From: Martin Kronbichler Date: Sat, 15 May 2021 08:19:31 +0000 (+0200) Subject: Let FEPointEvaluation use correct polynomial space X-Git-Tag: v9.3.0-rc1~69^2~1 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=e529bd972840556b94e55b4ad113b20be6de1e62;p=dealii.git Let FEPointEvaluation use correct polynomial space --- diff --git a/include/deal.II/fe/fe_point_evaluation.h b/include/deal.II/fe/fe_point_evaluation.h index 00dbb6ddda..4a1f52e345 100644 --- a/include/deal.II/fe/fe_point_evaluation.h +++ b/include/deal.II/fe/fe_point_evaluation.h @@ -347,7 +347,12 @@ namespace internal template bool - is_fast_path_supported(const FiniteElement &fe); + is_fast_path_supported(const FiniteElement &fe, + const unsigned int base_element_number); + + template + std::vector> + get_polynomial_space(const FiniteElement &fe); } // namespace FEPointEvaluation } // namespace internal @@ -564,33 +569,32 @@ FEPointEvaluation::FEPointEvaluation( dynamic_cast *>(&mapping)) , fe(&fe) { + bool same_base_element = true; + unsigned int base_element_number = 0; + unsigned int component = 0; + for (; base_element_number < fe.n_base_elements(); ++base_element_number) + if (component + fe.element_multiplicity(base_element_number) > + first_selected_component) + { + if (first_selected_component + n_components > + component + fe.element_multiplicity(base_element_number)) + same_base_element = false; + break; + } + else + component += fe.element_multiplicity(base_element_number); if (mapping_q_generic != nullptr && - internal::FEPointEvaluation::is_fast_path_supported(fe)) + internal::FEPointEvaluation::is_fast_path_supported( + fe, base_element_number) && + same_base_element) { internal::MatrixFreeFunctions::ShapeInfo shape_info; - unsigned int base_element_number = 0; - unsigned int component = 0; - for (; base_element_number < fe.n_base_elements(); ++base_element_number) - if (component + fe.element_multiplicity(base_element_number) > - first_selected_component) - { - Assert(first_selected_component + n_components <= - component + fe.element_multiplicity(base_element_number), - ExcMessage("You selected an evaluation which crosses " - "different base elements, a case not supported")); - break; - } - else - component += fe.element_multiplicity(base_element_number); shape_info.reinit(QMidpoint<1>(), fe, base_element_number); renumber = shape_info.lexicographic_numbering; dofs_per_component = shape_info.dofs_per_component_on_cell; - poly = - shape_info.data[0].fe_degree == 0 ? - Polynomials::LagrangeEquidistant::generate_complete_basis(0) : - Polynomials::generate_complete_Lagrange_basis( - QGaussLobatto<1>(shape_info.data[0].fe_degree + 1).get_points()); + poly = internal::FEPointEvaluation::get_polynomial_space( + fe.base_element(base_element_number)); } if (true /*TODO: as long as the fast path of integrate() is not working*/) { diff --git a/source/fe/fe_point_evaluation.cc b/source/fe/fe_point_evaluation.cc index b566432131..d08c6a0144 100644 --- a/source/fe/fe_point_evaluation.cc +++ b/source/fe/fe_point_evaluation.cc @@ -39,46 +39,32 @@ namespace internal */ template bool - is_fast_path_supported(const FiniteElement &fe) + is_fast_path_supported(const FiniteElement &fe, + const unsigned int base_element_number) { // check if supported const bool flag = [&]() { if (dim != spacedim) return false; - for (unsigned int base = 0; base < fe.n_base_elements(); ++base) + const FiniteElement *fe_ptr = + &(fe.base_element(base_element_number)); + if (fe_ptr->n_components() != 1) + return false; + + // then check if the base element is supported or not + if (dynamic_cast *>(fe_ptr) != nullptr) { - const FiniteElement *fe_ptr = - &(fe.base_element(base)); - if (fe_ptr->n_components() != 1) - return false; + const FE_Poly *fe_poly_ptr = + dynamic_cast *>(fe_ptr); - // then check if the base element is supported or not - if (dynamic_cast *>(fe_ptr) != nullptr) - { - const FE_Poly *fe_poly_ptr = - dynamic_cast *>(fe_ptr); - - if (dynamic_cast *>( - &fe_poly_ptr->get_poly_space()) == nullptr && - dynamic_cast> *>( - &fe_poly_ptr->get_poly_space()) == nullptr && - dynamic_cast *>(fe_ptr) == - nullptr && - dynamic_cast *>(fe_ptr) == - nullptr && - dynamic_cast *>( - fe_ptr) == nullptr) - return false; - } - else + if (dynamic_cast *>( + &fe_poly_ptr->get_poly_space()) == nullptr) return false; } + else + return false; - // if we arrived here, all base elements were supported so we can - // support the present element return true; }(); @@ -90,6 +76,27 @@ namespace internal return flag; } + + + template + std::vector> + get_polynomial_space(const FiniteElement &fe) + { + Assert(fe.n_components() == 1, ExcNotImplemented()); + const FE_Poly *fe_poly_ptr = + dynamic_cast *>(&fe); + + // we should catch the case that we cannot dynamic cast in + // is_fast_path_supported + Assert(fe_poly_ptr != nullptr, ExcNotImplemented()); + if (const auto polyspace = + dynamic_cast *>( + &fe_poly_ptr->get_poly_space())) + return polyspace->get_underlying_polynomials(); + else + Assert(false, ExcNotImplemented()); + return {}; + } } // namespace FEPointEvaluation } // namespace internal diff --git a/source/fe/fe_point_evaluation.inst.in b/source/fe/fe_point_evaluation.inst.in index 4f6f7d8095..74736be9ff 100644 --- a/source/fe/fe_point_evaluation.inst.in +++ b/source/fe/fe_point_evaluation.inst.in @@ -19,6 +19,10 @@ for (deal_II_dimension, deal_II_space_dimension : DIMENSIONS) { #if deal_II_dimension <= deal_II_space_dimension template bool internal::FEPointEvaluation::is_fast_path_supported( - const FiniteElement &fe); + const FiniteElement &, + const unsigned int); + template std::vector> + internal::FEPointEvaluation::get_polynomial_space( + const FiniteElement &); #endif } diff --git a/tests/fe/point_evaluation_10.cc b/tests/fe/point_evaluation_10.cc new file mode 100644 index 0000000000..66f1b51d1e --- /dev/null +++ b/tests/fe/point_evaluation_10.cc @@ -0,0 +1,144 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2021 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. +// +// --------------------------------------------------------------------- + + +// check FEPointEvaluation for scalar FE_DGQArbitraryNodes and MappingQGeneric +// by comparing to the output of FEValues with the same settings (apart from +// the finite element, this test is the same as point_evaluation_02) + +#include +#include + +#include + +#include +#include +#include +#include + +#include +#include + +#include + +#include + +#include + +#include "../tests.h" + + + +template +void +test(const unsigned int degree) +{ + using namespace dealii; + Triangulation tria; + + if (dim > 1) + GridGenerator::hyper_shell(tria, Point(), 0.5, 1, 6); + else + GridGenerator::subdivided_hyper_cube(tria, 2, 0, 1); + + MappingQGeneric mapping(degree); + deallog << "Mapping of degree " << degree << std::endl; + + std::vector> unit_points; + for (unsigned int i = 0; i < 13; ++i) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = static_cast(i) / 17. + 0.015625 * d; + unit_points.push_back(p); + } + + FE_DGQArbitraryNodes fe(QGauss<1>(degree + 1)); + FEValues fe_values(mapping, + fe, + Quadrature(unit_points), + update_values | update_gradients); + + DoFHandler dof_handler(tria); + dof_handler.distribute_dofs(fe); + Vector vector(dof_handler.n_dofs()); + + FEPointEvaluation<1, dim> evaluator(mapping, fe); + + Tensor<1, dim> exponents; + exponents[0] = 1.; + VectorTools::interpolate(mapping, + dof_handler, + Functions::Monomial(exponents), + vector); + + std::vector solution_values(fe.dofs_per_cell); + std::vector function_values(unit_points.size()); + std::vector> function_gradients(unit_points.size()); + + for (const auto &cell : dof_handler.active_cell_iterators()) + { + fe_values.reinit(cell); + fe_values.get_function_values(vector, function_values); + fe_values.get_function_gradients(vector, function_gradients); + + cell->get_dof_values(vector, + solution_values.begin(), + solution_values.end()); + + evaluator.evaluate(cell, + unit_points, + solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + deallog << "Cell with center " << cell->center(true) << std::endl; + for (unsigned int i = 0; i < function_values.size(); ++i) + deallog << mapping.transform_unit_to_real_cell(cell, unit_points[i]) + << ": " << evaluator.get_value(i) << " error value " + << function_values[i] - evaluator.get_value(i) << " error grad " + << (evaluator.get_gradient(i) - function_gradients[i]).norm() + << std::endl; + deallog << std::endl; + + for (unsigned int i = 0; i < unit_points.size(); ++i) + { + evaluator.submit_value(evaluator.get_value(i), i); + evaluator.submit_gradient(evaluator.get_gradient(i), i); + } + + evaluator.integrate(cell, + unit_points, + solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + for (const auto i : solution_values) + deallog << i << " "; + deallog << std::endl; + } +} + + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + test<1>(3); + test<2>(2); + test<2>(6); + test<3>(5); +} diff --git a/tests/fe/point_evaluation_10.output b/tests/fe/point_evaluation_10.output new file mode 100644 index 0000000000..b380fc2ef8 --- /dev/null +++ b/tests/fe/point_evaluation_10.output @@ -0,0 +1,325 @@ + +DEAL::Mapping of degree 3 +DEAL::Cell with center 0.2500000000 +DEAL::0.000000000: -6.093040680e-17 error value 0.000000000 error grad 6.661338148e-16 +DEAL::0.02941176471: 0.02941176471 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.05882352941: 0.05882352941 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.08823529412: 0.08823529412 error value 0.000000000 error grad 0.000000000 +DEAL::0.1176470588: 0.1176470588 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.1470588235: 0.1470588235 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.1764705882: 0.1764705882 error value 0.000000000 error grad 1.110223025e-16 +DEAL::0.2058823529: 0.2058823529 error value 0.000000000 error grad 0.000000000 +DEAL::0.2352941176: 0.2352941176 error value 0.000000000 error grad 3.330669074e-16 +DEAL::0.2647058824: 0.2647058824 error value 0.000000000 error grad 0.000000000 +DEAL::0.2941176471: 0.2941176471 error value 0.000000000 error grad 0.000000000 +DEAL::0.3235294118: 0.3235294118 error value 0.000000000 error grad 3.330669074e-16 +DEAL::0.3529411765: 0.3529411765 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-59.34844157 37.61796402 13.52982084 10.49477436 +DEAL::Cell with center 0.7500000000 +DEAL::0.5000000000: 0.5000000000 error value 0.000000000 error grad 1.998401444e-15 +DEAL::0.5294117647: 0.5294117647 error value 0.000000000 error grad 1.110223025e-15 +DEAL::0.5588235294: 0.5588235294 error value 0.000000000 error grad 4.440892099e-16 +DEAL::0.5882352941: 0.5882352941 error value 0.000000000 error grad 0.000000000 +DEAL::0.6176470588: 0.6176470588 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.6470588235: 0.6470588235 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.6764705882: 0.6764705882 error value 0.000000000 error grad 1.110223025e-16 +DEAL::0.7058823529: 0.7058823529 error value 0.000000000 error grad 5.551115123e-16 +DEAL::0.7352941176: 0.7352941176 error value 0.000000000 error grad 5.551115123e-16 +DEAL::0.7647058824: 0.7647058824 error value 0.000000000 error grad 5.551115123e-16 +DEAL::0.7941176471: 0.7941176471 error value 0.000000000 error grad 1.221245327e-15 +DEAL::0.8235294118: 0.8235294118 error value 0.000000000 error grad 3.330669074e-16 +DEAL::0.8529411765: 0.8529411765 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-57.51411065 40.34409093 15.59357137 10.37056600 +DEAL::Mapping of degree 2 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value 4.440892099e-16 error grad 2.913426368e-15 +DEAL::0.9591965610 0.06332871922: 0.9591965610 error value 0.000000000 error grad 1.693913639e-15 +DEAL::0.9234265460 0.1210574346: 0.9234265460 error value 0.000000000 error grad 1.042499610e-15 +DEAL::0.8851608469 0.1733497625: 0.8851608469 error value 0.000000000 error grad 1.443502979e-15 +DEAL::0.8446828558 0.2203693193: 0.8446828558 error value 0.000000000 error grad 4.508949900e-16 +DEAL::0.8022759646 0.2622797217: 0.8022759646 error value 0.000000000 error grad 6.728756067e-16 +DEAL::0.7582235654 0.2992445859: 0.7582235654 error value 0.000000000 error grad 4.912555618e-16 +DEAL::0.7128090500 0.3314275284: 0.7128090500 error value 0.000000000 error grad 6.826744321e-16 +DEAL::0.6663158106 0.3589921657: 0.6663158106 error value -1.110223025e-16 error grad 8.484410888e-16 +DEAL::0.6190272391 0.3821021142: 0.6190272391 error value 0.000000000 error grad 4.281290429e-16 +DEAL::0.5712267275 0.4009209903: 0.5712267275 error value 1.110223025e-16 error grad 8.165479411e-16 +DEAL::0.5231976677 0.4156124105: 0.5231976677 error value 0.000000000 error grad 2.230723768e-16 +DEAL::0.4752234518 0.4263399913: 0.4752234518 error value 0.000000000 error grad 6.713381600e-16 +DEAL:: +DEAL::49.95930350 7.875276791 1.272341777 -50.89586902 12.87881571 -4.974569633 13.86893008 -16.20089820 -4.050377216 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 error grad 1.365315562e-15 +DEAL::0.4247540009 0.8623529487: 0.4247540009 error value 5.551115123e-17 error grad 3.372258837e-16 +DEAL::0.3568744593 0.8602395646: 0.3568744593 error value 0.000000000 error grad 8.803538355e-16 +DEAL::0.2924551254 0.8532466611: 0.2924551254 error value 5.551115123e-17 error grad 4.725269614e-16 +DEAL::0.2314959991 0.8417014709: 0.2314959991 error value 0.000000000 error grad 7.377576974e-16 +DEAL::0.1739970804 0.8259312270: 0.1739970804 error value 0.000000000 error grad 2.798987023e-16 +DEAL::0.1199583694 0.8062631623: 0.1199583694 error value 0.000000000 error grad 1.578835979e-16 +DEAL::0.06937986592 0.7830245096: 0.06937986592 error value 0.000000000 error grad 3.362019981e-16 +DEAL::0.02226157007 0.7565425018: 0.02226157007 error value 3.469446952e-18 error grad 2.257575777e-17 +DEAL::-0.02139651817 0.7271443718: -0.02139651817 error value 0.000000000 error grad 2.221540174e-16 +DEAL::-0.06159439879 0.6951573525: -0.06159439879 error value 6.938893904e-18 error grad 7.762786727e-17 +DEAL::-0.09833207180 0.6609086767: -0.09833207180 error value 1.387778781e-17 error grad 2.220457056e-16 +DEAL::-0.1316095372 0.6247255774: -0.1316095372 error value 0.000000000 error grad 1.723435093e-17 +DEAL:: +DEAL::37.23360727 -26.21481232 7.462171364 -9.849961140 1.301816107 -14.73579405 4.912649317 3.694312864 -1.929651715 +DEAL::Cell with center -0.6495190528 0.3750000000 +DEAL::-0.4960937500 0.8592595803: -0.4960937500 error value 5.551115123e-17 error grad 1.012070732e-15 +DEAL::-0.5344425601 0.7990242294: -0.5344425601 error value 1.110223025e-16 error grad 4.561505407e-16 +DEAL::-0.5665520866 0.7391821301: -0.5665520866 error value 0.000000000 error grad 1.492800626e-15 +DEAL::-0.5927057215 0.6798968986: -0.5927057215 error value 0.000000000 error grad 1.539112613e-15 +DEAL::-0.6131868567 0.6213321516: -0.6131868567 error value 0.000000000 error grad 6.668626282e-16 +DEAL::-0.6282788842 0.5636515054: -0.6282788842 error value 1.110223025e-16 error grad 1.494819595e-15 +DEAL::-0.6382651960 0.5070185764: -0.6382651960 error value 0.000000000 error grad 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2.680268175e-16 +DEAL::0.6215297395 -0.2452962662: 0.6215297395 error value 1.110223025e-16 error grad 6.682069744e-16 +DEAL::0.6068329890 -0.1983855861: 0.6068329890 error value 0.000000000 error grad 6.149719154e-16 +DEAL:: +DEAL::12.72569623 34.09008911 -6.189829588 -41.04590788 11.57699961 9.761224419 8.956280767 -19.89521107 -2.120725501 +DEAL::Mapping of degree 6 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value -3.330669074e-16 error grad 1.085313874e-14 +DEAL::0.9609496573 0.05926936446: 0.9609496573 error value 3.330669074e-16 error grad 5.214208909e-15 +DEAL::0.9262895583 0.1146994816: 0.9262895583 error value -3.330669074e-16 error grad 6.018770151e-15 +DEAL::0.8885607198 0.1661007475: 0.8885607198 error value -3.330669074e-16 error grad 4.444552342e-16 +DEAL::0.8481266485 0.2133123969: 0.8481266485 error value 2.220446049e-16 error grad 3.124223562e-15 +DEAL::0.8053586039 0.2562030323: 0.8053586039 error value 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4.934025341 -5.173902859 1.514169514 -50.29728691 46.04113497 -48.47989694 22.83875690 5.739048368 3.171085801 -0.9720098819 30.65005702 -26.00773257 20.96846977 -20.45689044 -10.67921740 -5.088918117 1.242950483 -15.55004246 13.17172560 -10.41321874 8.658250384 -10.56187268 1.393220894 -0.4238848435 4.429844545 -3.728001461 2.896824509 -2.292881826 2.305499399 -0.4357066911 0.1283768001 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 error grad 2.206831658e-14 +DEAL::0.4291460533 0.8618414972: 0.4291460533 error value 1.110223025e-16 error grad 2.664683162e-15 +DEAL::0.3638121143 0.8595400296: 0.3638121143 error value -5.551115123e-17 error grad 2.238801232e-15 +DEAL::0.3004328929 0.8525665299: 0.3004328929 error value 1.665334537e-16 error grad 9.061888438e-16 +DEAL::0.2393293696 0.8411554217: 0.2393293696 error value -8.326672685e-17 error grad 8.552396937e-16 +DEAL::0.1808009674 0.8255625263: 0.1808009674 error value 0.000000000 error grad 8.097292851e-16 +DEAL::0.1251241296 0.8060632879: 0.1251241296 error value 5.551115123e-17 error grad 6.078040286e-16 +DEAL::0.07255105048 0.7829509083: 0.07255105048 error value -2.775557562e-17 error grad 1.117789079e-16 +DEAL::0.02330856204 0.7565344028: 0.02330856204 error value -6.938893904e-18 error grad 5.574554325e-16 +DEAL::-0.02240282557 0.7271365875: -0.02240282557 error value 3.469446952e-18 error grad 2.384590271e-16 +DEAL::-0.06440972863 0.6950920104: -0.06440972863 error value 0.000000000 error grad 5.153448220e-16 +DEAL::-0.1025665400 0.6607448360: -0.1025665400 error value 0.000000000 error grad 3.133847518e-16 +DEAL::-0.1367559248 0.6244466961: -0.1367559248 error value -5.551115123e-17 error grad 5.142162331e-16 +DEAL:: +DEAL::69.04739437 -65.23598656 48.80352694 -34.20263244 21.58608264 -10.79058761 3.077496174 -54.73792163 46.56562918 -39.25807479 27.61658687 -17.62988473 8.177897793 -2.305442179 37.34736956 -25.50788140 19.23781204 -29.22194640 17.57143748 -6.938652592 1.898258160 -25.07593192 17.49723721 1.724016363 4.005966727 -26.60387591 7.538380738 -1.914691647 15.45175480 -10.66847286 1.431765314 19.70895138 -8.862232108 -8.016285580 1.805251956 -8.183501538 6.743446843 -4.054409741 0.5093588710 2.786960573 0.3523522065 -0.1616392969 2.332027327 -1.916154128 1.160420854 -0.2588002095 -0.4345702275 -0.1484697162 0.05512671170 +DEAL::Cell with center -0.6495190528 0.3750000000 +DEAL::-0.4960937500 0.8592595803: -0.4960937500 error value 3.330669074e-16 error grad 7.884023496e-15 +DEAL::-0.5318036039 0.8025721327: -0.5318036039 error value 1.110223025e-16 error grad 3.811668959e-15 +DEAL::-0.5624774440 0.7448405480: -0.5624774440 error value -1.110223025e-16 error grad 9.461079410e-16 +DEAL::-0.5881278268 0.6864657824: -0.5881278268 error value 1.110223025e-16 error grad 1.486339207e-15 +DEAL::-0.6087972789 0.6278430248: -0.6087972789 error value 0.000000000 error grad 1.981513634e-15 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0.03349784057 0.03530064659 -38.60307148 56.52132397 -25.72375026 -25.04426447 12.63741214 -1.764749732 0.3840886464 25.22135499 -28.54389776 50.20391330 -18.83279018 -32.34292428 4.367294937 -0.9426817653 -15.19830222 15.33925971 -19.53670446 40.16584182 1.816985290 -2.927367463 0.5623014733 7.366540923 -6.428278754 6.358809000 -8.148891513 13.34883325 -1.040868688 0.2622455466 -2.097817218 1.811847334 -1.736403655 2.034081616 -2.740069627 0.2872369750 -0.07325008836 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: -0.9921875000 error value 1.110223025e-16 error grad 1.178069314e-14 +DEAL::-0.9609496573 -0.05926936446: -0.9609496573 error value -2.220446049e-16 error grad 6.661360770e-16 +DEAL::-0.9262895583 -0.1146994816: -0.9262895583 error value 1.110223025e-16 error grad 5.162696111e-15 +DEAL::-0.8885607198 -0.1661007475: -0.8885607198 error value -1.110223025e-16 error grad 6.344679701e-15 +DEAL::-0.8481266485 -0.2133123969: -0.8481266485 error value -2.220446049e-16 error grad 2.306548038e-15 +DEAL::-0.8053586039 -0.2562030323: -0.8053586039 error value 1.110223025e-16 error grad 1.804028338e-15 +DEAL::-0.7606333492 -0.2946709691: -0.7606333492 error value 1.110223025e-16 error grad 1.460460967e-15 +DEAL::-0.7143309018 -0.3286444014: -0.7143309018 error value -1.110223025e-16 error grad 7.550652228e-15 +DEAL::-0.6668322927 -0.3580813945: -0.6668322927 error value -4.440892099e-16 error grad 1.844111256e-15 +DEAL::-0.6185173440 -0.3829697098: -0.6185173440 error value -2.220446049e-16 error grad 1.782162475e-15 +DEAL::-0.5697624746 -0.4033264664: -0.5697624746 error value -1.110223025e-16 error grad 8.075684736e-16 +DEAL::-0.5209385434 -0.4191976473: -0.5209385434 error value 1.110223025e-16 error grad 2.710811174e-15 +DEAL::-0.4724087397 -0.4306574530: -0.4724087397 error value -5.551115123e-17 error grad 9.908876830e-16 +DEAL:: +DEAL::-80.08005145 25.27751482 -20.64665347 14.84112774 -9.256626666 5.010691969 -1.434519159 122.4705150 -83.00997420 24.99085697 -21.62773391 13.75070569 -8.144399953 2.340742826 -75.95044104 82.02920537 -44.96156230 4.177681933 -4.934025341 5.173902859 -1.514169514 50.29728691 -46.04113497 48.47989694 -22.83875690 -5.739048368 -3.171085801 0.9720098819 -30.65005702 26.00773257 -20.96846977 20.45689044 10.67921740 5.088918117 -1.242950483 15.55004246 -13.17172560 10.41321874 -8.658250384 10.56187268 -1.393220894 0.4238848435 -4.429844545 3.728001461 -2.896824509 2.292881826 -2.305499399 0.4357066911 -0.1283768001 +DEAL::Cell with center -1.377727649e-16 -0.7500000000 +DEAL::-0.4960937500 -0.8592595803: -0.4960937500 error value 2.775557562e-16 error grad 7.287231920e-15 +DEAL::-0.4291460533 -0.8618414972: -0.4291460533 error value -2.220446049e-16 error grad 3.231511969e-15 +DEAL::-0.3638121143 -0.8595400296: -0.3638121143 error value 0.000000000 error grad 1.974438343e-15 +DEAL::-0.3004328929 -0.8525665299: -0.3004328929 error value 0.000000000 error grad 2.637280350e-15 +DEAL::-0.2393293696 -0.8411554217: -0.2393293696 error value -1.110223025e-16 error grad 7.098746487e-16 +DEAL::-0.1808009674 -0.8255625263: -0.1808009674 error value 2.775557562e-17 error grad 1.437367088e-15 +DEAL::-0.1251241296 -0.8060632879: -0.1251241296 error value -2.775557562e-17 error grad 4.588182330e-16 +DEAL::-0.07255105048 -0.7829509083: -0.07255105048 error value 8.326672685e-17 error grad 3.859983517e-16 +DEAL::-0.02330856204 -0.7565344028: -0.02330856204 error value 3.469446952e-18 error grad 4.513176463e-16 +DEAL::0.02240282557 -0.7271365875: 0.02240282557 error value -3.469446952e-18 error grad 2.430799539e-16 +DEAL::0.06440972863 -0.6950920104: 0.06440972863 error value 2.775557562e-17 error grad 5.482470281e-16 +DEAL::0.1025665400 -0.6607448360: 0.1025665400 error value 1.387778781e-17 error grad 3.401877941e-16 +DEAL::0.1367559248 -0.6244466961: 0.1367559248 error value 5.551115123e-17 error grad 9.260552457e-16 +DEAL:: +DEAL::-69.04739437 65.23598656 -48.80352694 34.20263244 -21.58608264 10.79058761 -3.077496174 54.73792163 -46.56562918 39.25807479 -27.61658687 17.62988473 -8.177897793 2.305442179 -37.34736956 25.50788140 -19.23781204 29.22194640 -17.57143748 6.938652592 -1.898258160 25.07593192 -17.49723721 -1.724016363 -4.005966727 26.60387591 -7.538380738 1.914691647 -15.45175480 10.66847286 -1.431765314 -19.70895138 8.862232108 8.016285580 -1.805251956 8.183501538 -6.743446843 4.054409741 -0.5093588710 -2.786960573 -0.3523522065 0.1616392969 -2.332027327 1.916154128 -1.160420854 0.2588002095 0.4345702275 0.1484697162 -0.05512671170 +DEAL::Cell with center 0.6495190528 -0.3750000000 +DEAL::0.4960937500 -0.8592595803: 0.4960937500 error value 0.000000000 error grad 8.192093383e-15 +DEAL::0.5318036039 -0.8025721327: 0.5318036039 error value 3.330669074e-16 error grad 2.402447063e-15 +DEAL::0.5624774440 -0.7448405480: 0.5624774440 error value 1.110223025e-16 error grad 5.950554282e-15 +DEAL::0.5881278268 -0.6864657824: 0.5881278268 error value -1.110223025e-16 error grad 1.305987554e-15 +DEAL::0.6087972789 -0.6278430248: 0.6087972789 error value -1.110223025e-16 error grad 3.455901279e-15 +DEAL::0.6245576365 -0.5693594940: 0.6245576365 error value 0.000000000 error grad 2.314457685e-15 +DEAL::0.6355092196 -0.5113923188: 0.6355092196 error value -3.330669074e-16 error grad 1.381131749e-15 +DEAL::0.6417798513 -0.4543065070: 0.6417798513 error value 1.110223025e-16 error grad 2.386601751e-15 +DEAL::0.6435237306 -0.3984530082: 0.6435237306 error value -3.330669074e-16 error grad 1.322443367e-15 +DEAL::0.6409201696 -0.3441668777: 0.6409201696 error value -2.220446049e-16 error grad 1.843017420e-15 +DEAL::0.6341722033 -0.2917655439: 0.6341722033 error value 1.110223025e-16 error grad 4.474833320e-15 +DEAL::0.6235050834 -0.2415471888: 0.6235050834 error value 1.110223025e-16 error grad 2.571545500e-15 +DEAL::0.6091646645 -0.1937892431: 0.6091646645 error value -2.220446049e-16 error grad 6.574474745e-15 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2.775557562e-17 error grad 6.407594570e-16 +DEAL::0.1508930055 0.1673387801 -0.6212435337: 0.1508930055 error value 1.665334537e-16 error grad 9.536892957e-16 +DEAL::0.1953394317 0.2108952300 -0.5621980946: 0.1953394317 error value -5.551115123e-17 error grad 2.327657742e-15 +DEAL:: +DEAL::-57.16927575 50.51172711 -34.87056501 21.77899292 -11.07736588 3.168643524 11.47094067 -21.93399003 13.63999680 -8.541353946 4.312090727 -1.234509334 -8.498500905 12.50428103 -7.924465660 5.218282505 -2.552809671 0.7339108529 5.276490280 -7.359924962 4.834531503 -2.557811434 1.337552973 -0.4108251560 -2.667810011 3.648505740 -2.409048403 1.536971939 -0.8495216231 0.2302639351 0.7618828450 -1.036580421 0.6887922203 -0.4317466506 0.2312911443 -0.06425395721 54.52482982 -26.46043550 19.79746078 -12.40947111 6.283736432 -1.798618421 -24.86494356 12.15016295 -5.568096296 4.107386843 -2.021448542 0.5902797121 13.33570246 -17.97905326 4.471900656 -4.079034583 1.652671743 -0.4859691584 -7.920917110 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1.363274579 -0.3268451555 0.4196488013 -1.326057727 3.185690980 -0.4554699319 -0.4009444378 0.1448735815 -0.1869247253 0.3244719942 -0.5205939856 0.07842172056 -9.200389681 5.734691157 -3.833965176 2.486264073 -1.246577893 0.3460058701 4.318933042 -0.7113918286 1.504019423 -1.281661088 0.6037539628 -0.1351254308 -2.456242454 0.8633048256 -1.085661362 1.056409477 -0.5981017255 0.08858449956 1.416163906 -0.5082710493 0.8375095456 -8.479683290 2.360689418 -0.3065636207 -0.7300197812 0.3297141228 -0.2715798115 -2.614237883 0.8167976797 -0.05111082880 0.2081273699 -0.09900988573 0.08883285580 0.3554658146 -0.1128096434 0.004799791966 2.610741620 -1.628752025 1.087422360 -0.6778688750 0.3497321707 -0.09812060125 -1.224438373 0.2133008926 -0.4161634571 0.2570357492 -0.1545858394 0.03762979722 0.6945800993 -0.2404456786 0.2907337097 -0.07208125721 0.1357481864 -0.02492015892 -0.4001790770 0.1359552160 -0.1668690348 1.195617707 -0.4801326277 0.07143705334 0.2114045608 -0.1111193853 0.1224040555 0.1954650057 -0.1568718549 0.01269237342 -0.05965191923 0.03057567058 -0.03096308663 -0.01968833280 0.02039002437 -0.001006625733 +DEAL::Cell with center 0.7500000000 0.000000000 -4.163336342e-17 +DEAL::0.5879922187 -0.5879922187 -0.5412602679: 0.5879922187 error value -7.771561172e-16 error grad 2.020918803e-14 +DEAL::0.6317656581 -0.5359927398 -0.4904247681: 0.6317656581 error value -1.110223025e-16 error grad 4.721994524e-15 +DEAL::0.6752050943 -0.4774156808 -0.4328300536: 0.6752050943 error value -1.110223025e-16 error grad 1.143651163e-15 +DEAL::0.7149693757 -0.4123477836 -0.3686646352: 0.7149693757 error value -2.220446049e-16 error grad 2.215665938e-15 +DEAL::0.7476112822 -0.3415220448 -0.2987437738: 0.7476112822 error value 0.000000000 error grad 3.280054018e-15 +DEAL::0.7699931685 -0.2663289165 -0.2245218407: 0.7699931685 error value -1.110223025e-15 error grad 3.502343380e-15 +DEAL::0.7796633598 -0.1887262238 -0.1480024603: 0.7796633598 error value -3.330669074e-16 error grad 2.187205857e-15 +DEAL::0.7751382896 -0.1110685560 -0.07156802410: 0.7751382896 error value -4.440892099e-16 error grad 1.255518227e-15 +DEAL::0.7560592058 -0.03588516627 0.002241853775: 0.7560592058 error value 1.110223025e-16 error grad 9.796937681e-16 +DEAL::0.7232127397 0.03436118254 0.07097021235: 0.7232127397 error value 2.220446049e-16 error grad 2.085847261e-15 +DEAL::0.6784217227 0.09750269006 0.1324691326: 0.6784217227 error value -5.551115123e-16 error grad 3.329737364e-15 +DEAL::0.6243263560 0.1518546010 0.1850850191: 0.6243263560 error value 1.110223025e-16 error grad 2.107665257e-15 +DEAL::0.5640861853 0.1963417794 0.2277818661: 0.5640861853 error value -2.220446049e-16 error grad 1.964789452e-15 +DEAL:: +DEAL::-0.3489252520 22.69480322 -15.95687980 10.06537549 -5.150168429 1.475083316 -49.91177613 14.15848333 -10.82479197 6.376313963 -3.173865972 0.9034679363 30.79662504 -11.18726555 9.076048861 -4.613378700 2.347053091 -0.6736341098 -18.82891018 7.603771372 -5.469908083 2.457017340 -1.470201201 0.4164468016 9.485054776 -3.851705780 2.510201380 -1.164803468 0.8892312729 -0.2359226631 -2.704344398 1.109803327 -0.7241808786 0.3922215598 -0.2307424498 0.06384135179 34.91006840 0.6624726385 5.290454291 -3.724929637 1.982855740 -0.5725855843 -21.36119681 12.02054180 5.768509627 -1.921952119 0.7387594424 -0.2001728433 7.018867861 -28.26636133 -3.126359526 -2.086406165 0.9209824921 -0.2397796448 -3.602863585 11.89142482 0.2334267762 3.332958908 -0.7438613474 0.2160173298 1.803532997 -5.752085984 1.052259070 -1.969419198 -0.1554488084 -0.01858342050 -0.5019598605 1.575458083 -0.2833074538 0.3411278657 -0.04330643664 0.01883501740 -18.20672034 6.311617236 -8.378398482 3.739848538 -1.902362941 0.5365627627 8.388211315 12.91148434 23.24013493 -5.260597781 2.351232500 -0.6180453866 -2.616382829 -11.48058320 5.033702331 9.454680707 -3.464332187 0.8661248431 2.173698071 0.8062786741 -22.22451802 -6.466848577 0.7052666971 -0.2025232947 -1.261984076 0.5699704315 5.586786106 3.124112947 1.103379515 -0.1635049910 0.3468937568 -0.1425138071 -1.469470888 -0.3493191938 -0.1149557244 0.01625059819 10.77184750 -4.310176854 3.503744476 -0.5567447392 1.000920049 -0.2852012026 -5.403838148 -3.056828121 -4.027584993 -4.875254321 -0.2764574138 0.07541448176 2.792850809 -0.2878097010 15.57669812 21.75552113 -2.140708572 0.5030583420 -1.978545235 2.627377492 -12.29407358 2.088191144 3.648931561 -0.7441026420 0.8437973276 -0.7518381992 2.366759907 -17.19323795 -3.011050694 0.4442334680 -0.2012330395 0.07790851713 -0.2736084391 2.768777910 0.2459372354 -0.03075751906 -5.356114132 2.183144063 -1.712905204 1.178667478 -0.4444959285 0.1379567923 2.674974912 1.299134022 1.541218393 -0.9984838261 -0.06172622605 -0.01939545618 -1.233941542 -0.3699356474 -4.141315801 -0.04858766793 0.7898889717 -0.1282434023 0.7133032130 -0.2389379446 2.016028500 4.518427263 0.2369116154 -0.05125204264 -0.1490396221 -0.6333674567 1.372953337 -7.130999987 -3.342551015 0.5197843533 0.07545493988 0.05050273019 -0.1002721222 0.7804451228 0.3674839389 -0.05753102087 1.516942322 -0.6209996416 0.4801727768 -0.3118693629 0.1394361174 -0.04123301471 -0.7547151050 -0.3522966559 -0.3919046377 0.1966274443 -0.02717502698 0.01208184133 0.3405054718 0.1267628451 0.9855484434 0.1073295927 -0.1088705991 0.01740096827 -0.2034057796 0.07346196604 -0.5203995475 -0.8370237302 -0.05804253475 0.009665078417 0.07181190356 0.06713084038 -0.1285323124 0.9648705596 0.4328206224 -0.06806563313 -0.02456951218 -0.002065129149 0.001264522261 -0.1047817191 -0.04782721763 0.007700394328 +DEAL::Cell with center 0.000000000 -4.163336342e-17 0.7500000000 +DEAL::-0.5879922187 -0.5412602679 0.5879922187: -0.5879922187 error value 6.661338148e-16 error grad 5.826123635e-15 +DEAL::-0.5359927398 -0.4904247681 0.6317656581: -0.5359927398 error value -1.110223025e-16 error grad 4.384223999e-15 +DEAL::-0.4774156808 -0.4328300536 0.6752050943: -0.4774156808 error value 1.665334537e-16 error grad 1.311070100e-15 +DEAL::-0.4123477836 -0.3686646352 0.7149693757: -0.4123477836 error value -2.775557562e-16 error grad 2.564568452e-15 +DEAL::-0.3415220448 -0.2987437738 0.7476112822: -0.3415220448 error value -5.551115123e-17 error grad 2.493279064e-15 +DEAL::-0.2663289165 -0.2245218407 0.7699931685: -0.2663289165 error value 2.220446049e-16 error grad 2.806485636e-16 +DEAL::-0.1887262238 -0.1480024603 0.7796633598: -0.1887262238 error value -1.387778781e-16 error grad 1.492549284e-15 +DEAL::-0.1110685560 -0.07156802410 0.7751382896: -0.1110685560 error value -5.551115123e-17 error grad 4.713547550e-16 +DEAL::-0.03588516627 0.002241853775 0.7560592058: -0.03588516627 error value 2.081668171e-17 error grad 4.472434153e-16 +DEAL::0.03436118254 0.07097021235 0.7232127397: 0.03436118254 error value 3.469446952e-17 error grad 1.971246688e-16 +DEAL::0.09750269006 0.1324691326 0.6784217227: 0.09750269006 error value 0.000000000 error grad 8.898868154e-16 +DEAL::0.1518546010 0.1850850191 0.6243263560: 0.1518546010 error value -2.775557562e-17 error grad 3.950345751e-16 +DEAL::0.1963417794 0.2277818661 0.5640861853: 0.1963417794 error value 0.000000000 error grad 5.382509352e-16 +DEAL:: +DEAL::-54.28204109 48.87517752 -33.60679682 20.98902775 -10.67680417 3.053973433 61.70276795 -36.97082956 26.46915038 -16.60144656 8.426964640 -2.411645865 -39.39705987 26.01072433 -18.91775541 11.56106809 -5.764060853 1.648896693 24.15018996 -16.25276375 11.21825440 -6.719151608 3.280366680 -0.9682232730 -12.19100410 8.219905132 -5.654356043 3.615267829 -1.807057805 0.5086000686 3.475263808 -2.345564621 1.610655633 -1.006807084 0.5125624244 -0.1450147160 -8.340937124 -7.562098899 3.340983602 -2.100838620 1.038673519 -0.2977327850 -4.834958522 7.381676359 -0.3197229147 0.8980073206 -0.4171683935 0.1306741873 3.511034253 5.252447554 6.489650724 -2.701903468 0.8842053618 -0.2539132009 -2.384313904 -1.469355071 -1.486651682 -0.2239518299 0.5875722622 -0.05127158290 1.195491989 0.6742529906 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1.995608260e-15 +DEAL::-0.7854001879 -0.09242877894 -0.07246518026: -0.7854001879 error value 1.110223025e-16 error grad 2.309183456e-15 +DEAL::-0.7645345314 -0.01700078778 0.002266559507: -0.7645345314 error value -1.110223025e-16 error grad 2.384862445e-15 +DEAL::-0.7298790026 0.05314854421 0.07164727507: -0.7298790026 error value -5.551115123e-16 error grad 2.222888499e-15 +DEAL::-0.6833856700 0.1158765656 0.1335451305: -0.6833856700 error value -1.110223025e-16 error grad 1.848576759e-15 +DEAL::-0.6278029298 0.1695497377 0.1863429372: -0.6278029298 error value -1.110223025e-16 error grad 1.522529937e-15 +DEAL::-0.5663675440 0.2131627953 0.2290556314: -0.5663675440 error value 0.000000000 error grad 1.304331206e-15 +DEAL:: +DEAL::1.950586113 40.29540519 -28.22343710 17.85305041 -9.115407624 2.613117572 -26.64108088 9.159465455 -3.268183424 1.158841441 -0.5319507327 0.1360290870 16.73742308 -3.503834685 -0.1888481454 0.09928469166 0.1549941696 -0.03634041706 -10.18994703 2.306058272 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-2.972387478 0.3917227770 -0.2098090283 0.3870990533 -0.4864535277 4.438231621 0.2195363438 -0.07856559915 0.04726689265 -0.06242931269 0.02439968197 -0.5150591830 0.04791448486 -0.001566932322 -0.1670515410 -0.04404991544 0.08453976995 -0.03556253090 0.02116568162 -0.007202378703 -0.2151189742 0.7622676031 -0.2803766497 0.07911772969 -0.04244145398 0.01589322259 0.1508937699 -0.2115539998 -0.3588539850 0.008850759804 -0.02991598474 -0.001472867911 -0.09785380194 0.1352453900 0.07034861399 0.3845475397 0.3968321432 -0.05038111769 0.05099570569 -0.07820437522 0.05780567626 -0.6541176071 -0.02818372667 0.009931946019 -0.01281009378 0.01572503148 -0.001894612896 0.07898457659 -0.007224923234 0.0004585521556 diff --git a/tests/fe/point_evaluation_11.cc b/tests/fe/point_evaluation_11.cc new file mode 100644 index 0000000000..63f45a4484 --- /dev/null +++ b/tests/fe/point_evaluation_11.cc @@ -0,0 +1,142 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2021 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. +// +// --------------------------------------------------------------------- + + +// check FEPointEvaluation for scalar FE_DGQHermite and MappingQGeneric by +// comparing to the output of FEValues with the same settings (apart from the +// finite element and the interpolated function, this is the same as +// point_evaluation_02) + +#include + +#include + +#include +#include +#include +#include + +#include +#include + +#include + +#include + +#include + +#include "../tests.h" + + + +template +void +test(const unsigned int degree) +{ + using namespace dealii; + Triangulation tria; + + if (dim > 1) + GridGenerator::hyper_shell(tria, Point(), 0.5, 1, 6); + else + GridGenerator::subdivided_hyper_cube(tria, 2, 0, 1); + + MappingQGeneric mapping(degree); + deallog << "Mapping of degree " << degree << std::endl; + + std::vector> unit_points; + for (unsigned int i = 0; i < 13; ++i) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = static_cast(i) / 17. + 0.015625 * d; + unit_points.push_back(p); + } + + FE_DGQHermite fe(degree); + FEValues fe_values(mapping, + fe, + Quadrature(unit_points), + update_values | update_gradients); + + DoFHandler dof_handler(tria); + dof_handler.distribute_dofs(fe); + Vector vector(dof_handler.n_dofs()); + + FEPointEvaluation<1, dim> evaluator(mapping, fe); + + // FE_DGQHermite is not interpolatory, so we just set up some arbitrary + // content in the vector for the sake of comparison + for (unsigned int i = 0; i < vector.size(); ++i) + vector(i) = (i + 2) % 17; + + std::vector solution_values(fe.dofs_per_cell); + std::vector function_values(unit_points.size()); + std::vector> function_gradients(unit_points.size()); + + for (const auto &cell : dof_handler.active_cell_iterators()) + { + fe_values.reinit(cell); + fe_values.get_function_values(vector, function_values); + fe_values.get_function_gradients(vector, function_gradients); + + cell->get_dof_values(vector, + solution_values.begin(), + solution_values.end()); + + evaluator.evaluate(cell, + unit_points, + solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + deallog << "Cell with center " << cell->center(true) << std::endl; + for (unsigned int i = 0; i < function_values.size(); ++i) + deallog << mapping.transform_unit_to_real_cell(cell, unit_points[i]) + << ": " << evaluator.get_value(i) << " error value " + << function_values[i] - evaluator.get_value(i) << " error grad " + << (evaluator.get_gradient(i) - function_gradients[i]).norm() + << std::endl; + deallog << std::endl; + + for (unsigned int i = 0; i < unit_points.size(); ++i) + { + evaluator.submit_value(evaluator.get_value(i), i); + evaluator.submit_gradient(evaluator.get_gradient(i), i); + } + + evaluator.integrate(cell, + unit_points, + solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + for (const auto i : solution_values) + deallog << i << " "; + deallog << std::endl; + } +} + + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + test<1>(3); + test<2>(2); + test<2>(6); + test<3>(5); +} diff --git a/tests/fe/point_evaluation_11.output b/tests/fe/point_evaluation_11.output new file mode 100644 index 0000000000..5a451dd458 --- /dev/null +++ b/tests/fe/point_evaluation_11.output @@ -0,0 +1,325 @@ + +DEAL::Mapping of degree 3 +DEAL::Cell with center 0.2500000000 +DEAL::0.000000000: 2.000000000 error value 0.000000000 error grad 3.552713679e-15 +DEAL::0.02941176471: 2.298595563 error value 0.000000000 error grad 3.552713679e-15 +DEAL::0.05882352941: 2.551394260 error value 0.000000000 error grad 2.664535259e-15 +DEAL::0.08823529412: 2.764502341 error value 0.000000000 error grad 8.881784197e-16 +DEAL::0.1176470588: 2.944026053 error value 0.000000000 error grad 8.881784197e-16 +DEAL::0.1470588235: 3.096071647 error value 0.000000000 error grad 1.776356839e-15 +DEAL::0.1764705882: 3.226745369 error value 0.000000000 error grad 1.776356839e-15 +DEAL::0.2058823529: 3.342153470 error value 0.000000000 error grad 0.000000000 +DEAL::0.2352941176: 3.448402198 error value 0.000000000 error grad 4.440892099e-16 +DEAL::0.2647058824: 3.551597802 error value 0.000000000 error grad 1.332267630e-15 +DEAL::0.2941176471: 3.657846530 error value 0.000000000 error grad 1.332267630e-15 +DEAL::0.3235294118: 3.773254631 error value 0.000000000 error grad 0.000000000 +DEAL::0.3529411765: 3.903928353 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-351.8333721 248.2280361 152.6179674 -8.454113212 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0.000000000 error grad 4.440892099e-15 +DEAL::0.8529411765: 7.903928353 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-346.1390916 277.4509142 174.8552969 -13.60860131 +DEAL::Mapping of degree 2 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 2.093750000 error value 0.000000000 error grad 1.110223025e-15 +DEAL::0.9591965610 0.06332871922: 2.564338235 error value -8.881784197e-16 error grad 8.104628080e-15 +DEAL::0.9234265460 0.1210574346: 3.034926471 error value 0.000000000 error grad 1.878377933e-15 +DEAL::0.8851608469 0.1733497625: 3.505514706 error value -4.440892099e-16 error grad 4.407809125e-15 +DEAL::0.8446828558 0.2203693193: 3.976102941 error value 0.000000000 error grad 1.008349022e-14 +DEAL::0.8022759646 0.2622797217: 4.446691176 error value 8.881784197e-16 error grad 5.493080158e-15 +DEAL::0.7582235654 0.2992445859: 4.917279412 error value 0.000000000 error grad 7.944109290e-15 +DEAL::0.7128090500 0.3314275284: 5.387867647 error value 0.000000000 error grad 1.332267630e-15 +DEAL::0.6663158106 0.3589921657: 5.858455882 error value 0.000000000 error grad 3.972054645e-15 +DEAL::0.6190272391 0.3821021142: 6.329044118 error value 8.881784197e-16 error grad 4.189529227e-15 +DEAL::0.5712267275 0.4009209903: 6.799632353 error value 0.000000000 error grad 5.958081968e-15 +DEAL::0.5231976677 0.4156124105: 7.270220588 error value 0.000000000 error grad 2.512147934e-15 +DEAL::0.4752234518 0.4263399913: 7.740808824 error value 0.000000000 error grad 7.160723346e-15 +DEAL:: +DEAL::-230.9388032 -105.0937549 -36.43536725 146.2985059 37.33391539 7.023223848 63.67665824 105.1630651 76.89718920 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 11.08959961 error value 0.000000000 error grad 6.466036497e-15 +DEAL::0.4247540009 0.8623529487: 11.47011432 error value 0.000000000 error grad 9.272854936e-15 +DEAL::0.3568744593 0.8602395646: 11.73298196 error value -3.552713679e-15 error grad 5.063396036e-15 +DEAL::0.2924551254 0.8532466611: 11.87820255 error value -1.776356839e-15 error grad 1.601186417e-15 +DEAL::0.2314959991 0.8417014709: 11.90577608 error value 1.776356839e-15 error grad 6.728537760e-15 +DEAL::0.1739970804 0.8259312270: 11.81570255 error value 0.000000000 error grad 6.106226635e-16 +DEAL::0.1199583694 0.8062631623: 11.60798196 error value -1.776356839e-15 error grad 3.705967029e-15 +DEAL::0.06937986592 0.7830245096: 11.28261432 error value 1.776356839e-15 error grad 7.136584070e-15 +DEAL::0.02226157007 0.7565425018: 10.83959961 error value 0.000000000 error grad 8.379058453e-15 +DEAL::-0.02139651817 0.7271443718: 10.27893784 error value 0.000000000 error grad 2.664535259e-15 +DEAL::-0.06159439879 0.6951573525: 9.600629021 error value -1.776356839e-15 error grad 1.675811691e-14 +DEAL::-0.09833207180 0.6609086767: 8.804673139 error value 0.000000000 error grad 0.000000000 +DEAL::-0.1316095372 0.6247255774: 7.891070198 error value 0.000000000 error grad 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3.972054645e-15 +DEAL::-0.6440542406 0.3975503361: 6.858455882 error value -8.881784197e-16 error grad 0.000000000 +DEAL::-0.6404237573 0.3450422576: 7.329044118 error value 8.881784197e-16 error grad 3.972054645e-15 +DEAL::-0.6328211262 0.2942363621: 7.799632353 error value 0.000000000 error grad 3.552713679e-15 +DEAL::-0.6215297395 0.2452962662: 8.270220588 error value 0.000000000 error grad 5.617333550e-15 +DEAL::-0.6068329890 0.1983855861: 8.740808824 error value 0.000000000 error grad 8.379058453e-15 +DEAL:: +DEAL::-227.1702190 -103.5176541 -35.96708174 148.0602702 39.34877051 8.037942768 64.21897412 106.2503098 77.66331972 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: 12.08959961 error value 0.000000000 error grad 2.220446049e-15 +DEAL::-0.9591965610 -0.06332871922: 12.46200773 error value 0.000000000 error grad 2.753711214e-14 +DEAL::-0.9234265460 -0.1210574346: 12.67862402 error value -3.552713679e-15 error grad 5.653423088e-15 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2.664535259e-15 error grad 6.112319729e-14 +DEAL::-0.6435237306 0.3984530082: 4.802417227 error value 0.000000000 error grad 1.517719949e-14 +DEAL::-0.6409201696 0.3441668777: 5.834757322 error value 0.000000000 error grad 1.287337947e-13 +DEAL::-0.6341722033 0.2917655439: 8.035446638 error value 0.000000000 error grad 1.004859174e-13 +DEAL::-0.6235050834 0.2415471888: 10.69629992 error value -1.776356839e-15 error grad 1.891965973e-13 +DEAL::-0.6091646645 0.1937892431: 12.67418951 error value 5.329070518e-15 error grad 3.972054645e-14 +DEAL:: +DEAL::10535.93916 -107.7419897 -648.2290509 128.2457741 -0.4787405562 33.32449964 -18.29802505 -10148.49734 -313.2037387 786.8569542 24.08487466 -159.2324804 44.54546646 -21.89405986 -1531.296992 854.8739828 2839.999804 600.2974407 156.8239313 -15.30906273 7.679885762 849.5437317 -129.5604717 -3060.307386 -2295.304509 -949.6744307 145.3884032 -57.56301245 -582.1015114 274.8312463 647.8277103 1426.597918 1105.897193 -276.5877523 125.8938209 355.5301652 -76.71081592 -546.9103572 -140.9092091 160.6809843 -2.939912584 -0.3891901503 -187.5732759 38.83823453 279.4164454 52.24035633 -74.81956776 2.310361695 -0.2335171165 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: 10.09814232 error value 0.000000000 error grad 2.511514793e-12 +DEAL::-0.9609496573 -0.05926936446: 6.599568400 error value 8.881784197e-16 error grad 3.657742603e-14 +DEAL::-0.9262895583 -0.1146994816: 8.244066576 error value 0.000000000 error grad 3.128056081e-13 +DEAL::-0.8885607198 -0.1661007475: 10.67653501 error value -1.776356839e-15 error grad 4.497376303e-14 +DEAL::-0.8481266485 -0.2133123969: 11.93429102 error value -3.552713679e-15 error grad 1.001910925e-14 +DEAL::-0.8053586039 -0.2562030323: 11.14978659 error value 0.000000000 error grad 6.112319729e-14 +DEAL::-0.7606333492 -0.2946709691: 8.426151402 error value -3.552713679e-15 error grad 1.065814104e-13 +DEAL::-0.7143309018 -0.3286444014: 5.091338539 error value 8.881784197e-16 error grad 1.994588508e-13 +DEAL::-0.6668322927 -0.3580813945: 3.051763859 error value -4.440892099e-16 error grad 3.826389735e-14 +DEAL::-0.6185173440 -0.3829697098: 3.476804947 error value 8.881784197e-16 error grad 1.675811691e-14 +DEAL::-0.5697624746 -0.4033264664: 5.954934878 error value 8.881784197e-16 error grad 3.177643716e-14 +DEAL::-0.5209385434 -0.4191976473: 8.883552875 error value 0.000000000 error grad 1.034565839e-13 +DEAL::-0.4724087397 -0.4306574530: 10.72070928 error value 0.000000000 error grad 6.434238129e-14 +DEAL:: +DEAL::10632.76593 467.2244642 136.5533556 82.33524431 56.83453241 -13.42230741 6.589099186 -9995.344607 -621.7623421 -964.1748097 34.61274852 -227.9194851 104.3175811 -53.69253853 -1543.570811 183.1959209 2440.941356 1397.769485 -57.49670786 96.76905970 -48.99659903 799.3629924 312.9985770 -1248.819579 -2779.980788 -668.4225876 32.65397864 -2.220794498 -578.6244581 95.68007205 -230.7040314 1065.628394 1103.235257 -273.4502490 123.0361542 352.4340206 45.05730893 7.335875449 1.806365563 128.6452858 -5.382645888 1.783938101 -185.7060586 -25.23898936 -5.485547733 -15.58035665 -61.86424394 4.276302679 -1.675114673 +DEAL::Cell with center -1.377727649e-16 -0.7500000000 +DEAL::-0.4960937500 -0.8592595803: 7.900806516 error value 0.000000000 error grad 3.469311769e-13 +DEAL::-0.4291460533 -0.8618414972: 2.295127846 error value 0.000000000 error grad 1.992372474e-13 +DEAL::-0.3638121143 -0.8595400296: 3.589791659 error value 0.000000000 error grad 1.797546736e-13 +DEAL::-0.3004328929 -0.8525665299: 7.592448894 error value 2.664535259e-15 error grad 1.706782221e-13 +DEAL::-0.2393293696 -0.8411554217: 9.896630166 error value -5.329070518e-15 error grad 4.782987168e-14 +DEAL::-0.1808009674 -0.8255625263: 8.957801613 error value 1.776356839e-15 error grad 1.997434083e-13 +DEAL::-0.1251241296 -0.8060632879: 5.937382080 error value 1.776356839e-15 error grad 1.657256205e-13 +DEAL::-0.07255105048 -0.7829509083: 2.845244413 error value 4.440892099e-16 error grad 1.110223025e-13 +DEAL::-0.02330856204 -0.7565344028: 0.9319188540 error value 0.000000000 error grad 2.287296553e-13 +DEAL::0.02240282557 -0.7271365875: 0.3850030329 error value -5.551115123e-16 error grad 2.274846707e-14 +DEAL::0.06440972863 -0.6950920104: 1.089695629 error value 6.661338148e-16 error grad 1.551136925e-14 +DEAL::0.1025665400 -0.6607448360: 3.332969720 error value 1.332267630e-15 error grad 1.218456492e-13 +DEAL::0.1367559248 -0.6244466961: 7.402145001 error value -2.664535259e-15 error grad 6.674942991e-14 +DEAL:: +DEAL::12434.29865 1311.427084 401.2085933 158.7909310 308.2632012 -90.24757348 44.81638456 -11639.06366 -867.9919325 -942.1055763 -417.7235005 -566.3467831 148.3424426 -72.58653761 -1957.398031 -919.4830716 2504.722941 2616.783693 349.0197200 123.9303762 -69.80866140 962.6926517 898.9136354 -1557.526974 -2753.639731 -1748.320991 27.97964591 13.24335239 -686.3071421 -162.6930768 -236.8674747 34.45351647 1483.591555 -261.9088365 113.6056366 409.2810308 253.7539946 -36.90885248 582.1194012 928.5145720 -119.8607527 51.85909310 -218.1905200 -129.4579875 9.098935259 -280.3065686 -404.4719458 54.31252816 -23.65042714 +DEAL::Cell with center 0.6495190528 -0.3750000000 +DEAL::0.4960937500 -0.8592595803: 10.87884896 error value 0.000000000 error grad 4.225190863e-13 +DEAL::0.5318036039 -0.8025721327: 1.947934014 error value 4.440892099e-16 error grad 2.842170943e-13 +DEAL::0.5624774440 -0.7448405480: -1.478973017 error value 0.000000000 error grad 1.109903234e-13 +DEAL::0.5881278268 -0.6864657824: 2.207902670 error value -1.332267630e-15 error grad 7.652779469e-14 +DEAL::0.6087972789 -0.6278430248: 7.219246390 error value 2.664535259e-15 error grad 8.987733680e-14 +DEAL::0.6245576365 -0.5693594940: 12.00151758 error value -5.329070518e-15 error grad 4.263256415e-13 +DEAL::0.6355092196 -0.5113923188: 16.28664129 error value -7.105427358e-15 error grad 2.009718347e-13 +DEAL::0.6417798513 -0.4543065070: 18.65613046 error value -3.552713679e-15 error grad 3.202372834e-14 +DEAL::0.6435237306 -0.3984530082: 17.42768225 error value 0.000000000 error grad 6.787449953e-14 +DEAL::0.6409201696 -0.3441668777: 12.71292483 error value -3.552713679e-15 error grad 9.345730545e-14 +DEAL::0.6341722033 -0.2917655439: 7.091847635 error value -8.881784197e-16 error grad 9.800597115e-14 +DEAL::0.6235050834 -0.2415471888: 4.092024394 error value -1.776356839e-15 error grad 1.598721155e-13 +DEAL::0.6091646645 -0.1937892431: 5.631440717 error value -8.881784197e-16 error grad 4.121760359e-13 +DEAL:: +DEAL::-4972.327048 -67.64756938 1312.512595 -82.62056489 382.3040620 -134.4656678 67.07420510 7221.222601 -2283.482699 -4072.957628 578.1674158 -953.9708900 396.4846248 -200.4097878 616.6763746 -42.55392767 -1397.956753 -93.79069736 1076.231710 -291.2328647 138.3900184 -413.1254999 259.5002076 5035.474338 1521.471930 -2416.949847 458.4272197 -203.4683776 374.2456131 -427.5543997 -1602.221777 -831.3486191 -174.0543032 96.19074483 -46.97265649 -290.4018248 347.6144385 920.3095345 520.0229250 1034.896322 -174.2447877 77.96175022 151.0807201 -178.1857850 -480.6590228 -230.3189305 -452.4709967 79.79566335 -35.98692112 +DEAL::Mapping of degree 5 +DEAL::Cell with center 0.000000000 0.000000000 -0.7500000000 +DEAL::-0.5759520655 -0.5527659841 -0.5759520655: 4.300619546 error value 1.776356839e-15 error grad 3.121539668e-13 +DEAL::-0.5254898676 -0.5029040719 -0.6187865537: 9.123819127 error value 5.329070518e-15 error grad 7.930194913e-14 +DEAL::-0.4685426073 -0.4464599093 -0.6616551149: 7.200756218 error value -5.329070518e-15 error grad 2.302421613e-14 +DEAL::-0.4051542510 -0.3835292107 -0.7012978956: 3.982780289 error value 4.440892099e-16 error grad 5.902211244e-14 +DEAL::-0.3359932318 -0.3148223149 -0.7343028440: 3.054553970 error value 2.220446049e-15 error grad 2.617113832e-13 +DEAL::-0.2623766962 -0.2416891159 -0.7575161861: 3.289605388 error value -3.108624469e-15 error grad 2.869792301e-14 +DEAL::-0.1861925434 -0.1660412603 -0.7684224851: 3.432097972 error value 0.000000000 error grad 4.043894975e-14 +DEAL::-0.1097387169 -0.09019150189 -0.7654365722: 4.198840753 error value 1.776356839e-15 error grad 7.820006226e-14 +DEAL::-0.03550798632 -0.01663873419 -0.7480737719: 6.601356033 error value -1.776356839e-15 error grad 5.676009106e-14 +DEAL::0.03404970570 0.05216906594 -0.7169856075: 9.949264712 error value -3.552713679e-15 error grad 1.041443642e-13 +DEAL::0.09675558003 0.1140621810 -0.6738655685: 12.13512929 error value 7.105427358e-15 error grad 2.353672812e-14 +DEAL::0.1508930055 0.1673387801 -0.6212435337: 11.76137765 error value -1.776356839e-15 error grad 6.235659312e-14 +DEAL::0.1953394317 0.2108952300 -0.5621980946: 9.605387518 error value 3.552713679e-15 error grad 1.423969126e-13 +DEAL:: +DEAL::-1919.760527 325.0604051 -34.89879708 3.729477761 -5.082400667 2.590714176 275.0360298 159.5334495 91.43595234 -12.37703276 13.10613375 -6.654371038 0.3079005287 178.7162897 466.4065688 -116.2971544 53.95916117 -26.66723132 -19.58351446 -32.07445421 -81.47024123 -66.22273690 -0.6149376126 0.5859761784 12.18561456 22.01942197 36.39161513 15.65401042 4.777280582 -2.300152899 -6.434425493 -10.94178152 -18.09343908 -4.475037771 -2.100113796 1.052489988 38.96835780 274.4657239 130.3216229 -22.00874981 18.74819011 -9.461560667 694.1863462 -19.23517354 -352.4437354 65.00290976 -49.40362691 24.83036090 265.6442476 -585.8913581 -1478.850533 384.1792262 -192.7296930 95.62738076 -70.39448334 98.73510242 288.6830493 113.2881316 16.75704605 -9.128522602 47.43909558 -61.02192424 -140.2196400 -16.52429638 -19.30433151 9.517188241 -24.03009022 29.96789661 69.56469708 1.384238301 9.076621142 -4.562574255 105.1753687 -11.40982133 -169.1745839 -33.97945594 1.420711306 -0.1687185435 60.59489625 220.3806764 558.6154491 18.00906676 29.04751725 -15.83706819 -63.05980878 203.2390407 -466.1366897 -416.9387572 135.3839694 -63.24857782 -39.83155832 45.23788071 -595.5379898 -525.5501283 91.73131499 -41.32580037 6.891969970 12.44152983 234.0389536 143.5695843 -13.54661999 6.171915522 -3.066476346 -7.506418233 -112.9375808 -55.69815000 6.645801745 -2.896253857 -37.97047406 -40.37192252 9.896550045 108.9803100 -14.62102558 7.313403532 -77.17342322 50.73742594 -16.37419053 -228.1558369 32.86930226 -16.29238455 -37.81578419 133.1839773 1430.534011 340.2392824 -0.1791466776 -1.596145842 59.51543936 -136.3541130 285.5800715 554.8628071 -86.29132464 43.72010205 -15.55734995 36.42880910 -44.53917308 -446.7507150 0.9584401505 -3.798610802 8.653718581 -19.70079635 23.23239834 160.6447103 -6.447326252 3.949404185 28.54874043 19.67892844 22.07460962 7.862892757 4.443823374 -2.166581704 44.63121428 -20.17497859 -55.66960759 -13.49999582 -10.11183671 4.946082228 46.37639914 -134.2238155 -577.3882278 132.7835825 -43.04271959 21.43822792 -8.628284103 21.75382705 48.23301343 241.6877873 10.66657724 -3.423183999 7.500203268 -16.92301902 -15.91805750 -79.96031698 -11.63510236 4.749600237 -3.337328124 7.516599442 9.535573288 24.60878847 3.736689531 -1.617193448 -14.82177675 -9.936490611 -12.10154748 -2.648023217 -2.041976818 1.012220265 -22.85696405 10.15527594 30.49813490 4.160287972 4.748648957 -2.356295738 -24.07133900 69.30691897 278.3246429 -64.16759715 22.91522668 -11.35661608 3.503295343 -9.215514801 -30.25713359 -93.28141678 -1.211433689 0.2540272965 -3.409673551 7.759957044 10.69541945 29.67675380 4.253919404 -1.781678604 1.574821193 -3.563071285 -5.813300389 -9.304802106 -1.433819219 0.6407072923 +DEAL::Cell with center 0.7500000000 0.000000000 -4.163336342e-17 +DEAL::0.5879922187 -0.5879922187 -0.5412602679: 12.10065939 error value -3.552713679e-15 error grad 1.188625655e-12 +DEAL::0.6317656581 -0.5359927398 -0.4904247681: 6.720427646 error value 3.552713679e-15 error grad 6.204547701e-14 +DEAL::0.6752050943 -0.4774156808 -0.4328300536: 10.52900748 error value -3.552713679e-15 error grad 7.848201035e-14 +DEAL::0.7149693757 -0.4123477836 -0.3686646352: 14.06728863 error value -8.881784197e-15 error grad 8.614872835e-14 +DEAL::0.7476112822 -0.3415220448 -0.2987437738: 15.57447528 error value 5.329070518e-15 error grad 1.017536210e-14 +DEAL::0.7699931685 -0.2663289165 -0.2245218407: 15.45416528 error value -3.552713679e-15 error grad 4.256775187e-14 +DEAL::0.7796633598 -0.1887262238 -0.1480024603: 13.14924011 error value -3.552713679e-15 error grad 5.683127450e-14 +DEAL::0.7751382896 -0.1110685560 -0.07156802410: 8.895379180 error value -8.881784197e-15 error grad 6.788757341e-14 +DEAL::0.7560592058 -0.03588516627 0.002241853775: 4.732552371 error value -4.440892099e-15 error grad 4.121245968e-14 +DEAL::0.7232127397 0.03436118254 0.07097021235: 3.001128600 error value -1.776356839e-15 error grad 7.167880493e-14 +DEAL::0.6784217227 0.09750269006 0.1324691326: 4.390776520 error value 0.000000000 error grad 6.696182036e-14 +DEAL::0.6243263560 0.1518546010 0.1850850191: 7.846618202 error value 8.881784197e-16 error grad 7.536443802e-14 +DEAL::0.5640861853 0.1963417794 0.2277818661: 12.13335291 error value -1.776356839e-15 error grad 1.758144639e-13 +DEAL:: +DEAL::4775.639072 -345.6765934 6.729433664 -0.2036836376 7.081958656 -3.289238174 -3850.478235 -28.77546670 64.00667567 -28.74620922 4.165538780 -2.728650338 -348.0433205 -119.4327253 -130.4694848 68.82269354 -18.65849682 10.30102615 185.6164560 29.40245872 -31.32996871 12.10025715 7.567044338 -3.715076116 -124.2224859 -20.14813591 21.51256060 -58.69633731 -16.89844029 6.743185945 65.02589252 8.733444942 -8.235833829 16.48849200 5.978654671 -2.456666064 2795.378024 -898.2869539 -209.2752085 90.31407184 -72.44430794 36.44881547 -2522.065235 -177.0082616 -202.3330929 83.53408317 -24.07565187 13.42819808 -224.2569646 930.9444067 600.9640092 -279.2659907 125.4917638 -65.49712915 105.7926201 -282.1531391 -14.89718939 13.06992601 -40.20875656 20.24177055 -75.86064726 170.6781559 2.173403826 96.02562466 48.18784274 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78.63911561 -106.2844340 -7.609823749 -30.06834112 -23.33320539 10.32232670 -76.78699291 -28.62945151 -100.0264060 104.3330799 17.50435676 -5.762763890 -6.326960346 150.8824871 200.9095615 -196.3117964 -12.04572463 0.9432412791 7.602868924 -55.81434637 77.84099974 -57.03310973 -14.11441447 6.693165755 -19.11824779 60.98618868 -88.25555915 361.2248288 78.77443499 -29.82912481 6.675862156 -24.47643179 32.01884007 -107.9961730 -25.78275066 9.939084830 -40.24340666 53.25786096 6.440244027 6.563188912 9.929621448 -4.521467624 38.86708094 16.26795577 45.30515072 -35.80327432 -5.050490120 1.484649126 4.759963824 -79.74088595 -92.73053122 72.28668411 -0.4810456471 2.006665311 -3.619452868 27.75329636 -34.76099297 23.98185394 6.830674773 -3.229758931 7.042855088 -25.50204118 32.96937087 -119.8708738 -27.67204745 10.61520418 -2.538233989 10.67453367 -12.22990878 35.38617008 9.245796073 -3.625021694 +DEAL::Cell with center 0.000000000 -4.163336342e-17 0.7500000000 +DEAL::-0.5879922187 -0.5412602679 0.5879922187: 9.495404258 error value 0.000000000 error grad 1.512721955e-13 +DEAL::-0.5359927398 -0.4904247681 0.6317656581: 3.676198418 error value -1.332267630e-15 error grad 2.960499992e-13 +DEAL::-0.4774156808 -0.4328300536 0.6752050943: -0.5965055394 error value -2.220446049e-16 error grad 2.512147934e-14 +DEAL::-0.4123477836 -0.3686646352 0.7149693757: -0.4260724669 error value 1.110223025e-15 error grad 6.541239600e-14 +DEAL::-0.3415220448 -0.2987437738 0.7476112822: 2.664419193 error value 1.776356839e-15 error grad 5.772476473e-14 +DEAL::-0.2663289165 -0.2245218407 0.7699931685: 7.234075462 error value 7.105427358e-15 error grad 3.156921464e-13 +DEAL::-0.1887262238 -0.1480024603 0.7796633598: 11.08009699 error value 0.000000000 error grad 8.651423160e-14 +DEAL::-0.1110685560 -0.07156802410 0.7751382896: 12.07121590 error value -1.776356839e-15 error grad 5.706503147e-14 +DEAL::-0.03588516627 0.002241853775 0.7560592058: 9.924965839 error value 0.000000000 error grad 9.161593765e-14 +DEAL::0.03436118254 0.07097021235 0.7232127397: 6.389390166 error value 1.776356839e-15 error grad 1.470793696e-13 +DEAL::0.09750269006 0.1324691326 0.6784217227: 3.576171443 error value -8.881784197e-16 error grad 5.688677042e-14 +DEAL::0.1518546010 0.1850850191 0.6243263560: 2.276132571 error value 1.776356839e-15 error grad 4.067236554e-14 +DEAL::0.1963417794 0.2277818661 0.5640861853: 2.048493572 error value -8.881784197e-16 error grad 2.336432636e-14 +DEAL:: +DEAL::726.4082583 121.0703308 -0.4110664770 0.9414616873 0.2882707783 -0.3301802795 -491.1981422 98.77160569 106.2564813 -43.02798391 24.67539539 -12.17556586 -53.42100914 -60.57576626 -27.04429064 48.91679900 -21.28461630 10.02567135 35.04826259 -0.5968671966 -30.23265801 -56.83391444 3.254832968 -1.298300040 -26.63666521 7.879100564 7.069571250 1.352687677 6.214581327 -2.837192824 13.68567197 -3.985662922 -4.193041822 1.834405782 -2.912895438 1.360187376 659.7046041 990.4391396 267.4733014 -127.1257380 81.35382136 -41.44657953 -538.5410642 -736.1943205 -428.5377071 171.4210321 -102.6388686 51.48447283 -321.7672024 -573.2671233 -69.45188849 -35.88763026 -1.154920288 2.668391844 117.5330175 318.6586049 155.4979719 77.09371135 19.22095259 -10.67142291 -67.89713161 -216.8446395 -74.57412827 24.34304748 -29.85675735 14.57373569 34.76263627 110.3886842 39.36918537 -17.56254125 14.70991469 -7.257388827 97.90247607 480.1274805 780.4340116 -114.2471511 68.82662980 -35.03715098 48.65487199 -868.0273772 -2269.493159 346.9189368 -203.1189999 102.3719685 -166.8620773 -45.02654871 698.1315557 57.10649713 7.915789765 -6.915124301 -42.35740906 363.7067051 1386.212463 -448.1723277 127.2069502 -61.12312781 10.57850206 -196.4261142 -815.5632993 111.1565219 -37.64014920 19.84239434 -5.496133519 100.3909177 402.0959693 -46.60405800 20.03440046 -10.39250237 -50.86559712 -196.4753195 -21.48157465 231.1302149 -38.81184395 18.68038213 8.957358131 275.2601331 101.4736736 -501.0163563 88.99731524 -42.53098677 128.5066703 -72.18973951 321.2787886 1115.091499 -167.5096050 75.28210617 -52.95765647 7.513507387 -249.2243648 -609.3466074 102.4740766 -43.60932062 -3.814216953 76.26703484 -42.83921024 -685.9918321 22.27625274 -12.35490158 2.850996595 -40.73114068 23.68390513 271.2899660 -16.24124268 8.007049269 37.81289299 116.5954157 34.38903242 -22.59030103 15.97476904 -7.816092968 -17.76376336 -147.9090137 -102.4164874 54.20176358 -34.87450320 16.91954105 -51.80394728 -22.14508971 -41.42950682 -84.53163697 34.97585932 -15.58923458 14.61842966 35.56376755 58.80687111 244.0585250 -4.739206857 2.775579260 -1.031063286 -40.44093796 1.846213036 -33.37114401 -16.41448849 7.065830057 0.8035119370 20.07227510 0.6955873739 5.304772357 6.841201228 -3.057790053 -19.63647885 -59.22668957 -18.15915064 11.57078068 -7.759846870 3.818241238 9.751444338 73.98251953 52.73554254 -27.15214730 16.77053697 -8.174819396 25.39236252 13.94532942 16.21540392 38.32802495 -15.31383778 6.831039115 -7.455190604 -18.24797364 -28.68830230 -89.50892945 3.846151028 -1.774378463 0.9331822906 19.78552488 0.7868907760 10.49103044 7.000261665 -3.071180183 -0.5682777898 -9.908145894 -1.036212776 -1.046177220 -3.036153470 1.377306481 +DEAL::Cell with center -0.7500000000 0.000000000 0.000000000 +DEAL::-0.6012515503 -0.5766780283 -0.5531118850: 6.208622002 error value 8.881784197e-16 error grad 2.998625042e-13 +DEAL::-0.6458946236 -0.5236491363 -0.5006487306: 11.22707249 error value -1.776356839e-15 error grad 8.989488925e-14 +DEAL::-0.6898189280 -0.4638689601 -0.4413495827: 14.12544547 error value -7.105427358e-15 error grad 1.229702187e-13 +DEAL::-0.7296048967 -0.3975220470 -0.3754490693: 13.29088572 error value -1.243449788e-14 error grad 7.289559011e-14 +DEAL::-0.7617762381 -0.3254496235 -0.3038288032: 9.030801555 error value 1.776356839e-15 error grad 5.252281966e-14 +DEAL::-0.7832188522 -0.2491480826 -0.2280163559: 5.478484165 error value 1.776356839e-15 error grad 4.468561476e-15 +DEAL::-0.7915521155 -0.1706669598 -0.1500833118: 5.418767297 error value -7.105427358e-15 error grad 1.035785128e-14 +DEAL::-0.7854001879 -0.09242877894 -0.07246518026: 7.993832134 error value -5.329070518e-15 error grad 6.553288310e-14 +DEAL::-0.7645345314 -0.01700078778 0.002266559507: 10.81008053 error value 1.776356839e-15 error grad 6.104571169e-14 +DEAL::-0.7298790026 0.05314854421 0.07164727507: 12.64840570 error value 5.329070518e-15 error grad 1.191616394e-14 +DEAL::-0.6833856700 0.1158765656 0.1335451305: 13.81385930 error value -1.243449788e-14 error grad 3.117493601e-14 +DEAL::-0.6278029298 0.1695497377 0.1863429372: 14.44798961 error value -3.552713679e-15 error grad 3.768029723e-14 +DEAL::-0.5663675440 0.2131627953 0.2290556314: 13.40735584 error value -3.552713679e-15 error grad 3.499017183e-14 +DEAL:: +DEAL::-1425.483249 410.7394625 9.968134493 -2.498760411 0.9554094470 -0.6689162806 264.4708776 77.68744282 -65.03400023 18.92832724 -10.13030628 5.450843449 46.54660198 -0.5488972046 -23.72307709 26.97608797 -13.87679575 6.108904186 -23.79861833 5.392900227 -2.664373955 -29.85659372 13.58183876 -4.835860452 13.53918317 0.8983315191 -10.34403646 6.361420128 4.234607133 -1.198004605 -7.168122671 -0.07893474957 4.872685475 -1.733172830 -1.181088932 0.2728356614 -422.0532686 329.5913071 10.58587857 -11.63604977 9.079529477 -4.322763757 -239.8073221 511.0503065 576.9320207 -215.9834958 131.3863011 -67.38201580 -184.2766746 80.16925319 192.8720203 -117.6041112 65.26081530 -31.10162456 83.06445263 -60.17467103 -69.54374327 87.20432327 -44.87919876 18.63521712 -48.45335167 32.00477502 70.28344699 -31.15456610 2.957213057 -3.422088998 25.11171016 -17.37854512 -35.20627367 12.93486676 -3.534060050 2.453008826 3.611478098 17.68409128 -42.48297474 31.21459806 -16.92678416 7.588869346 -276.6341738 400.1720091 529.4633759 -236.4430896 138.6764921 -68.15327397 -88.06342302 8.694139196 -380.2022835 159.4559482 -49.74080372 19.42128360 64.61751198 -76.97569254 -178.9591791 12.81828153 -5.194654864 9.149621124 -47.94297112 63.98067418 70.96539881 -40.37226134 47.62821558 -20.20702339 23.68316094 -31.17790241 -38.07932171 25.31410406 -20.44347956 8.949547177 2.367697616 -17.71390944 -12.14480173 70.10052693 11.58452151 -3.640187883 104.3027668 -133.3446861 -133.8635039 -84.23458191 -60.49844897 26.25222651 50.80769002 -25.97060349 -169.2338461 377.6147442 3.562648877 4.629603206 7.020872243 -37.84132462 26.05935005 374.8033411 -212.3899565 67.13874925 28.14883923 -40.27954465 55.04987179 -302.6946117 -86.01476611 29.39077103 -11.56537911 14.94989651 -16.36436218 107.0202291 28.25770721 -9.672426730 -4.127694151 16.57647419 -3.231878527 -0.5724028292 5.589308609 -1.933724961 -60.58520905 73.17632893 104.6433570 -35.74053242 12.12644466 -7.977329723 -36.94761527 26.11338556 46.57093190 -47.23466229 36.36698937 -14.71711676 23.96771614 -31.09273422 41.58818723 185.2002111 -66.13467678 22.10435607 -3.461874900 -3.658207513 24.16976871 -31.89785578 -27.35350085 8.885947305 2.681803421 -0.006409571839 -9.564429380 7.906098963 8.785293305 -2.768399837 2.023416241 -8.291471404 1.312465024 0.4789271562 -2.026535780 0.7110368353 31.04852084 -37.61564182 -52.46909511 17.87897339 -7.798880434 4.599459942 18.16716361 -11.96153484 -23.44358091 22.68133116 -15.20705850 6.343780563 -10.60763489 12.57933969 -14.30655335 -60.60448851 23.66260881 -8.054177343 2.562698114 0.2846194355 -9.866251797 11.56493039 9.177719153 -2.924167547 -1.626815013 0.5137386815 4.122756721 -2.950135338 -2.894166873 0.8796324609 +DEAL::Cell with center 0.000000000 -0.7500000000 -4.163336342e-17 +DEAL::-0.5879922187 -0.5879922187 -0.5412602679: 8.986616205 error value 0.000000000 error grad 6.371155840e-13 +DEAL::-0.5359927398 -0.6317656581 -0.4904247681: 8.152985337 error value -5.329070518e-15 error grad 1.825417340e-13 +DEAL::-0.4774156808 -0.6752050943 -0.4328300536: 12.95516317 error value -7.105427358e-15 error grad 8.437227512e-14 +DEAL::-0.4123477836 -0.7149693757 -0.3686646352: 13.99089667 error value 7.105427358e-15 error grad 5.003054719e-14 +DEAL::-0.3415220448 -0.7476112822 -0.2987437738: 10.23510139 error value 3.552713679e-15 error grad 3.623071275e-14 +DEAL::-0.2663289165 -0.7699931685 -0.2245218407: 3.872995969 error value 8.881784197e-16 error grad 9.768347613e-14 +DEAL::-0.1887262238 -0.7796633598 -0.1480024603: -1.198837673 error value -1.332267630e-15 error grad 1.507288760e-14 +DEAL::-0.1110685560 -0.7751382896 -0.07156802410: -2.568378375 error value 4.440892099e-16 error grad 5.203997970e-14 +DEAL::-0.03588516627 -0.7560592058 0.002241853775: -0.6607669697 error value -2.331468352e-15 error grad 6.504959566e-14 +DEAL::0.03436118254 -0.7232127397 0.07097021235: 2.675880496 error value -8.881784197e-16 error grad 1.368119144e-13 +DEAL::0.09750269006 -0.6784217227 0.1324691326: 6.219295670 error value 1.776356839e-15 error grad 6.307942934e-14 +DEAL::0.1518546010 -0.6243263560 0.1850850191: 9.750847528 error value 3.552713679e-15 error grad 1.135201821e-13 +DEAL::0.1963417794 -0.5640861853 0.2277818661: 12.63574713 error value -5.329070518e-15 error grad 7.140866118e-14 +DEAL:: +DEAL::3495.609475 -1004.383337 9.162713864 -2.164490597 3.599261733 -1.527006805 -595.5977880 -235.0274899 -12.95757889 5.325567662 -7.335716781 3.130888755 -62.28629982 -49.10903590 -117.5953618 -30.71571370 11.57609999 -4.171477015 36.20398336 7.530564298 81.57143104 55.56805899 -8.065668568 3.506856788 -19.20369635 -15.49863271 -11.81498180 -31.54662687 -11.50858582 4.690378153 10.29560004 7.216489474 6.305861479 7.356344171 4.485728553 -1.898391697 -56.23952350 -1841.730498 -347.1623864 158.6032120 -107.9328987 54.79753564 -742.0886814 339.5321552 134.0654332 -63.69272830 49.29395288 -24.06767578 161.4491001 1157.288151 590.8653422 -84.47066384 75.02348554 -42.21207656 -68.20909987 -420.2254483 -305.0259742 -59.68908969 -19.43222339 11.34800558 29.67890819 280.2240627 103.3438410 28.08988125 46.05714837 -21.15975886 -15.47722551 -140.5592273 -52.63698368 3.163719443 -20.58816002 9.738362423 -228.9097214 -654.6583573 -488.2940570 117.5587612 -65.46486785 34.25608619 -109.1396167 388.4544258 942.4243107 -131.3126200 64.64921257 -34.39494878 -33.86964678 940.1669635 -540.2586668 -528.7394698 251.4928215 -118.8924919 58.85071059 -466.8468013 -325.8942176 465.0082562 -159.0367942 76.27993275 -1.981955908 207.9829084 375.3088449 -203.2815261 11.55455418 -9.906885434 1.312070943 -105.3403036 -186.9677307 69.34017593 -9.918076842 6.355728626 107.1625483 285.8036972 47.56472764 -438.0070343 41.51895687 -21.02527893 55.91396290 -148.8886703 31.95756757 864.7074072 -57.25604245 28.18800749 -123.6005478 -80.84545306 -776.1400299 -2042.973369 193.0160559 -86.91078915 99.71948366 -85.82658886 688.0312987 752.5525047 -209.0690768 91.98795640 -9.526711944 -60.47201169 -56.04241347 1582.105298 46.88279382 -11.85792040 0.3516716110 39.64316137 8.813583680 -590.7430706 -1.767934312 -1.889957357 -73.46877929 -176.3036134 -44.96015933 7.222852190 -24.87619008 11.61064613 -29.63836099 76.35717097 15.48509563 13.27448064 29.21719429 -12.59571685 41.87858487 129.4218967 247.9299169 39.39459760 -48.74656804 19.04998941 -20.32225558 -37.49115243 -164.8374280 -216.7901875 17.04752027 -8.172505926 -5.633708179 60.95161262 -6.119315521 201.0106513 48.78855376 -18.74512422 1.346437089 -27.76827483 -1.505057919 -56.26403722 -16.93923384 6.704972033 38.11561178 89.45577682 24.04180914 -7.673096240 11.43774371 -5.439312127 14.59698086 -37.29440986 -10.17823558 0.6760334509 -12.27863896 5.400884619 -19.35760726 -70.16302652 -114.0870548 -24.99850893 18.48669609 -7.110933156 9.846335512 20.32336989 77.38575539 80.80981624 -8.876369957 4.037932372 1.377263816 -28.01992843 -2.052939410 -67.04454040 -17.90958952 7.005996432 -0.1975749224 13.15282634 2.419409699 18.14873197 6.453765529 -2.612116509 +DEAL::Cell with center 0.000000000 0.7500000000 0.000000000 +DEAL::-0.5766780283 0.6012515503 -0.5531118850: 9.545568199 error value 0.000000000 error grad 4.361598159e-13 +DEAL::-0.5236491363 0.6458946236 -0.5006487306: 5.061939345 error value -2.664535259e-15 error grad 6.674942991e-14 +DEAL::-0.4638689601 0.6898189280 -0.4413495827: 4.678197821 error value -2.664535259e-15 error grad 5.387957063e-14 +DEAL::-0.3975220470 0.7296048967 -0.3754490693: 8.162588614 error value 1.776356839e-15 error grad 1.811535637e-14 +DEAL::-0.3254496235 0.7617762381 -0.3038288032: 11.78397925 error value -1.776356839e-15 error grad 3.932384251e-14 +DEAL::-0.2491480826 0.7832188522 -0.2280163559: 12.68139857 error value -7.105427358e-15 error grad 2.358030136e-14 +DEAL::-0.1706669598 0.7915521155 -0.1500833118: 11.19915004 error value -3.552713679e-15 error grad 2.206189426e-14 +DEAL::-0.09242877894 0.7854001879 -0.07246518026: 9.286227059 error value 7.105427358e-15 error grad 4.401876787e-14 +DEAL::-0.01700078778 0.7645345314 0.002266559507: 8.026331499 error value 5.329070518e-15 error grad 5.374947302e-14 +DEAL::0.05314854421 0.7298790026 0.07164727507: 6.948218148 error value 0.000000000 error grad 2.636259580e-14 +DEAL::0.1158765656 0.6833856700 0.1335451305: 5.293152917 error value 8.881784197e-16 error grad 2.913441837e-14 +DEAL::0.1695497377 0.6278029298 0.1863429372: 3.578122122 error value 1.332267630e-15 error grad 1.074108502e-14 +DEAL::0.2131627953 0.5663675440 0.2290556314: 3.605689908 error value 0.000000000 error grad 4.362936356e-14 +DEAL:: +DEAL::641.2329821 453.6419713 9.724020855 1.223104603 2.016469845 -1.061694173 -839.0295475 149.1114591 -23.67579489 -6.850063405 -0.9974929300 0.5137828236 -69.81661252 6.773773876 -75.14445319 63.27667710 -17.15294487 7.879362330 39.05071256 -4.138394615 -28.32674750 18.89756027 -2.202909074 0.2792760243 -27.12029283 3.986524300 3.439347167 -11.77907750 -0.9806081930 0.4012374540 14.13169974 -2.194057569 -0.8882556106 4.848377427 0.2559980292 -0.1153727890 105.5162732 499.0140409 31.58577474 -31.09391013 14.85365919 -7.620535294 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