27 December 2010 12:47:27.193 PM DUNAVANT_PRB: FORTRAN90 version Test routines in the DUNAVANT library. TEST01 DUNAVANT_RULE_NUM returns the number of rules; DUNAVANT_DEGREE returns the degree of a rule; DUNAVANT_ORDER_NUM returns the order of a rule. Number of available rules = 20 Rule Degree Order 1 1 1 2 2 3 3 3 4 4 4 6 5 5 7 6 6 12 7 7 13 8 8 16 9 9 19 10 10 25 11 11 27 12 12 33 13 13 37 14 14 42 15 15 48 16 16 52 17 17 61 18 18 70 19 19 73 20 20 79 TEST02 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 20 Rule Sum of weights 1 1.000000000000000 2 0.9999999999999989 3 0.9999999999999991 4 0.9999999999999990 5 0.9999999999999990 6 1.000000000000002 7 0.9999999999999981 8 1.000000000000000 9 0.9999999999999959 10 0.9999999999999992 11 1.000000000000002 12 0.9999999999999961 13 0.9999999999999991 14 1.000000000000008 15 1.000000000000005 16 0.9999999999999978 17 1.000000000000001 18 1.000000000000004 19 1.000000000000005 20 1.000000000000004 TEST03 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the triangle. In this test, we simply check that, for each quadrature point, the barycentric coordinates sum to 1. Rule Suborder Sum of coordinates 1 1 0.9999999999999989 2 1 1.000000000000001 3 2 0.9999999999999989 1.000000000000000 4 2 1.000000000000000 1.000000000000001 5 3 0.9999999999999989 1.000000000000000 0.9999999999999990 6 3 0.9999999999999990 1.000000000000000 1.000000000000000 7 4 0.9999999999999989 1.000000000000000 1.000000000000000 1.000000000000000 8 5 0.9999999999999989 1.000000000000000 1.000000000000000 0.9999999999999999 1.000000000000000 9 6 0.9999999999999989 1.000000000000001 1.000000000000001 1.000000000000001 1.000000000000001 1.000000000000000 10 6 0.9999999999999989 0.9999999999999990 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999990 11 7 0.9999999999999990 1.000000000000000 0.9999999999999989 0.9999999999999990 1.000000000000000 1.000000000000001 1.000000000000000 12 8 1.000000000000000 0.9999999999999989 1.000000000000000 1.000000000000000 0.9999999999999991 1.000000000000000 1.000000000000000 1.000000000000000 13 10 0.9999999999999989 1.000000000000001 1.000000000000000 1.000000000000001 0.9999999999999990 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 14 10 1.000000000000001 1.000000000000000 1.000000000000001 0.9999999999999990 1.000000000000001 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 15 11 1.000000000000000 1.000000000000001 0.9999999999999990 1.000000000000000 1.000000000000000 0.9999999999999990 0.9999999999999990 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000001 16 13 0.9999999999999989 0.9999999999999991 0.9999999999999989 0.9999999999999989 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000001 0.9999999999999990 17 15 0.9999999999999989 1.000000000000000 1.000000000000001 1.000000000000001 1.000000000000000 1.000000000000001 0.9999999999999990 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000001 1.000000000000000 0.9999999999999990 1.000000000000000 18 17 0.9999999999999989 0.9999999999999990 1.000000000000000 1.000000000000001 1.000000000000000 1.000000000000000 1.000000000000001 0.9999999999999991 1.000000000000000 1.000000000000001 1.000000000000000 1.000000000000000 1.000000000000001 0.9999999999999990 1.000000000000000 1.000000000000000 0.9999999999999999 19 17 0.9999999999999989 0.9999999999999991 1.000000000000001 1.000000000000000 1.000000000000001 1.000000000000001 1.000000000000000 1.000000000000001 1.000000000000001 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000001 1.000000000000000 1.000000000000000 1.000000000000000 20 19 0.9999999999999989 1.000000000000000 1.000000000000001 1.000000000000001 0.9999999999999990 0.9999999999999989 1.000000000000000 0.9999999999999989 0.9999999999999999 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999989 1.000000000000000 1.000000000000001 TEST04 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the unit triangle. This routine uses those rules to estimate the integral of monomomials in the unit triangle. Integrate 2.00000 * X ** 0 * Y ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 6.00000 * X ** 0 * Y ** 1 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 12.0000 * X ** 0 * Y ** 2 Rule QUAD ERROR 1 0.666667 0.33333333 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 20.0000 * X ** 0 * Y ** 3 Rule QUAD ERROR 1 0.370370 0.62962963 2 1.01852 0.01851852 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 30.0000 * X ** 0 * Y ** 4 Rule QUAD ERROR 1 0.185185 0.81481481 2 0.995370 0.00462963 3 0.933333 0.06666667 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 42.0000 * X ** 0 * Y ** 5 Rule QUAD ERROR 1 0.864198E-01 0.91358025 2 0.923611 0.07638889 3 0.808889 0.19111111 4 1.00527 0.00527393 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 56.0000 * X ** 0 * Y ** 6 Rule QUAD ERROR 1 0.384088E-01 0.96159122 2 0.819787 0.18021262 3 0.660662 0.33933827 4 1.01295 0.01294949 5 0.995414 0.00458554 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 72.0000 * X ** 0 * Y ** 7 Rule QUAD ERROR 1 0.164609E-01 0.98353909 2 0.702418 0.29758230 3 0.516101 0.48389926 4 1.01690 0.01690162 5 0.981708 0.01829176 6 1.00020 0.00019804 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 90.0000 * X ** 0 * Y ** 8 Rule QUAD ERROR 1 0.685871E-02 0.99314129 2 0.585294 0.41470550 3 0.389922 0.61007802 4 1.01216 0.01216139 5 0.956602 0.04339756 6 1.00044 0.00043938 7 0.999572 0.00042796 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 110.000 * X ** 0 * Y ** 9 Rule QUAD ERROR 1 0.279429E-02 0.99720571 2 0.476896 0.52310429 3 0.287142 0.71285845 4 0.996255 0.00374460 5 0.920084 0.07991597 6 1.00009 0.00008582 7 0.997886 0.00211358 8 0.999942 0.00005788 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 132.000 * X ** 0 * Y ** 10 Rule QUAD ERROR 1 0.111772E-02 0.99888228 2 0.381514 0.61848561 3 0.207231 0.79276920 4 0.968918 0.03108196 5 0.873671 0.12632881 6 0.998219 0.00178063 7 0.993975 0.00602508 8 0.999662 0.00033832 9 0.999970 0.00003026 10 1.00000 0.00000000 Integrate 6.00000 * X ** 1 * Y ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 24.0000 * X ** 1 * Y ** 1 Rule QUAD ERROR 1 1.33333 0.33333333 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 60.0000 * X ** 1 * Y ** 2 Rule QUAD ERROR 1 1.11111 0.11111111 2 0.972222 0.02777778 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 120.000 * X ** 1 * Y ** 3 Rule QUAD ERROR 1 0.740741 0.25925926 2 1.06481 0.06481481 3 1.13333 0.13333333 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 210.000 * X ** 1 * Y ** 4 Rule QUAD ERROR 1 0.432099 0.56790123 2 1.17477 0.17476852 3 1.24444 0.24444444 4 0.986815 0.01318484 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 336.000 * X ** 1 * Y ** 5 Rule QUAD ERROR 1 0.230453 0.76954733 2 1.23508 0.23508230 3 1.25357 0.25357037 4 0.982247 0.01775274 5 1.01376 0.01375661 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 504.000 * X ** 1 * Y ** 6 Rule QUAD ERROR 1 0.115226 0.88477366 2 1.23058 0.23058128 3 1.16663 0.16662519 4 0.999117 0.00088296 5 1.04339 0.04338624 6 0.999307 0.00069314 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 720.000 * X ** 1 * Y ** 7 Rule QUAD ERROR 1 0.548697E-01 0.94513032 2 1.17091 0.17091049 3 1.02082 0.02081580 4 1.03586 0.03586257 5 1.08213 0.08213142 6 0.999233 0.00076731 7 1.00171 0.00171183 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 990.000 * X ** 1 * Y ** 8 Rule QUAD ERROR 1 0.251486E-01 0.97485139 2 1.07309 0.07308903 3 0.852434 0.14756609 4 1.08374 0.08373832 5 1.12094 0.12093530 6 1.00203 0.00203040 7 1.00716 0.00715736 8 1.00026 0.00026047 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 1320.00 * X ** 1 * Y ** 9 Rule QUAD ERROR 1 0.111772E-01 0.98882284 2 0.953802 0.04619766 3 0.686695 0.31330475 4 1.13294 0.13294222 5 1.15215 0.15214823 6 1.00942 0.00941807 7 1.01744 0.01744391 8 1.00134 0.00134432 9 1.00015 0.00015132 10 1.00000 0.00000000 Integrate 12.0000 * X ** 2 * Y ** 0 Rule QUAD ERROR 1 0.666667 0.33333333 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 60.0000 * X ** 2 * Y ** 1 Rule QUAD ERROR 1 1.11111 0.11111111 2 0.972222 0.02777778 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 180.000 * X ** 2 * Y ** 2 Rule QUAD ERROR 1 1.11111 0.11111111 2 0.763889 0.23611111 3 0.800000 0.20000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 420.000 * X ** 2 * Y ** 3 Rule QUAD ERROR 1 0.864198 0.13580247 2 0.729167 0.27083333 3 0.808889 0.19111111 4 1.00527 0.00527393 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 840.000 * X ** 2 * Y ** 4 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.819187 0.18081276 3 0.949926 0.05007407 4 0.958434 0.04156566 5 0.962963 0.03703704 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 1512.00 * X ** 2 * Y ** 5 Rule QUAD ERROR 1 0.345679 0.65432099 2 0.937114 0.06288580 3 1.08068 0.08067556 4 0.881502 0.11849802 5 0.909751 0.09024943 6 1.00089 0.00089118 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 2520.00 * X ** 2 * Y ** 6 Rule QUAD ERROR 1 0.192044 0.80795610 2 1.02849 0.02848508 3 1.13350 0.13349531 4 0.811392 0.18860789 5 0.866501 0.13349890 6 0.996224 0.00377556 7 0.994117 0.00588301 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 3960.00 * X ** 2 * Y ** 7 Rule QUAD ERROR 1 0.100594 0.89940558 2 1.07412 0.07412051 3 1.10343 0.10343164 4 0.769683 0.23031716 5 0.846090 0.15390976 6 0.981678 0.01832186 7 0.979223 0.02077746 8 0.999209 0.00079060 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 5940.00 * X ** 2 * Y ** 8 Rule QUAD ERROR 1 0.502972E-01 0.94970279 2 1.07329 0.07328550 3 1.01255 0.01255422 4 0.761318 0.23868198 5 0.849523 0.15047725 6 0.957945 0.04205474 7 0.956754 0.04324599 8 0.996306 0.00369388 9 0.999303 0.00069732 10 1.00000 0.00000000 Integrate 20.0000 * X ** 3 * Y ** 0 Rule QUAD ERROR 1 0.370370 0.62962963 2 1.01852 0.01851852 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 120.000 * X ** 3 * Y ** 1 Rule QUAD ERROR 1 0.740741 0.25925926 2 1.06481 0.06481481 3 1.13333 0.13333333 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 420.000 * X ** 3 * Y ** 2 Rule QUAD ERROR 1 0.864198 0.13580247 2 0.729167 0.27083333 3 0.808889 0.19111111 4 1.00527 0.00527393 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 1120.00 * X ** 3 * Y ** 3 Rule QUAD ERROR 1 0.768176 0.23182442 2 0.516118 0.48388203 3 0.594568 0.40543210 4 1.06350 0.06349583 5 1.05115 0.05114638 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 2520.00 * X ** 3 * Y ** 4 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.481610 0.51838992 3 0.591526 0.40847407 4 1.05737 0.05737044 5 1.05367 0.05366591 6 0.999505 0.00049510 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 5040.00 * X ** 3 * Y ** 5 Rule QUAD ERROR 1 0.384088 0.61591221 2 0.544624 0.45537551 3 0.694511 0.30548938 4 0.972131 0.02786944 5 0.992477 0.00752259 6 1.01154 0.01153677 7 1.01166 0.01165761 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 9240.00 * X ** 3 * Y ** 6 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.635854 0.36414633 3 0.800594 0.19940618 4 0.846318 0.15368207 5 0.896388 0.10361195 6 1.03039 0.03039232 7 1.02893 0.02893207 8 1.00155 0.00155156 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 15840.0 * X ** 3 * Y ** 7 Rule QUAD ERROR 1 0.134126 0.86587410 2 0.718176 0.28182394 3 0.860170 0.13982982 4 0.720497 0.27950348 5 0.797080 0.20291962 6 1.04271 0.04270623 7 1.03934 0.03934337 8 1.00613 0.00613355 9 1.00188 0.00188136 10 1.00000 0.00000000 Integrate 30.0000 * X ** 4 * Y ** 0 Rule QUAD ERROR 1 0.185185 0.81481481 2 0.995370 0.00462963 3 0.933333 0.06666667 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 210.000 * X ** 4 * Y ** 1 Rule QUAD ERROR 1 0.432099 0.56790123 2 1.17477 0.17476852 3 1.24444 0.24444444 4 0.986815 0.01318484 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 840.000 * X ** 4 * Y ** 2 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.819187 0.18081276 3 0.949926 0.05007407 4 0.958434 0.04156566 5 0.962963 0.03703704 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 2520.00 * X ** 4 * Y ** 3 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.481610 0.51838992 3 0.591526 0.40847407 4 1.05737 0.05737044 5 1.05367 0.05366591 6 0.999505 0.00049510 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 6300.00 * X ** 4 * Y ** 4 Rule QUAD ERROR 1 0.480110 0.51989026 2 0.320698 0.67930170 3 0.414538 0.58546173 4 1.12991 0.12990697 5 1.13775 0.13774610 6 0.983592 0.01640758 7 0.985455 0.01454491 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 13860.0 * X ** 4 * Y ** 5 Rule QUAD ERROR 1 0.352080 0.64791952 2 0.293630 0.70637038 3 0.402555 0.59744527 4 1.10610 0.10610483 5 1.14249 0.14249035 6 0.982741 0.01725909 7 0.985505 0.01449536 8 0.999065 0.00093461 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 27720.0 * X ** 4 * Y ** 6 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.332597 0.66740314 3 0.467461 0.53253898 4 0.998828 0.00117160 5 1.06917 0.06917320 6 1.00786 0.00785815 7 1.01024 0.01024312 8 0.997890 0.00210973 9 0.996691 0.00330876 10 1.00000 0.00000000 Integrate 42.0000 * X ** 5 * Y ** 0 Rule QUAD ERROR 1 0.864198E-01 0.91358025 2 0.923611 0.07638889 3 0.808889 0.19111111 4 1.00527 0.00527393 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 336.000 * X ** 5 * Y ** 1 Rule QUAD ERROR 1 0.230453 0.76954733 2 1.23508 0.23508230 3 1.25357 0.25357037 4 0.982247 0.01775274 5 1.01376 0.01375661 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 1512.00 * X ** 5 * Y ** 2 Rule QUAD ERROR 1 0.345679 0.65432099 2 0.937114 0.06288580 3 1.08068 0.08067556 4 0.881502 0.11849802 5 0.909751 0.09024943 6 1.00089 0.00089118 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 5040.00 * X ** 5 * Y ** 3 Rule QUAD ERROR 1 0.384088 0.61591221 2 0.544624 0.45537551 3 0.694511 0.30548938 4 0.972131 0.02786944 5 0.992477 0.00752259 6 1.01154 0.01153677 7 1.01166 0.01165761 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 13860.0 * X ** 5 * Y ** 4 Rule QUAD ERROR 1 0.352080 0.64791952 2 0.293630 0.70637038 3 0.402555 0.59744527 4 1.10610 0.10610483 5 1.14249 0.14249035 6 0.982741 0.01725909 7 0.985505 0.01449536 8 0.999065 0.00093461 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 33264.0 * X ** 5 * Y ** 5 Rule QUAD ERROR 1 0.281664 0.71833562 2 0.187868 0.81213206 3 0.273552 0.72644773 4 1.16618 0.16618451 5 1.23958 0.23957884 6 0.950326 0.04967432 7 0.955574 0.04442596 8 0.997684 0.00231560 9 1.00398 0.00397707 10 1.00000 0.00000000 Integrate 56.0000 * X ** 6 * Y ** 0 Rule QUAD ERROR 1 0.384088E-01 0.96159122 2 0.819787 0.18021262 3 0.660662 0.33933827 4 1.01295 0.01294949 5 0.995414 0.00458554 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 504.000 * X ** 6 * Y ** 1 Rule QUAD ERROR 1 0.115226 0.88477366 2 1.23058 0.23058128 3 1.16663 0.16662519 4 0.999117 0.00088296 5 1.04339 0.04338624 6 0.999307 0.00069314 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 2520.00 * X ** 6 * Y ** 2 Rule QUAD ERROR 1 0.192044 0.80795610 2 1.02849 0.02848508 3 1.13350 0.13349531 4 0.811392 0.18860789 5 0.866501 0.13349890 6 0.996224 0.00377556 7 0.994117 0.00588301 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 9240.00 * X ** 6 * Y ** 3 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.635854 0.36414633 3 0.800594 0.19940618 4 0.846318 0.15368207 5 0.896388 0.10361195 6 1.03039 0.03039232 7 1.02893 0.02893207 8 1.00155 0.00155156 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 27720.0 * X ** 6 * Y ** 4 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.332597 0.66740314 3 0.467461 0.53253898 4 0.998828 0.00117160 5 1.06917 0.06917320 6 1.00786 0.00785815 7 1.01024 0.01024312 8 0.997890 0.00210973 9 0.996691 0.00330876 10 1.00000 0.00000000 Integrate 72.0000 * X ** 7 * Y ** 0 Rule QUAD ERROR 1 0.164609E-01 0.98353909 2 0.702418 0.29758230 3 0.516101 0.48389926 4 1.01690 0.01690162 5 0.981708 0.01829176 6 1.00020 0.00019804 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 720.000 * X ** 7 * Y ** 1 Rule QUAD ERROR 1 0.548697E-01 0.94513032 2 1.17091 0.17091049 3 1.02082 0.02081580 4 1.03586 0.03586257 5 1.08213 0.08213142 6 0.999233 0.00076731 7 1.00171 0.00171183 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 3960.00 * X ** 7 * Y ** 2 Rule QUAD ERROR 1 0.100594 0.89940558 2 1.07412 0.07412051 3 1.10343 0.10343164 4 0.769683 0.23031716 5 0.846090 0.15390976 6 0.981678 0.01832186 7 0.979223 0.02077746 8 0.999209 0.00079060 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 15840.0 * X ** 7 * Y ** 3 Rule QUAD ERROR 1 0.134126 0.86587410 2 0.718176 0.28182394 3 0.860170 0.13982982 4 0.720497 0.27950348 5 0.797080 0.20291962 6 1.04271 0.04270623 7 1.03934 0.03934337 8 1.00613 0.00613355 9 1.00188 0.00188136 10 1.00000 0.00000000 Integrate 90.0000 * X ** 8 * Y ** 0 Rule QUAD ERROR 1 0.685871E-02 0.99314129 2 0.585294 0.41470550 3 0.389922 0.61007802 4 1.01216 0.01216139 5 0.956602 0.04339756 6 1.00044 0.00043938 7 0.999572 0.00042796 8 1.00000 0.00000000 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 990.000 * X ** 8 * Y ** 1 Rule QUAD ERROR 1 0.251486E-01 0.97485139 2 1.07309 0.07308903 3 0.852434 0.14756609 4 1.08374 0.08373832 5 1.12094 0.12093530 6 1.00203 0.00203040 7 1.00716 0.00715736 8 1.00026 0.00026047 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 5940.00 * X ** 8 * Y ** 2 Rule QUAD ERROR 1 0.502972E-01 0.94970279 2 1.07329 0.07328550 3 1.01255 0.01255422 4 0.761318 0.23868198 5 0.849523 0.15047725 6 0.957945 0.04205474 7 0.956754 0.04324599 8 0.996306 0.00369388 9 0.999303 0.00069732 10 1.00000 0.00000000 Integrate 110.000 * X ** 9 * Y ** 0 Rule QUAD ERROR 1 0.279429E-02 0.99720571 2 0.476896 0.52310429 3 0.287142 0.71285845 4 0.996255 0.00374460 5 0.920084 0.07991597 6 1.00009 0.00008582 7 0.997886 0.00211358 8 0.999942 0.00005788 9 1.00000 0.00000000 10 1.00000 0.00000000 Integrate 1320.00 * X ** 9 * Y ** 1 Rule QUAD ERROR 1 0.111772E-01 0.98882284 2 0.953802 0.04619766 3 0.686695 0.31330475 4 1.13294 0.13294222 5 1.15215 0.15214823 6 1.00942 0.00941807 7 1.01744 0.01744391 8 1.00134 0.00134432 9 1.00015 0.00015132 10 1.00000 0.00000000 Integrate 132.000 * X ** 10 * Y ** 0 Rule QUAD ERROR 1 0.111772E-02 0.99888228 2 0.381514 0.61848561 3 0.207231 0.79276920 4 0.968918 0.03108196 5 0.873671 0.12632881 6 0.998219 0.00178063 7 0.993975 0.00602508 8 0.999662 0.00033832 9 0.999970 0.00003026 10 1.00000 0.00000000 TEST05 This routine creates an EPS plot of some of the sets of Dunavant points. Rule 1 plotted in "dunavant_rule_01.eps". Rule 2 plotted in "dunavant_rule_02.eps". Rule 3 plotted in "dunavant_rule_03.eps". Rule 4 plotted in "dunavant_rule_04.eps". Rule 5 plotted in "dunavant_rule_05.eps". Rule 6 plotted in "dunavant_rule_06.eps". Rule 7 plotted in "dunavant_rule_07.eps". Rule 8 plotted in "dunavant_rule_08.eps". Rule 9 plotted in "dunavant_rule_09.eps". Rule 10 plotted in "dunavant_rule_10.eps". TEST06 REFERENCE_TO_PHYSICAL_T3 transforms a rule on the unit (reference) triangle to a rule on an arbitrary (physical) triangle. The reference triangle: 1 0.00000 0.00000 2 1.00000 0.00000 3 0.00000 1.00000 Rule 2 for reference triangle with area = 0.500000 X Y W 1 0.666667 0.166667 0.333333 2 0.166667 0.166667 0.333333 3 0.166667 0.666667 0.333333 The physical triangle: 1 1.00000 2.00000 2 1.00000 1.00000 3 3.00000 2.00000 Rule 2 for physical triangle with area = 1.00000 X Y W 1 1.33333 1.33333 0.333333 2 1.33333 1.83333 0.333333 3 2.33333 1.83333 0.333333 DUNAVANT_PRB: Normal end of execution. 27 December 2010 12:47:27.203 PM