From: Martin Kronbichler Date: Mon, 9 Dec 2019 11:51:37 +0000 (+0100) Subject: Test case of inverse shape values field X-Git-Tag: v9.2.0-rc1~767^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a267d5cb973a37fa2275e6101c71b4da7f991270;p=dealii.git Test case of inverse shape values field --- diff --git a/tests/matrix_free/shape_info_inverse.cc b/tests/matrix_free/shape_info_inverse.cc new file mode 100644 index 0000000000..be98ff8a3a --- /dev/null +++ b/tests/matrix_free/shape_info_inverse.cc @@ -0,0 +1,122 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2019 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. +// +// --------------------------------------------------------------------- + + + +// test the correctness of the inverse_shape_values field of +// internal::MatrixFreeFunctions::ShapeInfo + +#include +#include + +#include + +#include + +#include + +#include "../tests.h" + +std::ofstream logfile("output"); + + +template +void +test(const FiniteElement &fe, + const Quadrature<1> & quad, + const std::string & quadrature_name) +{ + internal::MatrixFreeFunctions::ShapeInfo shape_info; + shape_info.reinit(quad, fe, 0); + deallog << "Testing " << fe.get_name() << " with " << quadrature_name << "(" + << quad.size() << ")" << std::endl; + deallog << "shape values: " << std::endl; + for (unsigned int i = 0; i < shape_info.fe_degree + 1; ++i) + { + for (unsigned int q = 0; q < quad.size(); ++q) + deallog << std::setw(15) << shape_info.shape_values[i * quad.size() + q] + << " "; + deallog << std::endl; + } + deallog << "inverse shape values: " << std::endl; + for (unsigned int i = 0; i < shape_info.fe_degree + 1; ++i) + { + for (unsigned int q = 0; q < quad.size(); ++q) + deallog << std::setw(15) + << shape_info.inverse_shape_values[i * quad.size() + q] << " "; + deallog << std::endl; + } + deallog << "inverse shapes' * shapes: " << std::endl; + for (unsigned int i = 0; i < quad.size(); ++i) + { + for (unsigned int j = 0; j < quad.size(); ++j) + { + double sum = 0; + for (unsigned int k = 0; k < shape_info.fe_degree + 1; ++k) + sum += shape_info.inverse_shape_values[k * quad.size() + i] * + shape_info.shape_values[k * quad.size() + j]; + deallog << std::setw(15) << sum << " "; + } + deallog << std::endl; + } + deallog << "inverse shapes * shapes': " << std::endl; + for (unsigned int i = 0; i < shape_info.fe_degree + 1; ++i) + { + for (unsigned int j = 0; j < shape_info.fe_degree + 1; ++j) + { + double sum = 0; + for (unsigned int k = 0; k < quad.size(); ++k) + sum += shape_info.inverse_shape_values[i * quad.size() + k] * + shape_info.shape_values[j * quad.size() + k]; + deallog << std::setw(15) << sum << " "; + } + deallog << std::endl; + } +} + + +int +main() +{ + initlog(); + deallog << std::setprecision(9); + test(FE_DGQ<1>(1), QGauss<1>(2), "QGauss"); + test(FE_DGQ<1>(1), QGauss<1>(3), "QGauss"); + test(FE_DGQ<1>(3), QGauss<1>(2), "QGauss"); + test(FE_DGQ<1>(3), QGauss<1>(4), "QGauss"); + test(FE_DGQ<1>(3), QGauss<1>(5), "QGauss"); + test(FE_DGQ<1>(8), QGauss<1>(7), "QGauss"); + test(FE_DGQ<1>(8), QGauss<1>(9), "QGauss"); + test(FE_DGQ<1>(8), QGauss<1>(12), "QGauss"); + test(FE_DGQHermite<1>(1), QGauss<1>(2), "QGauss"); + test(FE_DGQHermite<1>(1), QGauss<1>(3), "QGauss"); + test(FE_DGQHermite<1>(3), QGauss<1>(2), "QGauss"); + test(FE_DGQHermite<1>(3), QGauss<1>(4), "QGauss"); + test(FE_DGQHermite<1>(3), QGauss<1>(5), "QGauss"); + test(FE_DGQHermite<1>(8), QGauss<1>(7), "QGauss"); + test(FE_DGQHermite<1>(8), QGauss<1>(9), "QGauss"); + test(FE_DGQHermite<1>(8), QGauss<1>(12), "QGauss"); + test(FE_DGQArbitraryNodes<1>(QGauss<1>(9)), QGauss<1>(9), "QGauss"); + test(FE_DGQArbitraryNodes<1>(QGauss<1>(9)), QGauss<1>(12), "QGauss"); + test(FE_DGQ<1>(3), QGaussLobatto<1>(4), "QGaussLobatto"); + test(FE_DGQ<1>(3), QGaussLobatto<1>(5), "QGaussLobatto"); + test(FE_Q<1>(3), QGauss<1>(4), "QGauss"); + test(FE_Q<1>(3), QGauss<1>(5), "QGauss"); + + test(FE_DGQ<2>(3), QGauss<1>(4), "QGauss"); + test(FE_DGQ<2>(3), QGauss<1>(5), "QGauss"); + test(FE_Q<2>(3), QGauss<1>(4), "QGauss"); + test(FE_Q<2>(3), QGauss<1>(5), "QGauss"); +} diff --git a/tests/matrix_free/shape_info_inverse.output b/tests/matrix_free/shape_info_inverse.output new file mode 100644 index 0000000000..3909ac9d9d --- /dev/null +++ b/tests/matrix_free/shape_info_inverse.output @@ -0,0 +1,684 @@ + +DEAL::Testing FE_DGQ<1>(1) with QGauss(2) +DEAL::shape values: +DEAL::0.788675135 0.211324865 +DEAL::0.211324865 0.788675135 +DEAL::inverse shape values: +DEAL::1.36602540 -0.366025404 +DEAL::-0.366025404 1.36602540 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 0.00000000 +DEAL::5.55111512e-17 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 5.55111512e-17 +DEAL::0.00000000 1.00000000 +DEAL::Testing FE_DGQ<1>(1) with QGauss(3) +DEAL::shape values: +DEAL::0.887298335 0.500000000 0.112701665 +DEAL::0.112701665 0.500000000 0.887298335 +DEAL::inverse shape values: +DEAL::0.923275002 0.444444444 -0.367719447 +DEAL::-0.367719447 0.444444444 0.923275002 +DEAL::inverse shapes' * shapes: +DEAL::0.777777778 0.277777778 -0.222222222 +DEAL::0.444444444 0.444444444 0.444444444 +DEAL::-0.222222222 0.277777778 0.777777778 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -5.55111512e-17 +DEAL::-6.93889390e-17 1.00000000 +DEAL::Testing FE_DGQ<1>(3) with QGauss(2) +DEAL::shape values: +DEAL::0.131445856 0.0352208109 +DEAL::0.954581020 -0.121247687 +DEAL::-0.121247687 0.954581020 +DEAL::0.0352208109 0.131445856 +DEAL::inverse shape values: +DEAL::0.0188747757 0.981125224 +DEAL::1.48976241 -0.489762411 +DEAL::-0.489762411 1.48976241 +DEAL::0.981125224 0.0188747757 +DEAL::inverse shapes' * shapes: +DEAL::1.51851852 -0.518518519 +DEAL::-0.518518519 1.51851852 +DEAL::inverse shapes * shapes': +DEAL::0.0370370370 -0.100941661 0.934274995 0.129629630 +DEAL::0.178573266 1.48148148 -0.648148148 -0.0119065990 +DEAL::-0.0119065990 -0.648148148 1.48148148 0.178573266 +DEAL::0.129629630 0.934274995 -0.100941661 0.0370370370 +DEAL::Testing FE_DGQ<1>(3) with QGauss(4) +DEAL::shape values: +DEAL::0.629943166 -0.0706947953 -0.0348213172 0.0470015178 +DEAL::0.472558747 0.972976186 0.132539926 -0.149503431 +DEAL::-0.149503431 0.132539926 0.972976186 0.472558747 +DEAL::0.0470015178 -0.0348213172 -0.0706947953 0.629943166 +DEAL::inverse shape values: +DEAL::1.52678813 -0.813632449 0.400761520 -0.113917196 +DEAL::0.102442037 1.00158549 -0.136437118 0.0324095916 +DEAL::0.0324095916 -0.136437118 1.00158549 0.102442037 +DEAL::-0.113917196 0.400761520 -0.813632449 1.52678813 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 4.25007252e-17 0.00000000 -2.77555756e-17 +DEAL::6.93889390e-18 1.00000000 1.04083409e-17 5.55111512e-17 +DEAL::-6.24500451e-17 -9.02056208e-17 1.00000000 -1.11022302e-16 +DEAL::0.00000000 6.93889390e-18 0.00000000 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -3.26128013e-16 -1.73472348e-16 1.38777878e-17 +DEAL::-4.33680869e-18 1.00000000 5.20417043e-18 -3.46944695e-18 +DEAL::1.47451495e-17 -9.54097912e-17 1.00000000 2.77555756e-17 +DEAL::-2.77555756e-17 1.66533454e-16 2.22044605e-16 1.00000000 +DEAL::Testing FE_DGQ<1>(3) with QGauss(5) +DEAL::shape values: +DEAL::0.740028950 0.0864900503 -0.125000000 0.0259464471 0.0364234415 +DEAL::0.338258799 0.978118936 0.625000000 -0.0905554331 -0.114711190 +DEAL::-0.114711190 -0.0905554331 0.625000000 0.978118936 0.338258799 +DEAL::0.0364234415 0.0259464471 -0.125000000 0.0864900503 0.740028950 +DEAL::inverse shape values: +DEAL::1.28941203 -0.151162376 -0.426666667 0.474054364 -0.185637354 +DEAL::-0.0100043193 0.740467570 0.426666667 -0.230691563 0.0735616456 +DEAL::0.0735616456 -0.230691563 0.426666667 0.740467570 -0.0100043193 +DEAL::-0.185637354 0.474054364 -0.426666667 -0.151162376 1.28941203 +DEAL::inverse shapes' * shapes: +DEAL::0.935618289 0.0902578610 -0.0982485060 0.0902578610 -0.0643817113 +DEAL::0.182334732 0.744381711 0.278248506 -0.255618289 0.182334732 +DEAL::-0.235906041 0.330720856 0.640000000 0.330720856 -0.235906041 +DEAL::0.182334732 -0.255618289 0.278248506 0.744381711 0.182334732 +DEAL::-0.0643817113 0.0902578610 -0.0982485060 0.0902578610 0.935618289 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -1.73472348e-17 0.00000000 0.00000000 +DEAL::2.03830008e-17 1.00000000 -6.59194921e-17 6.93889390e-18 +DEAL::8.89045781e-18 -1.08637058e-16 1.00000000 -3.20923843e-17 +DEAL::-6.93889390e-17 3.33066907e-16 -3.33066907e-16 1.00000000 +DEAL::Testing FE_DGQ<1>(8) with QGauss(7) +DEAL::shape values: +DEAL::0.320613076 -0.0714863388 0.0198438864 0.00000000 -0.00838665716 0.0106096230 -0.00837135217 +DEAL::0.807029174 0.285033101 -0.0582666730 0.00000000 0.0220424240 -0.0274783254 0.0215412175 +DEAL::-0.188643039 0.902755372 0.136604120 0.00000000 -0.0342245986 0.0409438180 -0.0315417244 +DEAL::0.0983329399 -0.172433798 0.974484761 0.00000000 0.0541476004 -0.0590697461 0.0439117888 +DEAL::-0.0628720800 0.0911262946 -0.106244863 1.00000000 -0.106244863 0.0911262946 -0.0628720800 +DEAL::0.0439117888 -0.0590697461 0.0541476004 0.00000000 0.974484761 -0.172433798 0.0983329399 +DEAL::-0.0315417244 0.0409438180 -0.0342245986 0.00000000 0.136604120 0.902755372 -0.188643039 +DEAL::0.0215412175 -0.0274783254 0.0220424240 0.00000000 -0.0582666730 0.285033101 0.807029174 +DEAL::-0.00837135217 0.0106096230 -0.00838665716 0.00000000 0.0198438864 -0.0714863388 0.320613076 +DEAL::inverse shape values: +DEAL::1.40436954 -0.437558718 -0.176481446 0.514285714 -0.564535161 0.389097875 -0.129177808 +DEAL::0.668362110 0.366095901 0.0496221594 -0.210697944 0.234910897 -0.162082835 0.0537897112 +DEAL::-0.117649885 1.00952994 0.0470878798 0.163587989 -0.190501703 0.131499528 -0.0435537463 +DEAL::0.0622829176 -0.219150674 1.20128085 -0.145628507 0.186894410 -0.127620862 0.0419418640 +DEAL::-0.0465644803 0.145788119 -0.232036139 1.26562500 -0.232036139 0.145788119 -0.0465644803 +DEAL::0.0419418640 -0.127620862 0.186894410 -0.145628507 1.20128085 -0.219150674 0.0622829176 +DEAL::-0.0435537463 0.131499528 -0.190501703 0.163587989 0.0470878798 1.00952994 -0.117649885 +DEAL::0.0537897112 -0.162082835 0.234910897 -0.210697944 0.0496221594 0.366095901 0.668362110 +DEAL::-0.129177808 0.389097875 -0.564535161 0.514285714 -0.176481446 -0.437558718 1.40436954 +DEAL::inverse shapes' * shapes: +DEAL::1.02634845 -0.0381892370 0.0445251315 -0.0465644803 0.0445251315 -0.0381892370 0.0263484516 +DEAL::-0.0824940207 1.11956618 -0.139403149 0.145788119 -0.139403149 0.119566180 -0.0824940207 +DEAL::0.131297352 -0.190301342 1.22187383 -0.232036139 0.221873830 -0.190301342 0.131297352 +DEAL::-0.150303566 0.217848798 -0.253991626 1.26562500 -0.253991626 0.217848798 -0.150303566 +DEAL::0.131297352 -0.190301342 0.221873830 -0.232036139 1.22187383 -0.190301342 0.131297352 +DEAL::-0.0824940207 0.119566180 -0.139403149 0.145788119 -0.139403149 1.11956618 -0.0824940207 +DEAL::0.0263484516 -0.0381892370 0.0445251315 -0.0465644803 0.0445251315 -0.0381892370 1.02634845 +DEAL::inverse shapes * shapes': +DEAL::0.487980769 0.993013332 -0.644714481 -0.0176573481 0.508424908 -0.551968155 0.242339308 0.0779342319 -0.0953525641 +DEAL::0.184959425 0.651636320 0.194819131 0.0756067985 -0.267740352 0.272565653 -0.132168636 -0.0110451593 0.0313668192 +DEAL::-0.105595847 0.181308198 0.953262501 -0.159754896 0.292937966 -0.274847936 0.144338025 -0.0158041081 -0.0158439038 +DEAL::0.0562005392 -0.0736658109 -0.0584333636 1.23404349 -0.331267831 0.288982775 -0.149642644 0.0204251078 0.0133577407 +DEAL::-0.0260729667 0.00737181150 0.124077170 -0.279053900 1.34735577 -0.279053900 0.124077170 0.00737181150 -0.0260729667 +DEAL::0.0133577407 0.0204251078 -0.149642644 0.288982775 -0.331267831 1.23404349 -0.0584333636 -0.0736658109 0.0562005392 +DEAL::-0.0158439038 -0.0158041081 0.144338025 -0.274847936 0.292937966 -0.159754896 0.953262501 0.181308198 -0.105595847 +DEAL::0.0313668192 -0.0110451593 -0.132168636 0.272565653 -0.267740352 0.0756067985 0.194819131 0.651636320 0.184959425 +DEAL::-0.0953525641 0.0779342319 0.242339308 -0.551968155 0.508424908 -0.0176573481 -0.644714481 0.993013332 0.487980769 +DEAL::Testing FE_DGQ<1>(8) with QGauss(9) +DEAL::shape values: +DEAL::0.524442912 -0.129284795 0.0482092238 -0.0159529856 0.00000000 0.00814056828 -0.0115528655 0.0115459290 -0.00848413477 +DEAL::0.595856699 0.811952022 -0.158860383 0.0457215782 0.00000000 -0.0214973299 0.0300671432 -0.0298095982 0.0218199783 +DEAL::-0.180412629 0.419554984 0.918238283 -0.0960255456 0.00000000 0.0338418479 -0.0454045835 0.0440413517 -0.0319053624 +DEAL::0.0974630497 -0.158301539 0.263027508 0.979571052 0.00000000 -0.0553850762 0.0674085266 -0.0624300935 0.0442952766 +DEAL::-0.0630757895 0.0927317390 -0.111132852 0.121585891 1.00000000 0.121585891 -0.111132852 0.0927317390 -0.0630757895 +DEAL::0.0442952766 -0.0624300935 0.0674085266 -0.0553850762 0.00000000 0.979571052 0.263027508 -0.158301539 0.0974630497 +DEAL::-0.0319053624 0.0440413517 -0.0454045835 0.0338418479 0.00000000 -0.0960255456 0.918238283 0.419554984 -0.180412629 +DEAL::0.0218199783 -0.0298095982 0.0300671432 -0.0214973299 0.00000000 0.0457215782 -0.158860383 0.811952022 0.595856699 +DEAL::-0.00848413477 0.0115459290 -0.0115528655 0.00814056828 0.00000000 -0.0159529856 0.0482092238 -0.129284795 0.524442912 +DEAL::inverse shape values: +DEAL::1.58491942 -1.00568289 0.737396941 -0.553219335 0.406349206 -0.282299494 0.176709911 -0.0898136794 0.0256399118 +DEAL::0.271949448 0.953852810 -0.366964613 0.239449524 -0.166477388 0.112584159 -0.0694545570 0.0350192723 -0.00995865459 +DEAL::-0.0373575132 0.223616862 0.962340237 -0.228162474 0.129254707 -0.0804102667 0.0475853146 -0.0234734165 0.00660654971 +DEAL::0.00857590523 -0.0358533510 0.117139501 0.989059293 -0.115064499 0.0559215426 -0.0300204387 0.0141396481 -0.00389760115 +DEAL::0.00000000 0.00000000 0.00000000 0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +DEAL::-0.00389760115 0.0141396481 -0.0300204387 0.0559215426 -0.115064499 0.989059293 0.117139501 -0.0358533510 0.00857590523 +DEAL::0.00660654971 -0.0234734165 0.0475853146 -0.0804102667 0.129254707 -0.228162474 0.962340237 0.223616862 -0.0373575132 +DEAL::-0.00995865459 0.0350192723 -0.0694545570 0.112584159 -0.166477388 0.239449524 -0.366964613 0.953852810 0.271949448 +DEAL::0.0256399118 -0.0898136794 0.176709911 -0.282299494 0.406349206 -0.553219335 0.737396941 -1.00568289 1.58491942 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 5.69206141e-17 -1.08962318e-17 -2.76471554e-18 0.00000000 -4.87890978e-19 -1.30104261e-18 0.00000000 3.46944695e-18 +DEAL::4.40186082e-17 1.00000000 -9.56266316e-17 1.29020059e-17 0.00000000 -2.16840434e-18 9.54097912e-18 0.00000000 0.00000000 +DEAL::-2.08166817e-17 -6.28837260e-17 1.00000000 -1.92987987e-17 0.00000000 -1.30104261e-18 5.20417043e-18 1.04083409e-17 1.38777878e-17 +DEAL::2.81892565e-17 7.50267903e-17 -8.97719399e-17 1.00000000 0.00000000 2.16840434e-17 -4.33680869e-17 2.77555756e-17 -5.55111512e-17 +DEAL::-2.21177243e-17 -1.73472348e-17 -1.73472348e-18 9.97465999e-18 1.00000000 -1.82145965e-17 -1.04083409e-17 -6.93889390e-18 5.55111512e-17 +DEAL::5.29090660e-17 3.12250226e-17 -2.34187669e-17 1.38777878e-17 0.00000000 1.00000000 -5.20417043e-17 4.16333634e-17 -5.55111512e-17 +DEAL::-1.21430643e-17 5.20417043e-18 1.73472348e-17 1.73472348e-18 0.00000000 -1.21430643e-17 1.00000000 -2.77555756e-17 1.66533454e-16 +DEAL::1.21430643e-17 -3.46944695e-18 0.00000000 -1.73472348e-18 0.00000000 1.04083409e-17 -4.85722573e-17 1.00000000 -1.11022302e-16 +DEAL::-3.46944695e-18 3.46944695e-18 -1.04083409e-17 0.00000000 0.00000000 -6.93889390e-18 2.77555756e-17 -2.77555756e-17 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -1.33790548e-16 -3.12250226e-17 6.04984812e-17 -2.03830008e-17 3.42607887e-17 -3.55618313e-17 1.90819582e-17 -1.04083409e-17 +DEAL::1.85669622e-17 1.00000000 -1.74014449e-17 3.27429056e-17 -1.98408998e-17 3.74049750e-17 -5.20417043e-18 1.12757026e-17 -8.67361738e-19 +DEAL::8.36868552e-18 -5.75711354e-17 1.00000000 9.75781955e-18 -1.02999206e-17 -2.29850861e-17 1.30104261e-17 -4.33680869e-18 0.00000000 +DEAL::-1.70761842e-18 -1.36609474e-17 -1.57209315e-18 1.00000000 -8.07730619e-18 1.69135539e-17 -7.91467586e-18 4.77048956e-18 -2.16840434e-18 +DEAL::0.00000000 0.00000000 0.00000000 0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +DEAL::-1.19262239e-18 2.95445092e-18 -3.79470760e-19 -1.24683250e-18 -2.49366500e-18 1.00000000 -1.32272665e-17 -2.60208521e-18 -8.67361738e-19 +DEAL::-2.49366500e-18 -3.90312782e-18 -4.77048956e-18 -2.55871713e-17 -1.77809156e-17 -5.85469173e-17 1.00000000 -1.38777878e-17 6.93889390e-18 +DEAL::3.03576608e-18 -6.07153217e-18 3.29597460e-17 1.73472348e-18 0.00000000 4.51028104e-17 -2.08166817e-17 1.00000000 -2.77555756e-17 +DEAL::-6.93889390e-18 1.38777878e-17 -3.46944695e-17 -2.77555756e-17 5.55111512e-17 -1.11022302e-16 0.00000000 -1.11022302e-16 1.00000000 +DEAL::Testing FE_DGQ<1>(8) with QGauss(12) +DEAL::shape values: +DEAL::0.702031429 0.0186036035 -0.102052536 0.0585894230 0.00211090276 -0.0321525333 0.0249956691 -0.000975592561 -0.0152324888 0.0132674050 -0.000936793434 -0.00653273690 +DEAL::0.386259687 0.998777666 0.441387251 -0.188891438 -0.00612341396 0.0886372636 -0.0669778690 0.00256960645 0.0396867750 -0.0343282227 0.00241365498 0.0167951676 +DEAL::-0.133704961 -0.0247113682 0.796217803 0.845826317 0.0135611742 -0.160198496 0.110194230 -0.00401449063 -0.0601128826 0.0510144479 -0.00354629885 -0.0245344006 +DEAL::0.0739198029 0.0116439007 -0.203858245 0.380852053 0.999692252 0.417541951 -0.203391820 0.00644721407 0.0898401043 -0.0731906843 0.00497094007 0.0339971308 +DEAL::-0.0482311177 -0.00721530500 0.111542781 -0.150557864 -0.0132676525 0.821351604 0.821351604 -0.0132676525 -0.150557864 0.111542781 -0.00721530500 -0.0482311177 +DEAL::0.0339971308 0.00497094007 -0.0731906843 0.0898401043 0.00644721407 -0.203391820 0.417541951 0.999692252 0.380852053 -0.203858245 0.0116439007 0.0739198029 +DEAL::-0.0245344006 -0.00354629885 0.0510144479 -0.0601128826 -0.00401449063 0.110194230 -0.160198496 0.0135611742 0.845826317 0.796217803 -0.0247113682 -0.133704961 +DEAL::0.0167951676 0.00241365498 -0.0343282227 0.0396867750 0.00256960645 -0.0669778690 0.0886372636 -0.00612341396 -0.188891438 0.441387251 0.998777666 0.386259687 +DEAL::-0.00653273690 -0.000936793434 0.0132674050 -0.0152324888 -0.000975592561 0.0249956691 -0.0321525333 0.00211090276 0.0585894230 -0.102052536 0.0186036035 0.702031429 +DEAL::inverse shape values: +DEAL::1.28488812 -0.124805733 -0.499584932 0.593051903 -0.279509195 -0.140378802 0.372200207 -0.305453446 0.0531164203 0.164983111 -0.200032661 0.0815250121 +DEAL::0.0721600049 0.725861264 0.390671631 -0.299294449 0.113142319 0.0728031330 -0.161469600 0.125407046 -0.0186844856 -0.0694726128 0.0820335776 -0.0331578288 +DEAL::0.00648599228 -0.0721064253 0.492418396 0.678272631 -0.0830188524 -0.0983028592 0.147081657 -0.0979667864 0.00784865156 0.0579044199 -0.0638621299 0.0252453063 +DEAL::-0.0161606609 0.0592156877 -0.119266640 0.176766938 0.757963839 0.258380393 -0.188187397 0.0885174861 0.00609926195 -0.0588875315 0.0571558055 -0.0215971808 +DEAL::0.0192013185 -0.0557871603 0.0722671610 -0.0373455007 -0.0896185414 0.591282723 0.591282723 -0.0896185414 -0.0373455007 0.0722671610 -0.0557871603 0.0192013185 +DEAL::-0.0215971808 0.0571558055 -0.0588875315 0.00609926195 0.0885174861 -0.188187397 0.258380393 0.757963839 0.176766938 -0.119266640 0.0592156877 -0.0161606609 +DEAL::0.0252453063 -0.0638621299 0.0579044199 0.00784865156 -0.0979667864 0.147081657 -0.0983028592 -0.0830188524 0.678272631 0.492418396 -0.0721064253 0.00648599228 +DEAL::-0.0331578288 0.0820335776 -0.0694726128 -0.0186844856 0.125407046 -0.161469600 0.0728031330 0.113142319 -0.299294449 0.390671631 0.725861264 0.0721600049 +DEAL::0.0815250121 -0.200032661 0.164983111 0.0531164203 -0.305453446 0.372200207 -0.140378802 -0.279509195 0.593051903 -0.499584932 -0.124805733 1.28488812 +DEAL::inverse shapes' * shapes: +DEAL::0.924473344 0.0951350668 -0.0835866069 0.0520751215 -0.0144574044 -0.0154989189 0.0284339698 -0.0223261379 0.00272662466 0.0197737125 -0.0337473450 0.0306371624 +DEAL::0.215656754 0.726422037 0.244504824 -0.159182710 0.0552823933 0.0296500318 -0.0697484632 0.0587459442 -0.0107017439 -0.0466859679 0.0832770998 -0.0765001081 +DEAL::-0.283631350 0.366001218 0.659705797 0.243090674 -0.117909390 0.00849918782 0.0538957578 -0.0595237826 0.0212571049 0.0324792497 -0.0698845970 0.0670974091 +DEAL::0.224269062 -0.302421409 0.308524628 0.736451810 0.189398760 -0.108917729 0.0409102145 0.00399493461 -0.0245782798 0.0269789880 -0.0203315829 0.0117426045 +DEAL::-0.0715563742 0.120704204 -0.171984321 0.217668736 0.758095161 0.230354800 -0.177893991 0.0927214781 0.00459122522 -0.0868222396 0.128266560 -0.110502372 +DEAL::-0.0818544215 0.0690785899 0.0132281962 -0.133567328 0.245798939 0.694851851 0.285463290 -0.189820896 0.0501687660 0.0838837396 -0.162499842 0.150168290 +DEAL::0.150168290 -0.162499842 0.0838837396 0.0501687660 -0.189820896 0.285463290 0.694851851 0.245798939 -0.133567328 0.0132281962 0.0690785899 -0.0818544215 +DEAL::-0.110502372 0.128266560 -0.0868222396 0.00459122522 0.0927214781 -0.177893991 0.230354800 0.758095161 0.217668736 -0.171984321 0.120704204 -0.0715563742 +DEAL::0.0117426045 -0.0203315829 0.0269789880 -0.0245782798 0.00399493461 0.0409102145 -0.108917729 0.189398760 0.736451810 0.308524628 -0.302421409 0.224269062 +DEAL::0.0670974091 -0.0698845970 0.0324792497 0.0212571049 -0.0595237826 0.0538957578 0.00849918782 -0.117909390 0.243090674 0.659705797 0.366001218 -0.283631350 +DEAL::-0.0765001081 0.0832770998 -0.0466859679 -0.0107017439 0.0587459442 -0.0697484632 0.0296500318 0.0552823933 -0.159182710 0.244504824 0.726422037 0.215656754 +DEAL::0.0306371624 -0.0337473450 0.0197737125 0.00272662466 -0.0223261379 0.0284339698 -0.0154989189 -0.0144574044 0.0520751215 -0.0835866069 0.0951350668 0.924473344 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -3.53016227e-16 1.17961196e-16 7.94069671e-16 -5.81132364e-16 5.17814958e-16 -2.42861287e-17 1.38777878e-17 5.55111512e-16 +DEAL::-4.74338450e-17 1.00000000 2.54787511e-17 -3.46727855e-16 2.25947733e-16 -2.31585584e-16 3.38271078e-17 -3.46944695e-18 -2.22044605e-16 +DEAL::2.94631940e-17 2.00035301e-17 1.00000000 3.62340366e-16 -1.44632570e-16 2.31151903e-16 -2.64545330e-17 3.46944695e-18 1.70002901e-16 +DEAL::2.90566182e-17 -6.03900610e-17 3.69062420e-16 1.00000000 -6.13658430e-17 -1.65882932e-16 -2.42861287e-17 1.90819582e-17 -1.68268177e-16 +DEAL::6.80336863e-18 -2.75929453e-17 -2.10335221e-17 -1.25225351e-16 1.00000000 4.96130914e-16 -9.80118764e-17 -4.33680869e-18 1.47451495e-16 +DEAL::3.28513258e-17 -9.40545385e-17 1.96945325e-16 -2.32452946e-16 6.90745204e-16 1.00000000 -3.88144378e-16 2.34187669e-16 -2.32452946e-16 +DEAL::-1.72252620e-17 3.43556563e-17 -1.31540829e-16 8.00954355e-17 -2.92463536e-16 -3.49546780e-16 1.00000000 -2.35055031e-16 2.32452946e-16 +DEAL::3.46944695e-18 -1.84314369e-17 1.35091591e-16 -8.50014503e-17 2.35488712e-16 3.84241250e-16 -3.22658567e-16 1.00000000 -3.05311332e-16 +DEAL::1.38777878e-17 -3.46944695e-18 -2.15105711e-16 1.17961196e-16 -6.03683770e-16 -8.46545056e-16 5.27355937e-16 -2.77555756e-16 1.00000000 +DEAL::Testing FE_DGQHermite<1>(1) with QGauss(2) +DEAL::shape values: +DEAL::0.788675135 0.211324865 +DEAL::0.211324865 0.788675135 +DEAL::inverse shape values: +DEAL::1.36602540 -0.366025404 +DEAL::-0.366025404 1.36602540 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 1.11022302e-16 +DEAL::0.00000000 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 0.00000000 +DEAL::1.11022302e-16 1.00000000 +DEAL::Testing FE_DGQHermite<1>(1) with QGauss(3) +DEAL::shape values: +DEAL::0.887298335 0.500000000 0.112701665 +DEAL::0.112701665 0.500000000 0.887298335 +DEAL::inverse shape values: +DEAL::0.923275002 0.444444444 -0.367719447 +DEAL::-0.367719447 0.444444444 0.923275002 +DEAL::inverse shapes' * shapes: +DEAL::0.777777778 0.277777778 -0.222222222 +DEAL::0.444444444 0.444444444 0.444444444 +DEAL::-0.222222222 0.277777778 0.777777778 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 5.55111512e-17 +DEAL::-4.16333634e-17 1.00000000 +DEAL::Testing FE_DGQHermite<1>(3) with QGauss(2) +DEAL::shape values: +DEAL::0.161947973 -0.0786146394 +DEAL::0.722952207 0.193714460 +DEAL::0.193714460 0.722952207 +DEAL::-0.0786146394 0.161947973 +DEAL::inverse shape values: +DEAL::0.0188747757 0.981125224 +DEAL::2.64319418 -1.64319418 +DEAL::-1.64319418 2.64319418 +DEAL::0.981125224 0.0188747757 +DEAL::inverse shapes' * shapes: +DEAL::1.51851852 -0.518518519 +DEAL::-0.518518519 1.51851852 +DEAL::inverse shapes * shapes': +DEAL::-0.0740740741 0.203703704 0.712962963 0.157407407 +DEAL::0.557239057 1.59259259 -0.675925926 -0.473905724 +DEAL::-0.473905724 -0.675925926 1.59259259 0.557239057 +DEAL::0.157407407 0.712962963 0.203703704 -0.0740740741 +DEAL::Testing FE_DGQHermite<1>(3) with QGauss(4) +DEAL::shape values: +DEAL::0.655519600 -0.0695924227 -0.146475301 -0.0108804475 +DEAL::0.330687489 0.814753849 0.401313875 0.0246733590 +DEAL::0.0246733590 0.401313875 0.814753849 0.330687489 +DEAL::-0.0108804475 -0.146475301 -0.0695924227 0.655519600 +DEAL::inverse shape values: +DEAL::1.52678813 -0.813632449 0.400761520 -0.113917196 +DEAL::-0.0270343487 1.69676154 -0.947796738 0.278069550 +DEAL::0.278069550 -0.947796738 1.69676154 -0.0270343487 +DEAL::-0.113917196 0.400761520 -0.813632449 1.52678813 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 2.77555756e-17 -6.24500451e-17 1.38777878e-17 +DEAL::-6.62664368e-16 1.00000000 -4.30211422e-16 0.00000000 +DEAL::3.46944695e-16 1.17961196e-15 1.00000000 -1.11022302e-16 +DEAL::-6.59194921e-17 -3.33066907e-16 2.22044605e-16 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 1.33573708e-16 -2.63677968e-16 2.22044605e-16 +DEAL::-1.09287579e-16 1.00000000 6.10622664e-16 -3.88578059e-16 +DEAL::2.07299455e-16 -8.64109131e-17 1.00000000 4.47558657e-16 +DEAL::-3.81639165e-17 -2.08166817e-17 0.00000000 1.00000000 +DEAL::Testing FE_DGQHermite<1>(3) with QGauss(5) +DEAL::shape values: +DEAL::0.759237720 0.113800731 -0.187500000 -0.0901205841 -0.00514008955 +DEAL::0.234367070 0.751019065 0.687500000 0.225300788 0.0115352991 +DEAL::0.0115352991 0.225300788 0.687500000 0.751019065 0.234367070 +DEAL::-0.00514008955 -0.0901205841 -0.187500000 0.113800731 0.759237720 +DEAL::inverse shape values: +DEAL::1.28941203 -0.151162376 -0.426666667 0.474054364 -0.185637354 +DEAL::-0.207017818 1.31873094 0.349090909 -0.825944389 0.365140358 +DEAL::0.365140358 -0.825944389 0.349090909 1.31873094 -0.207017818 +DEAL::-0.185637354 0.474054364 -0.426666667 -0.151162376 1.28941203 +DEAL::inverse shapes' * shapes: +DEAL::0.935618289 0.0902578610 -0.0982485060 0.0902578610 -0.0643817113 +DEAL::0.182334732 0.744381711 0.278248506 -0.255618289 0.182334732 +DEAL::-0.235906041 0.330720856 0.640000000 0.330720856 -0.235906041 +DEAL::0.182334732 -0.255618289 0.278248506 0.744381711 0.182334732 +DEAL::-0.0643817113 0.0902578610 -0.0982485060 0.0902578610 0.935618289 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 5.01335085e-16 7.63278329e-17 8.32667268e-17 +DEAL::-6.72205347e-18 1.00000000 1.38777878e-16 -2.22044605e-16 +DEAL::1.73038667e-16 6.11923706e-16 1.00000000 2.22044605e-16 +DEAL::-9.54097912e-18 -2.06432094e-16 -1.66533454e-16 1.00000000 +DEAL::Testing FE_DGQHermite<1>(8) with QGauss(7) +DEAL::shape values: +DEAL::0.303602615 -0.0772560446 0.0244110344 0.00000000 -0.0114539402 0.0171629335 0.00865284609 +DEAL::0.613880272 0.215536663 -0.0512200702 0.00000000 0.0216472298 -0.0319888075 -0.0160286911 +DEAL::0.131737430 1.00974065 0.127270528 0.00000000 -0.0320103749 0.0447465155 0.0218935297 +DEAL::-0.0830590508 -0.228145975 0.988337808 0.00000000 0.0627230791 -0.0797464923 -0.0376162159 +DEAL::0.0569372647 0.129950554 -0.129705294 1.00000000 -0.129705294 0.129950554 0.0569372647 +DEAL::-0.0376162159 -0.0797464923 0.0627230791 0.00000000 0.988337808 -0.228145975 -0.0830590508 +DEAL::0.0218935297 0.0447465155 -0.0320103749 0.00000000 0.127270528 1.00974065 0.131737430 +DEAL::-0.0160286911 -0.0319888075 0.0216472298 0.00000000 -0.0512200702 0.215536663 0.613880272 +DEAL::0.00865284609 0.0171629335 -0.0114539402 0.00000000 0.0244110344 -0.0772560446 0.303602615 +DEAL::inverse shape values: 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0.0902578610 -0.0643817113 +DEAL::0.182334732 0.744381711 0.278248506 -0.255618289 0.182334732 +DEAL::-0.235906041 0.330720856 0.640000000 0.330720856 -0.235906041 +DEAL::0.182334732 -0.255618289 0.278248506 0.744381711 0.182334732 +DEAL::-0.0643817113 0.0902578610 -0.0982485060 0.0902578610 0.935618289 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -6.93889390e-17 -4.16333634e-17 0.00000000 +DEAL::1.34441069e-17 1.00000000 -1.00613962e-16 6.93889390e-18 +DEAL::1.24141149e-17 -1.22514845e-16 1.00000000 -2.34187669e-17 +DEAL::-6.93889390e-17 3.60822483e-16 -2.77555756e-16 1.00000000 +DEAL::Testing FE_Q<2>(3) with QGauss(4) +DEAL::shape values: +DEAL::0.629943166 -0.0706947953 -0.0348213172 0.0470015178 +DEAL::0.472558747 0.972976186 0.132539926 -0.149503431 +DEAL::-0.149503431 0.132539926 0.972976186 0.472558747 +DEAL::0.0470015178 -0.0348213172 -0.0706947953 0.629943166 +DEAL::inverse shape values: +DEAL::1.52678813 -0.813632449 0.400761520 -0.113917196 +DEAL::0.102442037 1.00158549 -0.136437118 0.0324095916 +DEAL::0.0324095916 -0.136437118 1.00158549 0.102442037 +DEAL::-0.113917196 0.400761520 -0.813632449 1.52678813 +DEAL::inverse shapes' * shapes: +DEAL::1.00000000 5.46437895e-17 5.20417043e-18 -2.77555756e-17 +DEAL::5.55111512e-17 1.00000000 1.38777878e-17 5.55111512e-17 +DEAL::-2.77555756e-17 -1.24900090e-16 1.00000000 0.00000000 +DEAL::0.00000000 6.93889390e-18 0.00000000 1.00000000 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -2.25514052e-16 -1.66533454e-16 1.38777878e-17 +DEAL::-5.42101086e-18 1.00000000 3.46944695e-18 -3.46944695e-18 +DEAL::1.38777878e-17 -1.19695920e-16 1.00000000 2.77555756e-17 +DEAL::-2.77555756e-17 2.22044605e-16 3.33066907e-16 1.00000000 +DEAL::Testing FE_Q<2>(3) with QGauss(5) +DEAL::shape values: +DEAL::0.740028950 0.0864900503 -0.125000000 0.0259464471 0.0364234415 +DEAL::0.338258799 0.978118936 0.625000000 -0.0905554331 -0.114711190 +DEAL::-0.114711190 -0.0905554331 0.625000000 0.978118936 0.338258799 +DEAL::0.0364234415 0.0259464471 -0.125000000 0.0864900503 0.740028950 +DEAL::inverse shape values: +DEAL::1.28941203 -0.151162376 -0.426666667 0.474054364 -0.185637354 +DEAL::-0.0100043193 0.740467570 0.426666667 -0.230691563 0.0735616456 +DEAL::0.0735616456 -0.230691563 0.426666667 0.740467570 -0.0100043193 +DEAL::-0.185637354 0.474054364 -0.426666667 -0.151162376 1.28941203 +DEAL::inverse shapes' * shapes: +DEAL::0.935618289 0.0902578610 -0.0982485060 0.0902578610 -0.0643817113 +DEAL::0.182334732 0.744381711 0.278248506 -0.255618289 0.182334732 +DEAL::-0.235906041 0.330720856 0.640000000 0.330720856 -0.235906041 +DEAL::0.182334732 -0.255618289 0.278248506 0.744381711 0.182334732 +DEAL::-0.0643817113 0.0902578610 -0.0982485060 0.0902578610 0.935618289 +DEAL::inverse shapes * shapes': +DEAL::1.00000000 -6.93889390e-17 -4.16333634e-17 0.00000000 +DEAL::1.34441069e-17 1.00000000 -1.00613962e-16 6.93889390e-18 +DEAL::1.24141149e-17 -1.22514845e-16 1.00000000 -2.34187669e-17 +DEAL::-6.93889390e-17 3.60822483e-16 -2.77555756e-16 1.00000000