d:L2::Error face- divergence: 0.010209 +DEAL:2d:L2::Error face+ values: 0.00021264 0.0014135 +DEAL:2d:L2::Error face+ gradients: 0.026697 0.056646 +DEAL:2d:L2::Error face+ divergence: 0.0080636 +DEAL:2d:L2::Error face b values: 8.3179e-05 1.0251e-06 +DEAL:2d:L2::Error face b gradients: 0.023934 0.022109 +DEAL:2d:L2::Error face b divergence: 0.0077525 +DEAL:2d:L2:: +DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(0) +DEAL:3d:L1::Error cell values: 1.7432 1.3640 0.49183 +DEAL:3d:L1::Error cell gradients: 17.586 12.412 5.5321 +DEAL:3d:L1::Error cell divergence: 2.1651 +DEAL:3d:L1::Error face- values: 5.3910 5.1728 1.9268 +DEAL:3d:L1::Error face- gradients: 44.471 31.919 15.098 +DEAL:3d:L1::Error face- divergence: 6.9450 +DEAL:3d:L1::Error face+ values: 5.3535 3.3645 1.0625 +DEAL:3d:L1::Error face+ gradients: 44.471 31.919 15.098 +DEAL:3d:L1::Error face+ divergence: 6.9450 +DEAL:3d:L1::Error face b values: 12.220 8.9571 3.0912 +DEAL:3d:L1::Error face b gradients: 88.943 63.837 30.196 +DEAL:3d:L1::Error face b divergence: 13.890 +DEAL:3d:L1:: +DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(0) +DEAL:3d:L2::Error cell values: 0.84880 0.69655 0.24846 +DEAL:3d:L2::Error cell gradients: 17.166 11.906 4.9397 +DEAL:3d:L2::Error cell divergence: 1.0855 +DEAL:3d:L2::Error face- values: 8.1676 7.2237 2.7157 +DEAL:3d:L2::Error face- gradients: 131.44 91.011 39.859 +DEAL:3d:L2::Error face- divergence: 10.563 +DEAL:3d:L2::Error face+ values: 8.1842 6.1136 2.1595 +DEAL:3d:L2::Error face+ gradients: 129.73 91.230 39.150 +DEAL:3d:L2::Error face+ divergence: 10.562 +DEAL:3d:L2::Error face b values: 6.0673 4.6128 1.5397 +DEAL:3d:L2::Error face b gradients: 86.159 60.569 25.724 +DEAL:3d:L2::Error face b divergence: 7.1112 +DEAL:3d:L2:: +DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(1) +DEAL:3d:L1::Error cell values: 0.66818 0.27115 0.26053 +DEAL:3d:L1::Error cell gradients: 4.1680 3.5791 2.5768 +DEAL:3d:L1::Error cell divergence: 0.94875 +DEAL:3d:L1::Error face- values: 1.0170 0.81232 0.76712 +DEAL:3d:L1::Error face- gradients: 15.419 11.678 7.9102 +DEAL:3d:L1::Error face- divergence: 2.6275 +DEAL:3d:L1::Error face+ values: 0.99721 0.82913 0.73940 +DEAL:3d:L1::Error face+ gradients: 14.487 11.520 7.6165 +DEAL:3d:L1::Error face+ divergence: 2.7748 +DEAL:3d:L1::Error face b values: 2.0660 1.3680 0.71188 +DEAL:3d:L1::Error face b gradients: 29.285 22.080 13.242 +DEAL:3d:L1::Error face b divergence: 4.8361 +DEAL:3d:L1:: +DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(1) +DEAL:3d:L2::Error cell values: 0.16658 0.067645 0.063432 +DEAL:3d:L2::Error cell gradients: 1.9130 1.5030 0.92443 +DEAL:3d:L2::Error cell divergence: 0.24685 +DEAL:3d:L2::Error face- values: 0.75475 0.54934 0.44999 +DEAL:3d:L2::Error face- gradients: 21.501 15.407 8.7615 +DEAL:3d:L2::Error face- divergence: 1.7590 +DEAL:3d:L2::Error face+ values: 0.75342 0.55080 0.44932 +DEAL:3d:L2::Error face+ gradients: 20.810 14.938 8.6456 +DEAL:3d:L2::Error face+ divergence: 1.7340 +DEAL:3d:L2::Error face b values: 0.51279 0.32049 0.17243 +DEAL:3d:L2::Error face b gradients: 13.912 9.8701 5.0657 +DEAL:3d:L2::Error face b divergence: 1.1911 +DEAL:3d:L2:: +DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(2) +DEAL:3d:L1::Error cell values: 0.011206 0.017434 0.020916 +DEAL:3d:L1::Error cell gradients: 0.25129 0.25923 0.28027 +DEAL:3d:L1::Error cell divergence: 0.052910 +DEAL:3d:L1::Error face- values: 0.023217 0.033124 0.052602 +DEAL:3d:L1::Error face- gradients: 0.65036 0.67093 0.89354 +DEAL:3d:L1::Error face- divergence: 0.18134 +DEAL:3d:L1::Error face+ values: 0.023066 0.032185 0.051233 +DEAL:3d:L1::Error face+ gradients: 1.1868 0.83573 0.93673 +DEAL:3d:L1::Error face+ divergence: 0.21746 +DEAL:3d:L1::Error face b values: 0.023435 0.057775 0.060372 +DEAL:3d:L1::Error face b gradients: 1.2755 1.2702 1.2949 +DEAL:3d:L1::Error face b divergence: 0.33420 +DEAL:3d:L1:: +DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(2) +DEAL:3d:L2::Error cell values: 0.0016697 0.0055041 0.0073614 +DEAL:3d:L2::Error cell gradients: 0.066790 0.11750 0.14010 +DEAL:3d:L2::Error cell divergence: 0.023259 +DEAL:3d:L2::Error face- values: 0.011054 0.039495 0.052916 +DEAL:3d:L2::Error face- gradients: 0.77293 1.1694 1.3631 +DEAL:3d:L2::Error face- divergence: 0.18844 +DEAL:3d:L2::Error face+ values: 0.011043 0.039429 0.053023 +DEAL:3d:L2::Error face+ gradients: 0.77385 1.1778 1.3552 +DEAL:3d:L2::Error face+ divergence: 0.18832 +DEAL:3d:L2::Error face b values: 0.0030012 0.011224 0.010566 +DEAL:3d:L2::Error face b gradients: 0.37621 0.46520 0.49611 +DEAL:3d:L2::Error face b divergence: 0.11592 +DEAL:3d:L2::