07-Apr-2019 21:36:16 triangle_symq_rule_test MATLAB version Test triangle_symq_rule. TRIANGLE_SYMQ_RULE_TEST01 Map points from one triangle to another. R = reference triangle S = simplex T = user-defined triangle. REF_TO_TRIANGLE: R => T SIMPLEX_TO_TRIANGLE: S => T TRIANGLE_TO_REF: T => R TRIANGLE_TO_SIMPLEX: T => S SP1: 0.7816 0.0437 TP1: 3.3011 3.2574 RP1: 0.6068 -0.5017 TP2: 3.3011 3.2574 SP2: 0.7816 0.0437 SP1: 0.1705 0.4383 TP1: 1.0732 1.9969 RP1: -0.2207 0.1818 TP2: 1.0732 1.9969 SP2: 0.1705 0.4383 SP1: 0.4153 0.0661 TP1: 2.1798 1.8596 RP1: -0.1033 -0.4628 TP2: 2.1798 1.8596 SP2: 0.4153 0.0661 SP1: 0.2576 0.1100 TP1: 1.6628 1.3602 RP1: -0.3749 -0.3869 TP2: 1.6628 1.3602 SP2: 0.2576 0.1100 SP1: 0.0438 0.6340 TP1: 0.4975 2.0772 RP1: -0.2784 0.5207 TP2: 0.4975 2.0772 SP2: 0.0438 0.6340 Region is user-defined triangle. Triangle: 1.0000 0.0000 4.0000 4.0000 0.0000 3.0000 TRIANGLE_SYMQ_RULE_TEST02 Symmetric quadrature rule for a triangle. Polynomial exactness degree DEGREE = 8 NUMNODES = 16 J W X Y 1 0.670913 1.34114 1.19399 2 0.670913 2.80601 3.14715 3 0.670913 0.852847 2.65886 4 0.618096 2.29646 2.08141 5 0.618096 1.91859 3.21505 6 0.618096 0.784952 1.70354 7 0.938051 1.66667 2.33333 8 0.21098 1.10109 0.353831 9 0.21098 3.64617 3.74726 10 0.21098 0.252736 2.89891 11 0.176997 1.78094 1.07764 12 0.176997 2.92236 3.70331 13 0.176997 0.296692 2.21906 14 0.176997 3.17708 2.93915 15 0.176997 1.06085 3.23793 16 0.176997 0.762072 0.822918 Sum 6.5 Area 6.5 TRIANGLE_SYMQ_RULE_TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created vertex file "user08_vertices.txt". Created node file "user08_nodes.txt". Created command file "user08_commands.txt". TRIANGLE_SYMQ_RULE_TEST04 Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree DEGREE = 8 Quadrature rule written to file "user08.txt". TRIANGLE_SYMQ_RULE_TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 2.75098e-16 Region is standard equilateral triangle. Triangle: -1.0000 -0.5774 1.0000 -0.5774 0.0000 1.1547 TRIANGLE_SYMQ_RULE_TEST02 Symmetric quadrature rule for a triangle. Polynomial exactness degree DEGREE = 8 NUMNODES = 16 J W X Y 1 0.178778 -0.488292 -0.281916 2 0.178778 0.488292 -0.281916 3 0.178778 4.44089e-16 0.563831 4 0.164704 0 -0.436336 5 0.164704 0.377878 0.218168 6 0.164704 -0.377878 0.218168 7 0.249962 0 2.22045e-16 8 0.0562198 -0.848358 -0.4898 9 0.0562198 0.848358 -0.4898 10 0.0562198 6.66134e-16 0.9796 11 0.0471643 -0.46538 -0.56281 12 0.0471643 0.720098 -0.121625 13 0.0471643 -0.254718 0.684436 14 0.0471643 0.46538 -0.56281 15 0.0471643 0.254718 0.684436 16 0.0471643 -0.720098 -0.121625 Sum 1.73205 Area 1.73205 TRIANGLE_SYMQ_RULE_TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created vertex file "equi08_vertices.txt". Created node file "equi08_nodes.txt". Created command file "equi08_commands.txt". TRIANGLE_SYMQ_RULE_TEST04 Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree DEGREE = 8 Quadrature rule written to file "equi08.txt". TRIANGLE_SYMQ_RULE_TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 1.39354e-16 Region is the simplex (0,0),(1,0),(0,1). Triangle: 0.0000 0.0000 1.0000 0.0000 0.0000 1.0000 TRIANGLE_SYMQ_RULE_TEST02 Symmetric quadrature rule for a triangle. Polynomial exactness degree DEGREE = 8 NUMNODES = 16 J W X Y 1 0.0516087 0.170569 0.170569 2 0.0516087 0.658861 0.170569 3 0.0516087 0.170569 0.658861 4 0.0475458 0.459293 0.0814148 5 0.0475458 0.459293 0.459293 6 0.0475458 0.0814148 0.459293 7 0.0721578 0.333333 0.333333 8 0.0162292 0.0505472 0.0505472 9 0.0162292 0.898906 0.0505472 10 0.0162292 0.0505472 0.898906 11 0.0136152 0.263113 0.00839478 12 0.0136152 0.728492 0.263113 13 0.0136152 0.00839478 0.728492 14 0.0136152 0.728492 0.00839478 15 0.0136152 0.263113 0.728492 16 0.0136152 0.00839478 0.263113 Sum 0.5 Area 0.5 TRIANGLE_SYMQ_RULE_TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created vertex file "simp08_vertices.txt". Created node file "simp08_nodes.txt". Created command file "simp08_commands.txt". TRIANGLE_SYMQ_RULE_TEST04 Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree DEGREE = 8 Quadrature rule written to file "simp08.txt". TRIANGLE_SYMQ_RULE_TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 6.97147e-17 triangle_symq_rule_test Normal end of execution. 07-Apr-2019 21:36:16