From f45973fc2990458435122869e2ff3ebf7ef21cd9 Mon Sep 17 00:00:00 2001 From: Luca Heltai Date: Thu, 21 Dec 2017 17:32:01 +0100 Subject: [PATCH] Test singular integration on vertices. --- tests/base/quadrature_simplex_06.cc | 89 ++ tests/base/quadrature_simplex_06.output | 1018 +++++++++++++++++++++++ tests/base/simplex.h | 184 ++++ 3 files changed, 1291 insertions(+) create mode 100644 tests/base/quadrature_simplex_06.cc create mode 100644 tests/base/quadrature_simplex_06.output diff --git a/tests/base/quadrature_simplex_06.cc b/tests/base/quadrature_simplex_06.cc new file mode 100644 index 0000000000..67338b412c --- /dev/null +++ b/tests/base/quadrature_simplex_06.cc @@ -0,0 +1,89 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2017 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 at +// the top level of the deal.II distribution. +// +// --------------------------------------------------------------------- + +// integrates the function *f(x,y)/R, where f(x,y) is a power of x and +// y on the set [0,1]x[0,1]. dim = 2 only. + +#include "../tests.h" +#include + +// all include files needed for the program +#include +#include +#include "simplex.h" + + +int main() +{ + initlog(); + + deallog << std::endl + << "Calculation of the integral of f(x,y)*1/R on [0,1]x[0,1]" << std::endl + << "for f(x,y) = x^i y^j, with i,j ranging from 0 to 5, and R being" << std::endl + << "the distance from (x,y) to four vertices of the square." << std::endl + << std::endl; + + double eps = 1e-10; + + // index m i j + double error[4][6][6][6] = {{{{0}}}}; + + for (unsigned int m=0; m<6; ++m) + { + for (unsigned int index=0; index<4; ++index) + { + auto split_point = GeometryInfo<2>::unit_cell_vertex(index); + + QSplit<2> quad(QTrianglePolar(m+1), split_point); + + for (unsigned int i=0; i<6; ++i) + for (unsigned int j=0; j<6; ++j) + { + double exact_integral = exact_integral_one_over_r(index, i,j); + double approx_integral = 0; + + for (unsigned int q=0; q< quad.size(); ++q) + { + double x = quad.point(q)[0]; + double y = quad.point(q)[1]; + approx_integral += ( pow(x, (double)i) * + pow(y, (double)j) * + quad.weight(q) / + (quad.point(q)-split_point).norm()); + } + error[index][m][i][j] = approx_integral - exact_integral; + } + } + } + + + // Now output the results. + for (unsigned int index=0; index<4; ++index) + { + deallog << " ===============Vertex Index: " << index + << " ==============================" << std::endl; + for (unsigned int i=0; i<6; ++i) + for (unsigned int j=0; j<6; ++j) + { + deallog << "======= f(x,y) = x^" << i + << " y^" << j << std::endl; + + for (unsigned int m=0; m<6; ++m) + deallog << "Order[" << m + 1 << "], error = " + << error[index][m][i][j] << std::endl; + } + } +} + diff --git a/tests/base/quadrature_simplex_06.output b/tests/base/quadrature_simplex_06.output new file mode 100644 index 0000000000..526a017ec1 --- /dev/null +++ b/tests/base/quadrature_simplex_06.output @@ -0,0 +1,1018 @@ + +DEAL:: +DEAL::Calculation of the integral of f(x,y)*1/R on [0,1]x[0,1] +DEAL::for f(x,y) = x^i y^j, with i,j ranging from 0 to 5, and R being +DEAL::the distance from (x,y) to four vertices of the square. +DEAL:: +DEAL:: ===============Vertex Index: 0 ============================== +DEAL::======= f(x,y) = x^0 y^0 +DEAL::Order[1], error = -0.357784 +DEAL::Order[2], error = -0.0413770 +DEAL::Order[3], error = -0.00349564 +DEAL::Order[4], error = -0.000233484 +DEAL::Order[5], error = -1.19260e-05 +DEAL::Order[6], error = -3.91498e-07 +DEAL::======= f(x,y) = x^0 y^1 +DEAL::Order[1], error = -0.120932 +DEAL::Order[2], error = -0.0121220 +DEAL::Order[3], error = -0.000828723 +DEAL::Order[4], error = -3.88017e-05 +DEAL::Order[5], error = -7.85203e-07 +DEAL::Order[6], error = 4.39204e-08 +DEAL::======= f(x,y) = x^0 y^2 +DEAL::Order[1], error = -0.163072 +DEAL::Order[2], error = -0.0135078 +DEAL::Order[3], error = -0.00165252 +DEAL::Order[4], error = -0.000183000 +DEAL::Order[5], error = -1.90192e-05 +DEAL::Order[6], error = -1.88270e-06 +DEAL::======= f(x,y) = x^0 y^3 +DEAL::Order[1], error = -0.170372 +DEAL::Order[2], error = -0.0119124 +DEAL::Order[3], error = -0.00151573 +DEAL::Order[4], error = -0.000165201 +DEAL::Order[5], error = -1.62581e-05 +DEAL::Order[6], error = -1.49708e-06 +DEAL::======= f(x,y) = x^0 y^4 +DEAL::Order[1], error = -0.160373 +DEAL::Order[2], error = -0.0160819 +DEAL::Order[3], error = -0.00157738 +DEAL::Order[4], error = -0.000211312 +DEAL::Order[5], error = -2.67349e-05 +DEAL::Order[6], error = -3.25021e-06 +DEAL::======= f(x,y) = x^0 y^5 +DEAL::Order[1], error = -0.145363 +DEAL::Order[2], error = -0.0228780 +DEAL::Order[3], error = -0.00168236 +DEAL::Order[4], error = -0.000261625 +DEAL::Order[5], error = -3.71252e-05 +DEAL::Order[6], error = -4.86539e-06 +DEAL::======= f(x,y) = x^1 y^0 +DEAL::Order[1], error = -0.120932 +DEAL::Order[2], error = -0.0121220 +DEAL::Order[3], error = -0.000828723 +DEAL::Order[4], error = -3.88017e-05 +DEAL::Order[5], error = -7.85203e-07 +DEAL::Order[6], error = 4.39204e-08 +DEAL::======= f(x,y) = x^1 y^1 +DEAL::Order[1], error = -0.100522 +DEAL::Order[2], error = -0.00237035 +DEAL::Order[3], error = 6.02499e-05 +DEAL::Order[4], error = 2.60924e-05 +DEAL::Order[5], error = 2.92841e-06 +DEAL::Order[6], error = 1.89060e-07 +DEAL::======= f(x,y) = x^1 y^2 +DEAL::Order[1], error = -0.104301 +DEAL::Order[2], error = -0.00584758 +DEAL::Order[3], error = -0.000779842 +DEAL::Order[4], error = -9.82802e-05 +DEAL::Order[5], error = -1.16755e-05 +DEAL::Order[6], error = -1.29219e-06 +DEAL::======= f(x,y) = x^1 y^3 +DEAL::Order[1], error = -0.0944545 +DEAL::Order[2], error = -0.00931973 +DEAL::Order[3], error = -0.000844945 +DEAL::Order[4], error = -0.000100985 +DEAL::Order[5], error = -1.09354e-05 +DEAL::Order[6], error = -1.10179e-06 +DEAL::======= f(x,y) = x^1 y^4 +DEAL::Order[1], error = -0.0823104 +DEAL::Order[2], error = -0.0133881 +DEAL::Order[3], error = -0.00100812 +DEAL::Order[4], error = -0.000150114 +DEAL::Order[5], error = -2.05532e-05 +DEAL::Order[6], error = -2.62862e-06 +DEAL::======= f(x,y) = x^1 y^5 +DEAL::Order[1], error = -0.0714326 +DEAL::Order[2], error = -0.0170943 +DEAL::Order[3], error = -0.00136963 +DEAL::Order[4], error = -0.000201982 +DEAL::Order[5], error = -3.03423e-05 +DEAL::Order[6], error = -4.10185e-06 +DEAL::======= f(x,y) = x^2 y^0 +DEAL::Order[1], error = -0.163072 +DEAL::Order[2], error = -0.0135078 +DEAL::Order[3], error = -0.00165252 +DEAL::Order[4], error = -0.000183000 +DEAL::Order[5], error = -1.90192e-05 +DEAL::Order[6], error = -1.88270e-06 +DEAL::======= f(x,y) = x^2 y^1 +DEAL::Order[1], error = -0.104301 +DEAL::Order[2], error = -0.00584758 +DEAL::Order[3], error = -0.000779842 +DEAL::Order[4], error = -9.82802e-05 +DEAL::Order[5], error = -1.16755e-05 +DEAL::Order[6], error = -1.29219e-06 +DEAL::======= f(x,y) = x^2 y^2 +DEAL::Order[1], error = -0.0846154 +DEAL::Order[2], error = -0.0106738 +DEAL::Order[3], error = -0.00128390 +DEAL::Order[4], error = -0.000172904 +DEAL::Order[5], error = -2.04379e-05 +DEAL::Order[6], error = -2.18094e-06 +DEAL::======= f(x,y) = x^2 y^3 +DEAL::Order[1], error = -0.0687148 +DEAL::Order[2], error = -0.0135616 +DEAL::Order[3], error = -0.00125414 +DEAL::Order[4], error = -0.000162720 +DEAL::Order[5], error = -1.83607e-05 +DEAL::Order[6], error = -1.87415e-06 +DEAL::======= f(x,y) = x^2 y^4 +DEAL::Order[1], error = -0.0565925 +DEAL::Order[2], error = -0.0157408 +DEAL::Order[3], error = -0.00148226 +DEAL::Order[4], error = -0.000196011 +DEAL::Order[5], error = -2.55438e-05 +DEAL::Order[6], error = -3.07252e-06 +DEAL::======= f(x,y) = x^2 y^5 +DEAL::Order[1], error = -0.0475881 +DEAL::Order[2], error = -0.0172621 +DEAL::Order[3], error = -0.00192138 +DEAL::Order[4], error = -0.000235659 +DEAL::Order[5], error = -3.34854e-05 +DEAL::Order[6], error = -4.30612e-06 +DEAL::======= f(x,y) = x^3 y^0 +DEAL::Order[1], error = -0.170372 +DEAL::Order[2], error = -0.0119124 +DEAL::Order[3], error = -0.00151573 +DEAL::Order[4], error = -0.000165201 +DEAL::Order[5], error = -1.62581e-05 +DEAL::Order[6], error = -1.49708e-06 +DEAL::======= f(x,y) = x^3 y^1 +DEAL::Order[1], error = -0.0944545 +DEAL::Order[2], error = -0.00931973 +DEAL::Order[3], error = -0.000844945 +DEAL::Order[4], error = -0.000100985 +DEAL::Order[5], error = -1.09354e-05 +DEAL::Order[6], error = -1.10179e-06 +DEAL::======= f(x,y) = x^3 y^2 +DEAL::Order[1], error = -0.0687148 +DEAL::Order[2], error = -0.0135616 +DEAL::Order[3], error = -0.00125414 +DEAL::Order[4], error = -0.000162720 +DEAL::Order[5], error = -1.83607e-05 +DEAL::Order[6], error = -1.87415e-06 +DEAL::======= f(x,y) = x^3 y^3 +DEAL::Order[1], error = -0.0530451 +DEAL::Order[2], error = -0.0152722 +DEAL::Order[3], error = -0.00136928 +DEAL::Order[4], error = -0.000155446 +DEAL::Order[5], error = -1.68770e-05 +DEAL::Order[6], error = -1.65502e-06 +DEAL::======= f(x,y) = x^3 y^4 +DEAL::Order[1], error = -0.0425960 +DEAL::Order[2], error = -0.0161403 +DEAL::Order[3], error = -0.00172995 +DEAL::Order[4], error = -0.000185485 +DEAL::Order[5], error = -2.33477e-05 +DEAL::Order[6], error = -2.73098e-06 +DEAL::======= f(x,y) = x^3 y^5 +DEAL::Order[1], error = -0.0353374 +DEAL::Order[2], error = -0.0164924 +DEAL::Order[3], error = -0.00222715 +DEAL::Order[4], error = -0.000229151 +DEAL::Order[5], error = -3.06509e-05 +DEAL::Order[6], error = -3.86546e-06 +DEAL::======= f(x,y) = x^4 y^0 +DEAL::Order[1], error = -0.160373 +DEAL::Order[2], error = -0.0160819 +DEAL::Order[3], error = -0.00157738 +DEAL::Order[4], error = -0.000211312 +DEAL::Order[5], error = -2.67349e-05 +DEAL::Order[6], error = -3.25021e-06 +DEAL::======= f(x,y) = x^4 y^1 +DEAL::Order[1], error = -0.0823104 +DEAL::Order[2], error = -0.0133881 +DEAL::Order[3], error = -0.00100812 +DEAL::Order[4], error = -0.000150114 +DEAL::Order[5], error = -2.05532e-05 +DEAL::Order[6], error = -2.62862e-06 +DEAL::======= f(x,y) = x^4 y^2 +DEAL::Order[1], error = -0.0565925 +DEAL::Order[2], error = -0.0157408 +DEAL::Order[3], error = -0.00148226 +DEAL::Order[4], error = -0.000196011 +DEAL::Order[5], error = -2.55438e-05 +DEAL::Order[6], error = -3.07252e-06 +DEAL::======= f(x,y) = x^4 y^3 +DEAL::Order[1], error = -0.0425960 +DEAL::Order[2], error = -0.0161403 +DEAL::Order[3], error = -0.00172995 +DEAL::Order[4], error = -0.000185485 +DEAL::Order[5], error = -2.33477e-05 +DEAL::Order[6], error = -2.73098e-06 +DEAL::======= f(x,y) = x^4 y^4 +DEAL::Order[1], error = -0.0338211 +DEAL::Order[2], error = -0.0160073 +DEAL::Order[3], error = -0.00214733 +DEAL::Order[4], error = -0.000215779 +DEAL::Order[5], error = -2.83804e-05 +DEAL::Order[6], error = -3.56784e-06 +DEAL::======= f(x,y) = x^4 y^5 +DEAL::Order[1], error = -0.0279085 +DEAL::Order[2], error = -0.0156115 +DEAL::Order[3], error = -0.00262841 +DEAL::Order[4], error = -0.000267648 +DEAL::Order[5], error = -3.44500e-05 +DEAL::Order[6], error = -4.50519e-06 +DEAL::======= f(x,y) = x^5 y^0 +DEAL::Order[1], error = -0.145363 +DEAL::Order[2], error = -0.0228780 +DEAL::Order[3], error = -0.00168236 +DEAL::Order[4], error = -0.000261625 +DEAL::Order[5], error = -3.71252e-05 +DEAL::Order[6], error = -4.86539e-06 +DEAL::======= f(x,y) = x^5 y^1 +DEAL::Order[1], error = -0.0714326 +DEAL::Order[2], error = -0.0170943 +DEAL::Order[3], error = -0.00136963 +DEAL::Order[4], error = -0.000201982 +DEAL::Order[5], error = -3.03423e-05 +DEAL::Order[6], error = -4.10185e-06 +DEAL::======= f(x,y) = x^5 y^2 +DEAL::Order[1], error = -0.0475881 +DEAL::Order[2], error = -0.0172621 +DEAL::Order[3], error = -0.00192138 +DEAL::Order[4], error = -0.000235659 +DEAL::Order[5], error = -3.34854e-05 +DEAL::Order[6], error = -4.30612e-06 +DEAL::======= f(x,y) = x^5 y^3 +DEAL::Order[1], error = -0.0353374 +DEAL::Order[2], error = -0.0164924 +DEAL::Order[3], error = -0.00222715 +DEAL::Order[4], error = -0.000229151 +DEAL::Order[5], error = -3.06509e-05 +DEAL::Order[6], error = -3.86546e-06 +DEAL::======= f(x,y) = x^5 y^4 +DEAL::Order[1], error = -0.0279085 +DEAL::Order[2], error = -0.0156115 +DEAL::Order[3], error = -0.00262841 +DEAL::Order[4], error = -0.000267648 +DEAL::Order[5], error = -3.44500e-05 +DEAL::Order[6], error = -4.50519e-06 +DEAL::======= f(x,y) = x^5 y^5 +DEAL::Order[1], error = -0.0229813 +DEAL::Order[2], error = -0.0147180 +DEAL::Order[3], error = -0.00304408 +DEAL::Order[4], error = -0.000331203 +DEAL::Order[5], error = -3.97780e-05 +DEAL::Order[6], error = -5.27210e-06 +DEAL:: ===============Vertex Index: 1 ============================== +DEAL::======= f(x,y) = x^0 y^0 +DEAL::Order[1], error = -0.357784 +DEAL::Order[2], error = -0.0413770 +DEAL::Order[3], error = -0.00349564 +DEAL::Order[4], error = -0.000233484 +DEAL::Order[5], error = -1.19260e-05 +DEAL::Order[6], error = -3.91498e-07 +DEAL::======= f(x,y) = x^0 y^1 +DEAL::Order[1], error = -0.120932 +DEAL::Order[2], error = -0.0121220 +DEAL::Order[3], error = -0.000828723 +DEAL::Order[4], error = -3.88017e-05 +DEAL::Order[5], error = -7.85203e-07 +DEAL::Order[6], error = 4.39204e-08 +DEAL::======= f(x,y) = x^0 y^2 +DEAL::Order[1], error = -0.163072 +DEAL::Order[2], error = -0.0135078 +DEAL::Order[3], error = -0.00165252 +DEAL::Order[4], error = -0.000183000 +DEAL::Order[5], error = -1.90192e-05 +DEAL::Order[6], error = -1.88270e-06 +DEAL::======= f(x,y) = x^0 y^3 +DEAL::Order[1], error = -0.170372 +DEAL::Order[2], error = -0.0119124 +DEAL::Order[3], error = -0.00151573 +DEAL::Order[4], error = -0.000165201 +DEAL::Order[5], error = -1.62581e-05 +DEAL::Order[6], error = -1.49708e-06 +DEAL::======= f(x,y) = x^0 y^4 +DEAL::Order[1], error = -0.160373 +DEAL::Order[2], error = -0.0160819 +DEAL::Order[3], error = -0.00157738 +DEAL::Order[4], error = -0.000211312 +DEAL::Order[5], error = -2.67349e-05 +DEAL::Order[6], error = -3.25021e-06 +DEAL::======= f(x,y) = x^0 y^5 +DEAL::Order[1], error = -0.145363 +DEAL::Order[2], error = -0.0228780 +DEAL::Order[3], error = -0.00168236 +DEAL::Order[4], error = -0.000261625 +DEAL::Order[5], error = -3.71252e-05 +DEAL::Order[6], error = -4.86539e-06 +DEAL::======= f(x,y) = x^1 y^0 +DEAL::Order[1], error = -0.236852 +DEAL::Order[2], error = -0.0292550 +DEAL::Order[3], error = -0.00266692 +DEAL::Order[4], error = -0.000194682 +DEAL::Order[5], error = -1.11408e-05 +DEAL::Order[6], error = -4.35418e-07 +DEAL::======= f(x,y) = x^1 y^1 +DEAL::Order[1], error = -0.0204105 +DEAL::Order[2], error = -0.00975165 +DEAL::Order[3], error = -0.000888973 +DEAL::Order[4], error = -6.48941e-05 +DEAL::Order[5], error = -3.71361e-06 +DEAL::Order[6], error = -1.45139e-07 +DEAL::======= f(x,y) = x^1 y^2 +DEAL::Order[1], error = -0.0587716 +DEAL::Order[2], error = -0.00766018 +DEAL::Order[3], error = -0.000872679 +DEAL::Order[4], error = -8.47202e-05 +DEAL::Order[5], error = -7.34372e-06 +DEAL::Order[6], error = -5.90510e-07 +DEAL::======= f(x,y) = x^1 y^3 +DEAL::Order[1], error = -0.0759180 +DEAL::Order[2], error = -0.00259262 +DEAL::Order[3], error = -0.000670785 +DEAL::Order[4], error = -6.42163e-05 +DEAL::Order[5], error = -5.32276e-06 +DEAL::Order[6], error = -3.95283e-07 +DEAL::======= f(x,y) = x^1 y^4 +DEAL::Order[1], error = -0.0780629 +DEAL::Order[2], error = -0.00269378 +DEAL::Order[3], error = -0.000569262 +DEAL::Order[4], error = -6.11988e-05 +DEAL::Order[5], error = -6.18176e-06 +DEAL::Order[6], error = -6.21591e-07 +DEAL::======= f(x,y) = x^1 y^5 +DEAL::Order[1], error = -0.0739299 +DEAL::Order[2], error = -0.00578370 +DEAL::Order[3], error = -0.000312725 +DEAL::Order[4], error = -5.96437e-05 +DEAL::Order[5], error = -6.78298e-06 +DEAL::Order[6], error = -7.63532e-07 +DEAL::======= f(x,y) = x^2 y^0 +DEAL::Order[1], error = -0.278992 +DEAL::Order[2], error = -0.0306407 +DEAL::Order[3], error = -0.00349072 +DEAL::Order[4], error = -0.000338881 +DEAL::Order[5], error = -2.93749e-05 +DEAL::Order[6], error = -2.36204e-06 +DEAL::======= f(x,y) = x^2 y^1 +DEAL::Order[1], error = -0.0241892 +DEAL::Order[2], error = -0.0132289 +DEAL::Order[3], error = -0.00172906 +DEAL::Order[4], error = -0.000189267 +DEAL::Order[5], error = -1.83175e-05 +DEAL::Order[6], error = -1.62639e-06 +DEAL::======= f(x,y) = x^2 y^2 +DEAL::Order[1], error = -0.0390863 +DEAL::Order[2], error = -0.0124864 +DEAL::Order[3], error = -0.00137673 +DEAL::Order[4], error = -0.000159344 +DEAL::Order[5], error = -1.61061e-05 +DEAL::Order[6], error = -1.47926e-06 +DEAL::======= f(x,y) = x^2 y^3 +DEAL::Order[1], error = -0.0501784 +DEAL::Order[2], error = -0.00683449 +DEAL::Order[3], error = -0.00107998 +DEAL::Order[4], error = -0.000125952 +DEAL::Order[5], error = -1.27481e-05 +DEAL::Order[6], error = -1.16764e-06 +DEAL::======= f(x,y) = x^2 y^4 +DEAL::Order[1], error = -0.0523451 +DEAL::Order[2], error = -0.00504646 +DEAL::Order[3], error = -0.00104341 +DEAL::Order[4], error = -0.000107097 +DEAL::Order[5], error = -1.11724e-05 +DEAL::Order[6], error = -1.06550e-06 +DEAL::======= f(x,y) = x^2 y^5 +DEAL::Order[1], error = -0.0500853 +DEAL::Order[2], error = -0.00595141 +DEAL::Order[3], error = -0.000864472 +DEAL::Order[4], error = -9.33207e-05 +DEAL::Order[5], error = -9.92611e-06 +DEAL::Order[6], error = -9.67794e-07 +DEAL::======= f(x,y) = x^3 y^0 +DEAL::Order[1], error = -0.313832 +DEAL::Order[2], error = -0.0336219 +DEAL::Order[3], error = -0.00445131 +DEAL::Order[4], error = -0.000500879 +DEAL::Order[5], error = -5.03700e-05 +DEAL::Order[6], error = -4.67429e-06 +DEAL::======= f(x,y) = x^3 y^1 +DEAL::Order[1], error = -0.0378142 +DEAL::Order[2], error = -0.0132340 +DEAL::Order[3], error = -0.00250405 +DEAL::Order[4], error = -0.000310935 +DEAL::Order[5], error = -3.36616e-05 +DEAL::Order[6], error = -3.29804e-06 +DEAL::======= f(x,y) = x^3 y^2 +DEAL::Order[1], error = -0.0353017 +DEAL::Order[2], error = -0.0144247 +DEAL::Order[3], error = -0.00191055 +DEAL::Order[4], error = -0.000244151 +DEAL::Order[5], error = -2.69456e-05 +DEAL::Order[6], error = -2.67480e-06 +DEAL::======= f(x,y) = x^3 y^3 +DEAL::Order[1], error = -0.0401084 +DEAL::Order[2], error = -0.00936574 +DEAL::Order[3], error = -0.00137404 +DEAL::Order[4], error = -0.000194961 +DEAL::Order[5], error = -2.16571e-05 +DEAL::Order[6], error = -2.15914e-06 +DEAL::======= f(x,y) = x^3 y^4 +DEAL::Order[1], error = -0.0406238 +DEAL::Order[2], error = -0.00699967 +DEAL::Order[3], error = -0.00126986 +DEAL::Order[4], error = -0.000163520 +DEAL::Order[5], error = -1.83590e-05 +DEAL::Order[6], error = -1.85094e-06 +DEAL::======= f(x,y) = x^3 y^5 +DEAL::Order[1], error = -0.0384915 +DEAL::Order[2], error = -0.00688875 +DEAL::Order[3], error = -0.00111045 +DEAL::Order[4], error = -0.000133506 +DEAL::Order[5], error = -1.59037e-05 +DEAL::Order[6], error = -1.61271e-06 +DEAL::======= f(x,y) = x^4 y^0 +DEAL::Order[1], error = -0.331372 +DEAL::Order[2], error = -0.0423680 +DEAL::Order[3], error = -0.00561033 +DEAL::Order[4], error = -0.000726788 +DEAL::Order[5], error = -8.46030e-05 +DEAL::Order[6], error = -9.12530e-06 +DEAL::======= f(x,y) = x^4 y^1 +DEAL::Order[1], error = -0.0491415 +DEAL::Order[2], error = -0.0138353 +DEAL::Order[3], error = -0.00337711 +DEAL::Order[4], error = -0.000479027 +DEAL::Order[5], error = -5.93636e-05 +DEAL::Order[6], error = -6.68691e-06 +DEAL::======= f(x,y) = x^4 y^2 +DEAL::Order[1], error = -0.0352954 +DEAL::Order[2], error = -0.0156544 +DEAL::Order[3], error = -0.00270223 +DEAL::Order[4], error = -0.000372433 +DEAL::Order[5], error = -4.70453e-05 +DEAL::Order[6], error = -5.37550e-06 +DEAL::======= f(x,y) = x^4 y^3 +DEAL::Order[1], error = -0.0352591 +DEAL::Order[2], error = -0.0110544 +DEAL::Order[3], error = -0.00191364 +DEAL::Order[4], error = -0.000301284 +DEAL::Order[5], error = -3.85204e-05 +DEAL::Order[6], error = -4.44573e-06 +DEAL::======= f(x,y) = x^4 y^4 +DEAL::Order[1], error = -0.0341240 +DEAL::Order[2], error = -0.00842045 +DEAL::Order[3], error = -0.00166600 +DEAL::Order[4], error = -0.000260764 +DEAL::Order[5], error = -3.27746e-05 +DEAL::Order[6], error = -3.81479e-06 +DEAL::======= f(x,y) = x^4 y^5 +DEAL::Order[1], error = -0.0317195 +DEAL::Order[2], error = -0.00771472 +DEAL::Order[3], error = -0.00145190 +DEAL::Order[4], error = -0.000218696 +DEAL::Order[5], error = -2.85150e-05 +DEAL::Order[6], error = -3.33802e-06 +DEAL::======= f(x,y) = x^5 y^0 +DEAL::Order[1], error = -0.336625 +DEAL::Order[2], error = -0.0542525 +DEAL::Order[3], error = -0.00692446 +DEAL::Order[4], error = -0.00101241 +DEAL::Order[5], error = -0.000132160 +DEAL::Order[6], error = -1.58530e-05 +DEAL::======= f(x,y) = x^5 y^1 +DEAL::Order[1], error = -0.0569045 +DEAL::Order[2], error = -0.0153951 +DEAL::Order[3], error = -0.00414988 +DEAL::Order[4], error = -0.000690805 +DEAL::Order[5], error = -9.52522e-05 +DEAL::Order[6], error = -1.18466e-05 +DEAL::======= f(x,y) = x^5 y^2 +DEAL::Order[1], error = -0.0359496 +DEAL::Order[2], error = -0.0168334 +DEAL::Order[3], error = -0.00354081 +DEAL::Order[4], error = -0.000537833 +DEAL::Order[5], error = -7.56468e-05 +DEAL::Order[6], error = -9.54614e-06 +DEAL::======= f(x,y) = x^5 y^3 +DEAL::Order[1], error = -0.0324400 +DEAL::Order[2], error = -0.0124164 +DEAL::Order[3], error = -0.00256226 +DEAL::Order[4], error = -0.000431293 +DEAL::Order[5], error = -6.25055e-05 +DEAL::Order[6], error = -7.96891e-06 +DEAL::======= f(x,y) = x^5 y^4 +DEAL::Order[1], error = -0.0299833 +DEAL::Order[2], error = -0.00957177 +DEAL::Order[3], error = -0.00216814 +DEAL::Order[4], error = -0.000377250 +DEAL::Order[5], error = -5.33820e-05 +DEAL::Order[6], error = -6.85655e-06 +DEAL::======= f(x,y) = x^5 y^5 +DEAL::Order[1], error = -0.0272677 +DEAL::Order[2], error = -0.00844182 +DEAL::Order[3], error = -0.00187441 +DEAL::Order[4], error = -0.000323834 +DEAL::Order[5], error = -4.62310e-05 +DEAL::Order[6], error = -6.01651e-06 +DEAL:: ===============Vertex Index: 2 ============================== +DEAL::======= f(x,y) = x^0 y^0 +DEAL::Order[1], error = -0.357784 +DEAL::Order[2], error = -0.0413770 +DEAL::Order[3], error = -0.00349564 +DEAL::Order[4], error = -0.000233484 +DEAL::Order[5], error = -1.19260e-05 +DEAL::Order[6], error = -3.91498e-07 +DEAL::======= f(x,y) = x^0 y^1 +DEAL::Order[1], error = -0.236852 +DEAL::Order[2], error = -0.0292550 +DEAL::Order[3], error = -0.00266692 +DEAL::Order[4], error = -0.000194682 +DEAL::Order[5], error = -1.11408e-05 +DEAL::Order[6], error = -4.35418e-07 +DEAL::======= f(x,y) = x^0 y^2 +DEAL::Order[1], error = -0.278992 +DEAL::Order[2], error = -0.0306407 +DEAL::Order[3], error = -0.00349072 +DEAL::Order[4], error = -0.000338881 +DEAL::Order[5], error = -2.93749e-05 +DEAL::Order[6], error = -2.36204e-06 +DEAL::======= f(x,y) = x^0 y^3 +DEAL::Order[1], error = -0.313832 +DEAL::Order[2], error = -0.0336219 +DEAL::Order[3], error = -0.00445131 +DEAL::Order[4], error = -0.000500879 +DEAL::Order[5], error = -5.03700e-05 +DEAL::Order[6], error = -4.67429e-06 +DEAL::======= f(x,y) = x^0 y^4 +DEAL::Order[1], error = -0.331372 +DEAL::Order[2], error = -0.0423680 +DEAL::Order[3], error = -0.00561033 +DEAL::Order[4], error = -0.000726788 +DEAL::Order[5], error = -8.46030e-05 +DEAL::Order[6], error = -9.12530e-06 +DEAL::======= f(x,y) = x^0 y^5 +DEAL::Order[1], error = -0.336625 +DEAL::Order[2], error = -0.0542525 +DEAL::Order[3], error = -0.00692446 +DEAL::Order[4], error = -0.00101241 +DEAL::Order[5], error = -0.000132160 +DEAL::Order[6], error = -1.58530e-05 +DEAL::======= f(x,y) = x^1 y^0 +DEAL::Order[1], error = -0.120932 +DEAL::Order[2], error = -0.0121220 +DEAL::Order[3], error = -0.000828723 +DEAL::Order[4], error = -3.88017e-05 +DEAL::Order[5], error = -7.85203e-07 +DEAL::Order[6], error = 4.39204e-08 +DEAL::======= f(x,y) = x^1 y^1 +DEAL::Order[1], error = -0.0204105 +DEAL::Order[2], error = -0.00975165 +DEAL::Order[3], error = -0.000888973 +DEAL::Order[4], error = -6.48941e-05 +DEAL::Order[5], error = -3.71361e-06 +DEAL::Order[6], error = -1.45139e-07 +DEAL::======= f(x,y) = x^1 y^2 +DEAL::Order[1], error = -0.0241892 +DEAL::Order[2], error = -0.0132289 +DEAL::Order[3], error = -0.00172906 +DEAL::Order[4], error = -0.000189267 +DEAL::Order[5], error = -1.83175e-05 +DEAL::Order[6], error = -1.62639e-06 +DEAL::======= f(x,y) = x^1 y^3 +DEAL::Order[1], error = -0.0378142 +DEAL::Order[2], error = -0.0132340 +DEAL::Order[3], error = -0.00250405 +DEAL::Order[4], error = -0.000310935 +DEAL::Order[5], error = -3.36616e-05 +DEAL::Order[6], error = -3.29804e-06 +DEAL::======= f(x,y) = x^1 y^4 +DEAL::Order[1], error = -0.0491415 +DEAL::Order[2], error = -0.0138353 +DEAL::Order[3], error = -0.00337711 +DEAL::Order[4], error = -0.000479027 +DEAL::Order[5], error = -5.93636e-05 +DEAL::Order[6], error = -6.68691e-06 +DEAL::======= f(x,y) = x^1 y^5 +DEAL::Order[1], error = -0.0569045 +DEAL::Order[2], error = -0.0153951 +DEAL::Order[3], error = -0.00414988 +DEAL::Order[4], error = -0.000690805 +DEAL::Order[5], error = -9.52522e-05 +DEAL::Order[6], error = -1.18466e-05 +DEAL::======= f(x,y) = x^2 y^0 +DEAL::Order[1], error = -0.163072 +DEAL::Order[2], error = -0.0135078 +DEAL::Order[3], error = -0.00165252 +DEAL::Order[4], error = -0.000183000 +DEAL::Order[5], error = -1.90192e-05 +DEAL::Order[6], error = -1.88270e-06 +DEAL::======= f(x,y) = x^2 y^1 +DEAL::Order[1], error = -0.0587716 +DEAL::Order[2], error = -0.00766018 +DEAL::Order[3], error = -0.000872679 +DEAL::Order[4], error = -8.47202e-05 +DEAL::Order[5], error = -7.34372e-06 +DEAL::Order[6], error = -5.90510e-07 +DEAL::======= f(x,y) = x^2 y^2 +DEAL::Order[1], error = -0.0390863 +DEAL::Order[2], error = -0.0124864 +DEAL::Order[3], error = -0.00137673 +DEAL::Order[4], error = -0.000159344 +DEAL::Order[5], error = -1.61061e-05 +DEAL::Order[6], error = -1.47926e-06 +DEAL::======= f(x,y) = x^2 y^3 +DEAL::Order[1], error = -0.0353017 +DEAL::Order[2], error = -0.0144247 +DEAL::Order[3], error = -0.00191055 +DEAL::Order[4], error = -0.000244151 +DEAL::Order[5], error = -2.69456e-05 +DEAL::Order[6], error = -2.67480e-06 +DEAL::======= f(x,y) = x^2 y^4 +DEAL::Order[1], error = -0.0352954 +DEAL::Order[2], error = -0.0156544 +DEAL::Order[3], error = -0.00270223 +DEAL::Order[4], error = -0.000372433 +DEAL::Order[5], error = -4.70453e-05 +DEAL::Order[6], error = -5.37550e-06 +DEAL::======= f(x,y) = x^2 y^5 +DEAL::Order[1], error = -0.0359496 +DEAL::Order[2], error = -0.0168334 +DEAL::Order[3], error = -0.00354081 +DEAL::Order[4], error = -0.000537833 +DEAL::Order[5], error = -7.56468e-05 +DEAL::Order[6], error = -9.54614e-06 +DEAL::======= f(x,y) = x^3 y^0 +DEAL::Order[1], error = -0.170372 +DEAL::Order[2], error = -0.0119124 +DEAL::Order[3], error = -0.00151573 +DEAL::Order[4], error = -0.000165201 +DEAL::Order[5], error = -1.62581e-05 +DEAL::Order[6], error = -1.49708e-06 +DEAL::======= f(x,y) = x^3 y^1 +DEAL::Order[1], error = -0.0759180 +DEAL::Order[2], error = -0.00259262 +DEAL::Order[3], error = -0.000670785 +DEAL::Order[4], error = -6.42163e-05 +DEAL::Order[5], error = -5.32276e-06 +DEAL::Order[6], error = -3.95283e-07 +DEAL::======= f(x,y) = x^3 y^2 +DEAL::Order[1], error = -0.0501784 +DEAL::Order[2], error = -0.00683449 +DEAL::Order[3], error = -0.00107998 +DEAL::Order[4], error = -0.000125952 +DEAL::Order[5], error = -1.27481e-05 +DEAL::Order[6], error = -1.16764e-06 +DEAL::======= f(x,y) = x^3 y^3 +DEAL::Order[1], error = -0.0401084 +DEAL::Order[2], error = -0.00936574 +DEAL::Order[3], error = -0.00137404 +DEAL::Order[4], error = -0.000194961 +DEAL::Order[5], error = -2.16571e-05 +DEAL::Order[6], error = -2.15914e-06 +DEAL::======= f(x,y) = x^3 y^4 +DEAL::Order[1], error = -0.0352591 +DEAL::Order[2], error = -0.0110544 +DEAL::Order[3], error = -0.00191364 +DEAL::Order[4], error = -0.000301284 +DEAL::Order[5], error = -3.85204e-05 +DEAL::Order[6], error = -4.44573e-06 +DEAL::======= f(x,y) = x^3 y^5 +DEAL::Order[1], error = -0.0324400 +DEAL::Order[2], error = -0.0124164 +DEAL::Order[3], error = -0.00256226 +DEAL::Order[4], error = -0.000431293 +DEAL::Order[5], error = -6.25055e-05 +DEAL::Order[6], error = -7.96891e-06 +DEAL::======= f(x,y) = x^4 y^0 +DEAL::Order[1], error = -0.160373 +DEAL::Order[2], error = -0.0160819 +DEAL::Order[3], error = -0.00157738 +DEAL::Order[4], error = -0.000211312 +DEAL::Order[5], error = -2.67349e-05 +DEAL::Order[6], error = -3.25021e-06 +DEAL::======= f(x,y) = x^4 y^1 +DEAL::Order[1], error = -0.0780629 +DEAL::Order[2], error = -0.00269378 +DEAL::Order[3], error = -0.000569262 +DEAL::Order[4], error = -6.11988e-05 +DEAL::Order[5], error = -6.18176e-06 +DEAL::Order[6], error = -6.21591e-07 +DEAL::======= f(x,y) = x^4 y^2 +DEAL::Order[1], error = -0.0523451 +DEAL::Order[2], error = -0.00504646 +DEAL::Order[3], error = -0.00104341 +DEAL::Order[4], error = -0.000107097 +DEAL::Order[5], error = -1.11724e-05 +DEAL::Order[6], error = -1.06550e-06 +DEAL::======= f(x,y) = x^4 y^3 +DEAL::Order[1], error = -0.0406238 +DEAL::Order[2], error = -0.00699967 +DEAL::Order[3], error = -0.00126986 +DEAL::Order[4], error = -0.000163520 +DEAL::Order[5], error = -1.83590e-05 +DEAL::Order[6], error = -1.85094e-06 +DEAL::======= f(x,y) = x^4 y^4 +DEAL::Order[1], error = -0.0341240 +DEAL::Order[2], error = -0.00842045 +DEAL::Order[3], error = -0.00166600 +DEAL::Order[4], error = -0.000260764 +DEAL::Order[5], error = -3.27746e-05 +DEAL::Order[6], error = -3.81479e-06 +DEAL::======= f(x,y) = x^4 y^5 +DEAL::Order[1], error = -0.0299833 +DEAL::Order[2], error = -0.00957177 +DEAL::Order[3], error = -0.00216814 +DEAL::Order[4], error = -0.000377250 +DEAL::Order[5], error = -5.33820e-05 +DEAL::Order[6], error = -6.85655e-06 +DEAL::======= f(x,y) = x^5 y^0 +DEAL::Order[1], error = -0.145363 +DEAL::Order[2], error = -0.0228780 +DEAL::Order[3], error = -0.00168236 +DEAL::Order[4], error = -0.000261625 +DEAL::Order[5], error = -3.71252e-05 +DEAL::Order[6], error = -4.86539e-06 +DEAL::======= f(x,y) = x^5 y^1 +DEAL::Order[1], error = -0.0739299 +DEAL::Order[2], error = -0.00578370 +DEAL::Order[3], error = -0.000312725 +DEAL::Order[4], error = -5.96437e-05 +DEAL::Order[5], error = -6.78298e-06 +DEAL::Order[6], error = -7.63532e-07 +DEAL::======= f(x,y) = x^5 y^2 +DEAL::Order[1], error = -0.0500853 +DEAL::Order[2], error = -0.00595141 +DEAL::Order[3], error = -0.000864472 +DEAL::Order[4], error = -9.33207e-05 +DEAL::Order[5], error = -9.92611e-06 +DEAL::Order[6], error = -9.67794e-07 +DEAL::======= f(x,y) = x^5 y^3 +DEAL::Order[1], error = -0.0384915 +DEAL::Order[2], error = -0.00688875 +DEAL::Order[3], error = -0.00111045 +DEAL::Order[4], error = -0.000133506 +DEAL::Order[5], error = -1.59037e-05 +DEAL::Order[6], error = -1.61271e-06 +DEAL::======= f(x,y) = x^5 y^4 +DEAL::Order[1], error = -0.0317195 +DEAL::Order[2], error = -0.00771472 +DEAL::Order[3], error = -0.00145190 +DEAL::Order[4], error = -0.000218696 +DEAL::Order[5], error = -2.85150e-05 +DEAL::Order[6], error = -3.33802e-06 +DEAL::======= f(x,y) = x^5 y^5 +DEAL::Order[1], error = -0.0272677 +DEAL::Order[2], error = -0.00844182 +DEAL::Order[3], error = -0.00187441 +DEAL::Order[4], error = -0.000323834 +DEAL::Order[5], error = -4.62310e-05 +DEAL::Order[6], error = -6.01651e-06 +DEAL:: ===============Vertex Index: 3 ============================== +DEAL::======= f(x,y) = x^0 y^0 +DEAL::Order[1], error = -0.357784 +DEAL::Order[2], error = -0.0413770 +DEAL::Order[3], error = -0.00349564 +DEAL::Order[4], error = -0.000233484 +DEAL::Order[5], error = -1.19260e-05 +DEAL::Order[6], error = -3.91498e-07 +DEAL::======= f(x,y) = x^0 y^1 +DEAL::Order[1], error = -0.236852 +DEAL::Order[2], error = -0.0292550 +DEAL::Order[3], error = -0.00266692 +DEAL::Order[4], error = -0.000194682 +DEAL::Order[5], error = -1.11408e-05 +DEAL::Order[6], error = -4.35418e-07 +DEAL::======= f(x,y) = x^0 y^2 +DEAL::Order[1], error = -0.278992 +DEAL::Order[2], error = -0.0306407 +DEAL::Order[3], error = -0.00349072 +DEAL::Order[4], error = -0.000338881 +DEAL::Order[5], error = -2.93749e-05 +DEAL::Order[6], error = -2.36204e-06 +DEAL::======= f(x,y) = x^0 y^3 +DEAL::Order[1], error = -0.313832 +DEAL::Order[2], error = -0.0336219 +DEAL::Order[3], error = -0.00445131 +DEAL::Order[4], error = -0.000500879 +DEAL::Order[5], error = -5.03700e-05 +DEAL::Order[6], error = -4.67429e-06 +DEAL::======= f(x,y) = x^0 y^4 +DEAL::Order[1], error = -0.331372 +DEAL::Order[2], error = -0.0423680 +DEAL::Order[3], error = -0.00561033 +DEAL::Order[4], error = -0.000726788 +DEAL::Order[5], error = -8.46030e-05 +DEAL::Order[6], error = -9.12530e-06 +DEAL::======= f(x,y) = x^0 y^5 +DEAL::Order[1], error = -0.336625 +DEAL::Order[2], error = -0.0542525 +DEAL::Order[3], error = -0.00692446 +DEAL::Order[4], error = -0.00101241 +DEAL::Order[5], error = -0.000132160 +DEAL::Order[6], error = -1.58530e-05 +DEAL::======= f(x,y) = x^1 y^0 +DEAL::Order[1], error = -0.236852 +DEAL::Order[2], error = -0.0292550 +DEAL::Order[3], error = -0.00266692 +DEAL::Order[4], error = -0.000194682 +DEAL::Order[5], error = -1.11408e-05 +DEAL::Order[6], error = -4.35418e-07 +DEAL::======= f(x,y) = x^1 y^1 +DEAL::Order[1], error = -0.216441 +DEAL::Order[2], error = -0.0195033 +DEAL::Order[3], error = -0.00177795 +DEAL::Order[4], error = -0.000129788 +DEAL::Order[5], error = -7.42723e-06 +DEAL::Order[6], error = -2.90279e-07 +DEAL::======= f(x,y) = x^1 y^2 +DEAL::Order[1], error = -0.254802 +DEAL::Order[2], error = -0.0174118 +DEAL::Order[3], error = -0.00176165 +DEAL::Order[4], error = -0.000149614 +DEAL::Order[5], error = -1.10573e-05 +DEAL::Order[6], error = -7.35650e-07 +DEAL::======= f(x,y) = x^1 y^3 +DEAL::Order[1], error = -0.276017 +DEAL::Order[2], error = -0.0203879 +DEAL::Order[3], error = -0.00194725 +DEAL::Order[4], error = -0.000189944 +DEAL::Order[5], error = -1.67084e-05 +DEAL::Order[6], error = -1.37625e-06 +DEAL::======= f(x,y) = x^1 y^4 +DEAL::Order[1], error = -0.282231 +DEAL::Order[2], error = -0.0285327 +DEAL::Order[3], error = -0.00223322 +DEAL::Order[4], error = -0.000247761 +DEAL::Order[5], error = -2.52394e-05 +DEAL::Order[6], error = -2.43838e-06 +DEAL::======= f(x,y) = x^1 y^5 +DEAL::Order[1], error = -0.279720 +DEAL::Order[2], error = -0.0388575 +DEAL::Order[3], error = -0.00277458 +DEAL::Order[4], error = -0.000321602 +DEAL::Order[5], error = -3.69082e-05 +DEAL::Order[6], error = -4.00642e-06 +DEAL::======= f(x,y) = x^2 y^0 +DEAL::Order[1], error = -0.278992 +DEAL::Order[2], error = -0.0306407 +DEAL::Order[3], error = -0.00349072 +DEAL::Order[4], error = -0.000338881 +DEAL::Order[5], error = -2.93749e-05 +DEAL::Order[6], error = -2.36204e-06 +DEAL::======= f(x,y) = x^2 y^1 +DEAL::Order[1], error = -0.254802 +DEAL::Order[2], error = -0.0174118 +DEAL::Order[3], error = -0.00176165 +DEAL::Order[4], error = -0.000149614 +DEAL::Order[5], error = -1.10573e-05 +DEAL::Order[6], error = -7.35650e-07 +DEAL::======= f(x,y) = x^2 y^2 +DEAL::Order[1], error = -0.269700 +DEAL::Order[2], error = -0.0166693 +DEAL::Order[3], error = -0.00140932 +DEAL::Order[4], error = -0.000119691 +DEAL::Order[5], error = -8.84587e-06 +DEAL::Order[6], error = -5.88520e-07 +DEAL::======= f(x,y) = x^2 y^3 +DEAL::Order[1], error = -0.273505 +DEAL::Order[2], error = -0.0215786 +DEAL::Order[3], error = -0.00135375 +DEAL::Order[4], error = -0.000123161 +DEAL::Order[5], error = -9.99240e-06 +DEAL::Order[6], error = -7.53009e-07 +DEAL::======= f(x,y) = x^2 y^4 +DEAL::Order[1], error = -0.268385 +DEAL::Order[2], error = -0.0303518 +DEAL::Order[3], error = -0.00155835 +DEAL::Order[4], error = -0.000141166 +DEAL::Order[5], error = -1.29212e-05 +DEAL::Order[6], error = -1.12697e-06 +DEAL::======= f(x,y) = x^2 y^5 +DEAL::Order[1], error = -0.258765 +DEAL::Order[2], error = -0.0402958 +DEAL::Order[3], error = -0.00216550 +DEAL::Order[4], error = -0.000168629 +DEAL::Order[5], error = -1.73028e-05 +DEAL::Order[6], error = -1.70596e-06 +DEAL::======= f(x,y) = x^3 y^0 +DEAL::Order[1], error = -0.313832 +DEAL::Order[2], error = -0.0336219 +DEAL::Order[3], error = -0.00445131 +DEAL::Order[4], error = -0.000500879 +DEAL::Order[5], error = -5.03700e-05 +DEAL::Order[6], error = -4.67429e-06 +DEAL::======= f(x,y) = x^3 y^1 +DEAL::Order[1], error = -0.276017 +DEAL::Order[2], error = -0.0203879 +DEAL::Order[3], error = -0.00194725 +DEAL::Order[4], error = -0.000189944 +DEAL::Order[5], error = -1.67084e-05 +DEAL::Order[6], error = -1.37625e-06 +DEAL::======= f(x,y) = x^3 y^2 +DEAL::Order[1], error = -0.273505 +DEAL::Order[2], error = -0.0215786 +DEAL::Order[3], error = -0.00135375 +DEAL::Order[4], error = -0.000123161 +DEAL::Order[5], error = -9.99240e-06 +DEAL::Order[6], error = -7.53009e-07 +DEAL::======= f(x,y) = x^3 y^3 +DEAL::Order[1], error = -0.266185 +DEAL::Order[2], error = -0.0278283 +DEAL::Order[3], error = -0.00129674 +DEAL::Order[4], error = -0.000105566 +DEAL::Order[5], error = -8.56491e-06 +DEAL::Order[6], error = -6.45437e-07 +DEAL::======= f(x,y) = x^3 y^4 +DEAL::Order[1], error = -0.254575 +DEAL::Order[2], error = -0.0367709 +DEAL::Order[3], error = -0.00167207 +DEAL::Order[4], error = -0.000105720 +DEAL::Order[5], error = -9.12791e-06 +DEAL::Order[6], error = -7.45333e-07 +DEAL::======= f(x,y) = x^3 y^5 +DEAL::Order[1], error = -0.241320 +DEAL::Order[2], error = -0.0461511 +DEAL::Order[3], error = -0.00253497 +DEAL::Order[4], error = -0.000122197 +DEAL::Order[5], error = -1.08387e-05 +DEAL::Order[6], error = -9.82727e-07 +DEAL::======= f(x,y) = x^4 y^0 +DEAL::Order[1], error = -0.331372 +DEAL::Order[2], error = -0.0423680 +DEAL::Order[3], error = -0.00561033 +DEAL::Order[4], error = -0.000726788 +DEAL::Order[5], error = -8.46030e-05 +DEAL::Order[6], error = -9.12530e-06 +DEAL::======= f(x,y) = x^4 y^1 +DEAL::Order[1], error = -0.282231 +DEAL::Order[2], error = -0.0285327 +DEAL::Order[3], error = -0.00223322 +DEAL::Order[4], error = -0.000247761 +DEAL::Order[5], error = -2.52394e-05 +DEAL::Order[6], error = -2.43838e-06 +DEAL::======= f(x,y) = x^4 y^2 +DEAL::Order[1], error = -0.268385 +DEAL::Order[2], error = -0.0303518 +DEAL::Order[3], error = -0.00155835 +DEAL::Order[4], error = -0.000141166 +DEAL::Order[5], error = -1.29212e-05 +DEAL::Order[6], error = -1.12697e-06 +DEAL::======= f(x,y) = x^4 y^3 +DEAL::Order[1], error = -0.254575 +DEAL::Order[2], error = -0.0367709 +DEAL::Order[3], error = -0.00167207 +DEAL::Order[4], error = -0.000105720 +DEAL::Order[5], error = -9.12791e-06 +DEAL::Order[6], error = -7.45333e-07 +DEAL::======= f(x,y) = x^4 y^4 +DEAL::Order[1], error = -0.239666 +DEAL::Order[2], error = -0.0451559 +DEAL::Order[3], error = -0.00232675 +DEAL::Order[4], error = -0.000100903 +DEAL::Order[5], error = -8.11370e-06 +DEAL::Order[6], error = -6.62518e-07 +DEAL::======= f(x,y) = x^4 y^5 +DEAL::Order[1], error = -0.224928 +DEAL::Order[2], error = -0.0535787 +DEAL::Order[3], error = -0.00348887 +DEAL::Order[4], error = -0.000128263 +DEAL::Order[5], error = -8.39231e-06 +DEAL::Order[6], error = -7.24350e-07 +DEAL::======= f(x,y) = x^5 y^0 +DEAL::Order[1], error = -0.336625 +DEAL::Order[2], error = -0.0542525 +DEAL::Order[3], error = -0.00692446 +DEAL::Order[4], error = -0.00101241 +DEAL::Order[5], error = -0.000132160 +DEAL::Order[6], error = -1.58530e-05 +DEAL::======= f(x,y) = x^5 y^1 +DEAL::Order[1], error = -0.279720 +DEAL::Order[2], error = -0.0388575 +DEAL::Order[3], error = -0.00277458 +DEAL::Order[4], error = -0.000321602 +DEAL::Order[5], error = -3.69082e-05 +DEAL::Order[6], error = -4.00642e-06 +DEAL::======= f(x,y) = x^5 y^2 +DEAL::Order[1], error = -0.258765 +DEAL::Order[2], error = -0.0402958 +DEAL::Order[3], error = -0.00216550 +DEAL::Order[4], error = -0.000168629 +DEAL::Order[5], error = -1.73028e-05 +DEAL::Order[6], error = -1.70596e-06 +DEAL::======= f(x,y) = x^5 y^3 +DEAL::Order[1], error = -0.241320 +DEAL::Order[2], error = -0.0461511 +DEAL::Order[3], error = -0.00253497 +DEAL::Order[4], error = -0.000122197 +DEAL::Order[5], error = -1.08387e-05 +DEAL::Order[6], error = -9.82727e-07 +DEAL::======= f(x,y) = x^5 y^4 +DEAL::Order[1], error = -0.224928 +DEAL::Order[2], error = -0.0535787 +DEAL::Order[3], error = -0.00348887 +DEAL::Order[4], error = -0.000128263 +DEAL::Order[5], error = -8.39231e-06 +DEAL::Order[6], error = -7.24350e-07 +DEAL::======= f(x,y) = x^5 y^5 +DEAL::Order[1], error = -0.209847 +DEAL::Order[2], error = -0.0608639 +DEAL::Order[3], error = -0.00492680 +DEAL::Order[4], error = -0.000186200 +DEAL::Order[5], error = -7.99132e-06 +DEAL::Order[6], error = -6.58500e-07 diff --git a/tests/base/simplex.h b/tests/base/simplex.h index 5eefe544fa..a6e92c1d71 100644 --- a/tests/base/simplex.h +++ b/tests/base/simplex.h @@ -52,4 +52,188 @@ std::array, 4> get_simplex() } +// Exact integral of 1/R times a polynomial computed using Maple. +double exact_integral_one_over_r(const unsigned int vertex_index, + const unsigned int i, + const unsigned int j) +{ + Assert(vertex_index < 4, ExcInternalError()); + Assert(i<6, ExcNotImplemented()); + Assert(j<6, ExcNotImplemented()); + + // The integrals are computed using the following maple snippet of + // code: + // + // sing_int := proc(index, N, M) + // if index = 0 then + // return int(int(x^N *y^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0); + // elif index = 1 then + // return int(int(x^N *y^M/sqrt((x-1)^2+y^2), x=0.0..1.0), y=0.0..1.0); + // elif index = 2 then + // return int(int(x^N *y^M/sqrt(x^2+(y-1)^2), x=0.0..1.0), y=0.0..1.0); + // elif index = 3 then + // return int(int((1-x)^N *(1-y)^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0); + // end if; + // end proc; + // Digits := 20; + // for i from 3 to 3 do + // for n from 0 to 5 do + // for m from 0 to 5 do + // C( v[i+1][n+1][m+1] = sing_int(i, n, m), resultname="a"); + // end do; + // end do; + // end do; + + static double v[4][6][6] = {{{0}}}; + if (v[0][0][0] == 0) + { + v[0][0][0] = 0.17627471740390860505e1; + v[0][0][1] = 0.64779357469631903702e0; + v[0][0][2] = 0.38259785823210634567e0; + v[0][0][3] = 0.26915893322379450224e0; + v[0][0][4] = 0.20702239737104695572e0; + v[0][0][5] = 0.16800109713227567467e0; + v[0][1][0] = 0.64779357469631903702e0; + v[0][1][1] = 0.27614237491539669920e0; + v[0][1][2] = 0.17015838751246776515e0; + v[0][1][3] = 0.12189514164974600651e0; + v[0][1][4] = 0.94658660368131133694e-1; + v[0][1][5] = 0.77263794021029438797e-1; + v[0][2][0] = 0.38259785823210634567e0; + v[0][2][1] = 0.17015838751246776515e0; + v[0][2][2] = 0.10656799507071040471e0; + v[0][2][3] = 0.76947022258735165920e-1; + v[0][2][4] = 0.60022626787495395021e-1; + v[0][2][5] = 0.49131622931360879320e-1; + v[0][3][0] = 0.26915893322379450224e0; + v[0][3][1] = 0.12189514164974600651e0; + v[0][3][2] = 0.76947022258735165919e-1; + v[0][3][3] = 0.55789184535895709637e-1; + v[0][3][4] = 0.43625068213915842136e-1; + v[0][3][5] = 0.35766126849971778500e-1; + v[0][4][0] = 0.20702239737104695572e0; + v[0][4][1] = 0.94658660368131133694e-1; + v[0][4][2] = 0.60022626787495395021e-1; + v[0][4][3] = 0.43625068213915842137e-1; + v[0][4][4] = 0.34164088852375945192e-1; + v[0][4][5] = 0.28037139560980277614e-1; + v[0][5][0] = 0.16800109713227567467e0; + v[0][5][1] = 0.77263794021029438797e-1; + v[0][5][2] = 0.49131622931360879320e-1; + v[0][5][3] = 0.35766126849971778501e-1; + v[0][5][4] = 0.28037139560980277614e-1; + v[0][5][5] = 0.23024181049838367777e-1; + v[1][0][0] = 0.17627471740390860505e1; + v[1][0][1] = 0.64779357469631903702e0; + v[1][0][2] = 0.38259785823210634567e0; + v[1][0][3] = 0.26915893322379450224e0; + v[1][0][4] = 0.20702239737104695572e0; + v[1][0][5] = 0.16800109713227567467e0; + v[1][1][0] = 0.11149535993427670134e1; + v[1][1][1] = 0.37165119978092233782e0; + v[1][1][2] = 0.21243947071963858053e0; + v[1][1][3] = 0.14726379157404849573e0; + v[1][1][4] = 0.11236373700291582202e0; + v[1][1][5] = 0.90737303111246235871e-1; + v[1][2][0] = 0.84975788287855432210e0; + v[1][2][1] = 0.26566721237799340376e0; + v[1][2][2] = 0.14884907827788122009e0; + v[1][2][3] = 0.10231567218303765515e0; + v[1][2][4] = 0.77727703422280083352e-1; + v[1][2][5] = 0.62605132021577676395e-1; + v[1][3][0] = 0.69800109142265347423e0; + v[1][3][1] = 0.20794647083778622837e0; + v[1][3][2] = 0.11487965864809909847e0; + v[1][3][3] = 0.78525390514866270852e-1; + v[1][3][4] = 0.59489228415223897572e-1; + v[1][3][5] = 0.47838457013298217744e-1; + v[1][4][0] = 0.59754668912231692323e0; + v[1][4][1] = 0.17125249387868593878e0; + v[1][4][2] = 0.93606816359052444729e-1; + v[1][4][3] = 0.63728830247554475330e-1; + v[1][4][4] = 0.48187332620207367724e-1; + v[1][4][5] = 0.38708290797416359020e-1; + v[1][5][0] = 0.52527944036356840363e0; + v[1][5][1] = 0.14574366656617935708e0; + v[1][5][2] = 0.78997159795636003667e-1; + v[1][5][3] = 0.53620816423066464705e-1; + v[1][5][4] = 0.40487985967086264433e-1; + v[1][5][5] = 0.32498604596082509165e-1; + v[2][0][0] = 0.17627471740390860505e1; + v[2][0][1] = 0.11149535993427670134e1; + v[2][0][2] = 0.84975788287855432210e0; + v[2][0][3] = 0.69800109142265347419e0; + v[2][0][4] = 0.59754668912231692318e0; + v[2][0][5] = 0.52527944036356840362e0; + v[2][1][0] = 0.64779357469631903702e0; + v[2][1][1] = 0.37165119978092233782e0; + v[2][1][2] = 0.26566721237799340376e0; + v[2][1][3] = 0.20794647083778622835e0; + v[2][1][4] = 0.17125249387868593876e0; + v[2][1][5] = 0.14574366656617935708e0; + v[2][2][0] = 0.38259785823210634567e0; + v[2][2][1] = 0.21243947071963858053e0; + v[2][2][2] = 0.14884907827788122009e0; + v[2][2][3] = 0.11487965864809909845e0; + v[2][2][4] = 0.93606816359052444712e-1; + v[2][2][5] = 0.78997159795636003667e-1; + v[2][3][0] = 0.26915893322379450223e0; + v[2][3][1] = 0.14726379157404849572e0; + v[2][3][2] = 0.10231567218303765514e0; + v[2][3][3] = 0.78525390514866270835e-1; + v[2][3][4] = 0.63728830247554475311e-1; + v[2][3][5] = 0.53620816423066464702e-1; + v[2][4][0] = 0.20702239737104695572e0; + v[2][4][1] = 0.11236373700291582202e0; + v[2][4][2] = 0.77727703422280083352e-1; + v[2][4][3] = 0.59489228415223897563e-1; + v[2][4][4] = 0.48187332620207367713e-1; + v[2][4][5] = 0.40487985967086264434e-1; + v[2][5][0] = 0.16800109713227567468e0; + v[2][5][1] = 0.90737303111246235879e-1; + v[2][5][2] = 0.62605132021577676399e-1; + v[2][5][3] = 0.47838457013298217740e-1; + v[2][5][4] = 0.38708290797416359014e-1; + v[2][5][5] = 0.32498604596082509169e-1; + v[3][0][0] = 0.17627471740390860505e1; + v[3][0][1] = 0.11149535993427670134e1; + v[3][0][2] = 0.84975788287855432210e0; + v[3][0][3] = 0.69800109142265347419e0; + v[3][0][4] = 0.59754668912231692318e0; + v[3][0][5] = 0.52527944036356840362e0; + v[3][1][0] = 0.11149535993427670134e1; + v[3][1][1] = 0.74330239956184467563e0; + v[3][1][2] = 0.58409067050056091834e0; + v[3][1][3] = 0.49005462058486724584e0; + v[3][1][4] = 0.42629419524363098443e0; + v[3][1][5] = 0.37953577379738904654e0; + v[3][2][0] = 0.84975788287855432210e0; + v[3][2][1] = 0.58409067050056091834e0; + v[3][2][2] = 0.46727253640044873467e0; + v[3][2][3] = 0.39698780839518011595e0; + v[3][2][4] = 0.34864851772399749038e0; + v[3][2][5] = 0.31278926702684569312e0; + v[3][3][0] = 0.69800109142265347423e0; + v[3][3][1] = 0.49005462058486724586e0; + v[3][3][2] = 0.39698780839518011599e0; + v[3][3][3] = 0.34027526433872581371e0; + v[3][3][4] = 0.30088082631586196583e0; + v[3][3][5] = 0.27141910362887187844e0; + v[3][4][0] = 0.59754668912231692323e0; + v[3][4][1] = 0.42629419524363098445e0; + v[3][4][2] = 0.34864851772399749044e0; + v[3][4][3] = 0.30088082631586196576e0; + v[3][4][4] = 0.26744962339187730308e0; + v[3][4][5] = 0.24229245314748740295e0; + v[3][5][0] = 0.52527944036356840363e0; + v[3][5][1] = 0.37953577379738904655e0; + v[3][5][2] = 0.31278926702684569301e0; + v[3][5][3] = 0.27141910362887187862e0; + v[3][5][4] = 0.24229245314748740263e0; + v[3][5][5] = 0.22026586649771582089e0; + } + return v[vertex_index][i][j]; +} + + #endif -- 2.39.5