28 June 2014 10:55:39.101 AM TRIANGLE_SYMQ_RULE_PRB FORTRAN90 version Test the TRIANGLE_SYMQ_RULE library. 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: 0.781582 0.436824E-01 TP1: 3.30106 3.25737 RP1: 0.606846 -0.501690 TP2: 3.30106 3.25737 SP2: 0.781582 0.436824E-01 SP1: 0.170491 0.438305 TP1: 1.07317 1.99688 RP1: -0.220714 0.181815 TP2: 1.07317 1.99688 SP2: 0.170491 0.438305 SP1: 0.415307 0.661187E-01 TP1: 2.17980 1.85958 RP1: -0.103267 -0.462829 TP2: 2.17980 1.85958 SP2: 0.415307 0.661187E-01 SP1: 0.257578 0.109957 TP1: 1.66278 1.36018 RP1: -0.374888 -0.386900 TP2: 1.66278 1.36018 SP2: 0.257578 0.109957 SP1: 0.438290E-01 0.633966 TP1: 0.497521 2.07721 RP1: -0.278376 0.520711 TP2: 0.497521 2.07721 SP2: 0.438290E-01 0.633966 Region is user-defined triangle. Triangle: 1.00000 0.00000 4.00000 4.00000 0.00000 3.00000 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 0.210980 1.10109 0.353831 9 0.210980 3.64617 3.74726 10 0.210980 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 6.50000 Area 6.50000 TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created triangle file "user08_triangle.txt". Created node file "user08_nodes.txt". Created command file "user08_commands.txt". 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". TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 0.275098E-15 Region is standard equilateral triangle. Triangle: -1.00000 -0.577350 1.00000 -0.577350 0.00000 1.15470 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 0.444089E-15 0.563831 4 0.164704 0.00000 -0.436336 5 0.164704 0.377878 0.218168 6 0.164704 -0.377878 0.218168 7 0.249962 0.00000 0.222045E-15 8 0.562198E-01 -0.848358 -0.489800 9 0.562198E-01 0.848358 -0.489800 10 0.562198E-01 0.666134E-15 0.979600 11 0.471643E-01 -0.465380 -0.562810 12 0.471643E-01 0.720098 -0.121625 13 0.471643E-01 -0.254718 0.684436 14 0.471643E-01 0.465380 -0.562810 15 0.471643E-01 0.254718 0.684436 16 0.471643E-01 -0.720098 -0.121625 Sum 1.73205 Area 1.73205 TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created triangle file "equi08_triangle.txt". Created node file "equi08_nodes.txt". Created command file "equi08_commands.txt". 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". TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 0.139354E-15 Region is the simplex (0,0),(1,0),(0,1). Triangle: 0.00000 0.00000 1.00000 0.00000 0.00000 1.00000 TEST02 Symmetric quadrature rule for a triangle. Polynomial exactness degree DEGREE = 8 NUMNODES = 16 J W X Y 1 0.516087E-01 0.170569 0.170569 2 0.516087E-01 0.658861 0.170569 3 0.516087E-01 0.170569 0.658861 4 0.475458E-01 0.459293 0.814148E-01 5 0.475458E-01 0.459293 0.459293 6 0.475458E-01 0.814148E-01 0.459293 7 0.721578E-01 0.333333 0.333333 8 0.162292E-01 0.505472E-01 0.505472E-01 9 0.162292E-01 0.898906 0.505472E-01 10 0.162292E-01 0.505472E-01 0.898906 11 0.136152E-01 0.263113 0.839478E-02 12 0.136152E-01 0.728492 0.263113 13 0.136152E-01 0.839478E-02 0.728492 14 0.136152E-01 0.728492 0.839478E-02 15 0.136152E-01 0.263113 0.728492 16 0.136152E-01 0.839478E-02 0.263113 Sum 0.500000 Area 0.500000 TEST03 TRIASYMQ_GNUPLOT creates gnuplot graphics files. Polynomial exactness degree DEGREE = 8 Number of nodes = 16 Created triangle file "simp08_triangle.txt". Created node file "simp08_nodes.txt". Created command file "simp08_commands.txt". 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". TEST05 Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 0.697147E-16 TRIANGLE_SYMQ_RULE_PRB Normal end of execution. 28 June 2014 10:55:39.339 AM