03 March 2022 09:19:26 AM TRIANGLE_DUNAVANT_RULE_TEST: C++ version Test the TRIANGLE_DUNAVANT_RULE 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 Order Sum of weights 1 1 1 2 3 1 3 4 1 4 6 1 5 7 1 6 12 1 7 13 1 8 16 1 9 19 1 10 25 1 11 27 1 12 33 1 13 37 1 14 42 1 15 48 1 16 52 1 17 61 1 18 70 1 19 73 1 20 79 1 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 add up to 1. Rule Suborder Sum of coordinates 1 1 0.9999999999999989 2 1 1.000000000000001 3 2 0.9999999999999989 1 4 2 1 1.000000000000001 5 3 0.9999999999999989 1 0.999999999999999 6 3 0.999999999999999 1 1 7 4 0.9999999999999989 1 1 1 8 5 0.9999999999999989 1 1 0.9999999999999999 1 9 6 0.9999999999999989 1.000000000000001 1.000000000000001 1.000000000000001 1.000000000000001 1 10 6 0.9999999999999989 0.999999999999999 1 1 1 0.999999999999999 11 7 0.999999999999999 1 0.9999999999999989 0.999999999999999 1 1.000000000000001 1 12 8 1 0.9999999999999989 1 1 0.9999999999999991 1 1 1 13 10 0.9999999999999989 1.000000000000001 1 1.000000000000001 0.999999999999999 1 1 1 1 1 14 10 1.000000000000001 1 1.000000000000001 0.999999999999999 1.000000000000001 1 1 1 1 1 15 11 1 1.000000000000001 0.999999999999999 1 1 0.999999999999999 0.999999999999999 1 1 1 1.000000000000001 16 13 0.9999999999999989 0.9999999999999991 0.9999999999999989 0.9999999999999989 1 1 1 1 1 1 1 1.000000000000001 0.999999999999999 17 15 0.9999999999999989 1 1.000000000000001 1.000000000000001 1 1.000000000000001 0.999999999999999 1 1 1 1 1.000000000000001 1 0.999999999999999 1 18 17 0.9999999999999989 0.999999999999999 1 1.000000000000001 1 1 1.000000000000001 0.9999999999999991 1 1.000000000000001 1 1 1.000000000000001 0.999999999999999 1 1 0.9999999999999999 19 17 0.9999999999999989 0.9999999999999991 1.000000000000001 1 1.000000000000001 1.000000000000001 1 1.000000000000001 1.000000000000001 1 1 1 1 1.000000000000001 1 1 1 20 19 0.9999999999999989 1 1.000000000000001 1.000000000000001 0.999999999999999 0.9999999999999989 1 0.9999999999999989 0.9999999999999999 1 1 1 1 1 1 1 0.9999999999999989 1 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 * X^0 * Y^0 Rule QUAD ERROR 1 1 0 2 0.9999999999999989 1.110223024625157e-15 3 0.9999999999999991 8.881784197001252e-16 4 0.999999999999999 9.992007221626409e-16 5 0.999999999999999 9.992007221626409e-16 6 1.000000000000002 1.998401444325282e-15 7 0.9999999999999981 1.887379141862766e-15 8 1 0 9 0.9999999999999959 4.107825191113079e-15 10 0.9999999999999992 7.771561172376096e-16 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 0.9999999999999989 1.110223024625157e-15 2 1 0 3 0.9999999999999998 2.220446049250313e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999983 1.665334536937735e-15 6 1.000000000000002 1.77635683940025e-15 7 0.9999999999999982 1.77635683940025e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999963 3.663735981263017e-15 10 0.999999999999999 9.992007221626409e-16 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 0.6666666666666653 0.3333333333333347 2 1 2.220446049250313e-16 3 1 0 4 1 2.220446049250313e-16 5 0.9999999999999978 2.220446049250313e-15 6 1.000000000000002 2.442490654175344e-15 7 0.9999999999999973 2.664535259100376e-15 8 0.9999999999999997 3.33066907387547e-16 9 0.9999999999999966 3.441691376337985e-15 10 0.9999999999999989 1.110223024625157e-15 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 0.3703703703703692 0.6296296296296309 2 1.018518518518519 0.01851851851851904 3 0.9999999999999998 2.220446049250313e-16 4 1.000000000000001 1.332267629550188e-15 5 0.9999999999999976 2.442490654175344e-15 6 1.000000000000004 3.996802888650564e-15 7 0.999999999999996 3.996802888650564e-15 8 0.9999999999999992 7.771561172376096e-16 9 0.9999999999999962 3.774758283725532e-15 10 0.9999999999999996 4.440892098500626e-16 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 0.1851851851851844 0.8148148148148155 2 0.9953703703703711 0.004629629629628873 3 0.933333333333333 0.06666666666666698 4 1.000000000000002 2.220446049250313e-15 5 0.9999999999999971 2.886579864025407e-15 6 1.000000000000005 4.884981308350689e-15 7 0.9999999999999947 5.329070518200751e-15 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999964 3.552713678800501e-15 10 1 0 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 0.0864197530864193 0.9135802469135808 2 0.9236111111111122 0.07638888888888784 3 0.8088888888888884 0.1911111111111116 4 1.005273934867111 0.005273934867110919 5 0.9999999999999967 3.33066907387547e-15 6 1.000000000000006 5.773159728050814e-15 7 0.9999999999999938 6.217248937900877e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999967 3.33066907387547e-15 10 1.000000000000001 8.881784197001252e-16 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 0.03840877914951964 0.9615912208504803 2 0.8197873799725665 0.1802126200274335 3 0.6606617283950613 0.3393382716049387 4 1.012949494765379 0.01294949476537899 5 0.9954144620811249 0.00458553791887506 6 1.000000000000007 6.661338147750939e-15 7 0.9999999999999922 7.771561172376096e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999973 2.664535259100376e-15 10 1.000000000000002 2.220446049250313e-15 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 0.01646090534979412 0.9835390946502058 2 0.7024176954732525 0.2975823045267475 3 0.5161007407407404 0.4838992592592596 4 1.016901624524834 0.0169016245248339 5 0.9817082388510919 0.01829176114890807 6 1.000198039172351 0.0001980391723512831 7 0.9999999999999916 8.43769498715119e-15 8 0.9999999999999984 1.554312234475219e-15 9 0.9999999999999978 2.220446049250313e-15 10 1.000000000000004 3.774758283725532e-15 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 0.006858710562414208 0.9931412894375858 2 0.5852944958847751 0.4147055041152249 3 0.3899219753086416 0.6100780246913584 4 1.012161388071187 0.01216138807118683 5 0.9566024444547238 0.04339755554527625 6 1.000439376969608 0.0004393769696078298 7 0.9995720416471456 0.0004279583528543629 8 0.999999999999998 1.998401444325282e-15 9 0.999999999999998 1.998401444325282e-15 10 1.000000000000004 4.440892098500626e-15 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 0.002794289488390971 0.997205710511609 2 0.4768957110831696 0.5231042889168305 3 0.2871415454961132 0.7128584545038867 4 0.9962554029129936 0.003744597087006363 5 0.9200840310048876 0.07991596899511244 6 1.000085816069184 8.581606918367513e-05 7 0.9978864157721261 0.002113584227873888 8 0.9999421173630616 5.788263693840001e-05 9 0.9999999999999988 1.221245327087672e-15 10 1.000000000000006 5.551115123125783e-15 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 0.001117715795356387 0.9988822842046436 2 0.3815143858278731 0.6184856141721269 3 0.2072308048651118 0.7927691951348882 4 0.9689180401081772 0.03108195989182283 5 0.8736711916041175 0.1263288083958825 6 0.998219365607757 0.001780634392242963 7 0.9939749176968415 0.006025082303158458 8 0.9996616764904409 0.0003383235095590909 9 0.9999697359697353 3.026403026473723e-05 10 1.000000000000007 6.883382752675971e-15 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 0.9999999999999989 1.110223024625157e-15 2 1 0 3 0.9999999999999998 2.220446049250313e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999983 1.665334536937735e-15 6 1.000000000000002 1.77635683940025e-15 7 0.9999999999999982 1.77635683940025e-15 8 1 0 9 0.9999999999999963 3.663735981263017e-15 10 0.999999999999999 9.992007221626409e-16 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1.33333333333333 0.3333333333333304 2 1.000000000000002 1.554312234475219e-15 3 1.000000000000001 8.881784197001252e-16 4 0.9999999999999991 8.881784197001252e-16 5 0.9999999999999973 2.664535259100376e-15 6 1 2.220446049250313e-16 7 0.9999999999999992 7.771561172376096e-16 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999978 2.220446049250313e-15 10 0.9999999999999978 2.220446049250313e-15 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1.111111111111108 0.1111111111111076 2 0.9722222222222243 0.02777777777777568 3 1.000000000000001 1.110223024625157e-15 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999969 3.108624468950438e-15 6 1 0 7 0.9999999999999993 6.661338147750939e-16 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999981 1.887379141862766e-15 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 0.7407407407407376 0.2592592592592624 2 1.064814814814817 0.06481481481481732 3 1.133333333333334 0.133333333333334 4 1.000000000000001 8.881784197001252e-16 5 0.9999999999999962 3.774758283725532e-15 6 1.000000000000001 1.332267629550188e-15 7 0.9999999999999988 1.221245327087672e-15 8 0.9999999999999997 3.33066907387547e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999974 2.55351295663786e-15 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 0.4320987654320965 0.5679012345679035 2 1.174768518518522 0.1747685185185219 3 1.244444444444445 0.2444444444444449 4 0.9868151628322328 0.01318483716776719 5 0.9999999999999953 4.662936703425657e-15 6 1.000000000000002 2.220446049250313e-15 7 0.999999999999998 1.998401444325282e-15 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999979 2.109423746787797e-15 10 0.9999999999999966 3.441691376337985e-15 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 0.2304526748971179 0.7695473251028822 2 1.235082304526753 0.2350823045267527 3 1.25357037037037 0.25357037037037 4 0.9822472551723103 0.01775274482768974 5 1.013756613756608 0.01375661375660808 6 1.000000000000003 3.33066907387547e-15 7 0.9999999999999971 2.886579864025407e-15 8 0.9999999999999994 5.551115123125783e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999962 3.774758283725532e-15 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 0.1152263374485588 0.8847736625514412 2 1.230581275720169 0.2305812757201686 3 1.166625185185185 0.1666251851851848 4 0.9991170406072905 0.000882959392709548 5 1.043386243386237 0.04338624338623664 6 0.9993068628967992 0.0006931371032008471 7 0.9999999999999964 3.552713678800501e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999962 3.774758283725532e-15 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 0.05486968449931367 0.9451303155006864 2 1.170910493827165 0.1709104938271651 3 1.020815802469135 0.02081580246913517 4 1.035862570339427 0.03586257033942686 5 1.082131416436559 0.08213141643655941 6 0.999232687983325 0.0007673120166750147 7 1.001711833411374 0.001711833411374375 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999984 1.554312234475219e-15 10 0.9999999999999964 3.552713678800501e-15 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 0.02514860539551874 0.9748513946044812 2 1.073089027492003 0.07308902749200308 3 0.8524339094650198 0.1475660905349802 4 1.083738321283062 0.08373832128306158 5 1.120935304978982 0.1209353049789819 6 1.002030401021518 0.002030401021517747 7 1.007157358084734 0.007157358084733945 8 1.000260471866212 0.0002604718662118088 9 0.9999999999999989 1.110223024625157e-15 10 0.9999999999999969 3.108624468950438e-15 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 0.01117715795356387 0.9888228420464361 2 0.9538023373596549 0.04619766264034508 3 0.6866952486511197 0.3133047513488803 4 1.132942216937082 0.1329422169370817 5 1.152148228008733 0.1521482280087325 6 1.009418068376315 0.009418068376315203 7 1.017443906148548 0.01744390614854807 8 1.001344321726166 0.001344321726165942 9 1.000151320151319 0.0001513201513192453 10 0.9999999999999972 2.775557561562891e-15 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 0.6666666666666653 0.3333333333333347 2 1 2.220446049250313e-16 3 1 0 4 1 2.220446049250313e-16 5 0.9999999999999979 2.109423746787797e-15 6 1.000000000000003 2.664535259100376e-15 7 0.9999999999999973 2.664535259100376e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999966 3.441691376337985e-15 10 0.9999999999999989 1.110223024625157e-15 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1.111111111111108 0.1111111111111076 2 0.9722222222222243 0.02777777777777568 3 1.000000000000001 8.881784197001252e-16 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999968 3.219646771412954e-15 6 1 2.220446049250313e-16 7 0.9999999999999993 6.661338147750939e-16 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999981 1.887379141862766e-15 10 0.999999999999998 1.998401444325282e-15 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.111111111111106 0.1111111111111065 2 0.7638888888888919 0.2361111111111081 3 0.8000000000000018 0.1999999999999982 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999964 3.552713678800501e-15 6 0.9999999999999996 4.440892098500626e-16 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999992 7.771561172376096e-16 9 0.9999999999999989 1.110223024625157e-15 10 0.9999999999999979 2.109423746787797e-15 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 0.8641975308641929 0.1358024691358071 2 0.72916666666667 0.27083333333333 3 0.808888888888891 0.191111111111109 4 1.005273934867108 0.00527393486710781 5 0.999999999999996 3.996802888650564e-15 6 1 0 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999991 8.881784197001252e-16 9 0.9999999999999993 6.661338147750939e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 0.5761316872427947 0.4238683127572053 2 0.8191872427983579 0.1808127572016421 3 0.9499259259259276 0.05007407407407238 4 0.9584343448152447 0.0415656551847553 5 0.9629629629629585 0.03703703703704153 6 1.000000000000001 6.661338147750939e-16 7 1 4.440892098500626e-16 8 0.9999999999999988 1.221245327087672e-15 9 0.9999999999999997 3.33066907387547e-16 10 0.9999999999999968 3.219646771412954e-15 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 0.3456790123456765 0.6543209876543234 2 0.9371141975308689 0.06288580246913111 3 1.080675555555556 0.08067555555555628 4 0.8815019770050568 0.1184980229949432 5 0.9097505668934189 0.09024943310658107 6 1.000891176275551 0.00089117627555102 7 1 4.440892098500626e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999997 3.33066907387547e-16 10 0.9999999999999961 3.885780586188048e-15 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 0.1920438957475978 0.8079561042524022 2 1.028485082304532 0.02848508230453239 3 1.133495308641976 0.1334953086419757 4 0.8113921072273262 0.1886078927726738 5 0.866501097793609 0.133498902206391 6 0.9962244428697232 0.003775557130276774 7 0.9941169905707083 0.005883009429291652 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999953 4.662936703425657e-15 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 0.1005944215820749 0.899405578417925 2 1.074120513260181 0.07412051326018054 3 1.103431637860082 0.1034316378600821 4 0.7696828411439617 0.2303171588560383 5 0.8460902411571046 0.1539097588428954 6 0.9816781406020068 0.01832185939799325 7 0.9792225441811703 0.02077745581882973 8 0.9992094022584868 0.0007905977415132437 9 0.9999999999999991 8.881784197001252e-16 10 0.999999999999995 4.996003610813204e-15 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 0.05029721079103742 0.9497027892089626 2 1.073285500971658 0.07328550097165776 3 1.012554218930041 0.01255421893004072 4 0.7613180219665323 0.2386819780334677 5 0.849522750364323 0.150477249635677 6 0.9579452617335613 0.04205473826643868 7 0.9567540055313337 0.04324599446866628 8 0.9963061209271792 0.003693879072820816 9 0.9993026793026784 0.0006973206973216461 10 0.9999999999999947 5.329070518200751e-15 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 0.3703703703703692 0.6296296296296309 2 1.018518518518519 0.01851851851851904 3 0.9999999999999997 3.33066907387547e-16 4 1.000000000000001 1.110223024625157e-15 5 0.9999999999999976 2.442490654175344e-15 6 1.000000000000004 3.996802888650564e-15 7 0.999999999999996 3.996802888650564e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999963 3.663735981263017e-15 10 0.9999999999999996 4.440892098500626e-16 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 0.7407407407407376 0.2592592592592624 2 1.064814814814817 0.06481481481481732 3 1.133333333333334 0.133333333333334 4 1.000000000000001 8.881784197001252e-16 5 0.9999999999999962 3.774758283725532e-15 6 1.000000000000001 1.110223024625157e-15 7 0.9999999999999989 1.110223024625157e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999972 2.775557561562891e-15 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 0.8641975308641929 0.1358024691358071 2 0.7291666666666698 0.2708333333333302 3 0.8088888888888909 0.1911111111111091 4 1.005273934867108 0.00527393486710781 5 0.9999999999999961 3.885780586188048e-15 6 1 0 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999991 8.881784197001252e-16 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 0.7681755829903928 0.2318244170096072 2 0.5161179698216767 0.4838820301783233 3 0.5945679012345703 0.4054320987654297 4 1.063495826322662 0.06349582632266215 5 1.051146384479714 0.05114638447971398 6 0.9999999999999998 2.220446049250313e-16 7 1.000000000000001 1.332267629550188e-15 8 0.9999999999999989 1.110223024625157e-15 9 1.000000000000001 6.661338147750939e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 0.5761316872427941 0.4238683127572059 2 0.4816100823045301 0.5183899176954699 3 0.5915259259259279 0.4084740740740721 4 1.057370444436663 0.05737044443666339 5 1.053665910808764 0.05366591080876359 6 0.9995049020691392 0.0004950979308607772 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999989 1.110223024625157e-15 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 0.3840877914951957 0.6159122085048043 2 0.5446244855967117 0.4553755144032883 3 0.6945106172839519 0.3054893827160481 4 0.9721305594358866 0.02786944056411345 5 0.9924774142461171 0.007522585753882871 6 1.011536773794916 0.01153677379491591 7 1.011657611348051 0.01165761134805088 8 0.9999999999999988 1.221245327087672e-15 9 1.000000000000001 1.110223024625157e-15 10 0.999999999999997 2.997602166487923e-15 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 0.2347203170248415 0.7652796829751585 2 0.635853671315353 0.364146328684647 3 0.8005938216735261 0.1994061783264739 4 0.8463179268812919 0.1536820731187081 5 0.8963880504750773 0.1036119495249227 6 1.030392324808048 0.03039232480804777 7 1.028932067888712 0.02893206788871172 8 1.001551556719631 0.001551556719631142 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999959 4.107825191113079e-15 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 0.1341258954427665 0.8658741045572336 2 0.718176059289748 0.281823940710252 3 0.8601701838134432 0.1398298161865568 4 0.7204965241704401 0.2795034758295599 5 0.7970803762944992 0.2029196237055008 6 1.042706234947614 0.04270623494761439 7 1.039343367901023 0.03934336790102266 8 1.006133549344604 0.006133549344604194 9 1.001881361881363 0.001881361881362675 10 0.999999999999995 4.996003610813204e-15 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 0.1851851851851844 0.8148148148148155 2 0.9953703703703712 0.004629629629628762 3 0.933333333333333 0.06666666666666698 4 1.000000000000002 2.220446049250313e-15 5 0.9999999999999971 2.886579864025407e-15 6 1.000000000000005 4.884981308350689e-15 7 0.9999999999999947 5.329070518200751e-15 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999966 3.441691376337985e-15 10 0.9999999999999999 1.110223024625157e-16 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 0.4320987654320965 0.5679012345679035 2 1.174768518518521 0.1747685185185215 3 1.244444444444445 0.2444444444444449 4 0.9868151628322329 0.01318483716776708 5 0.9999999999999954 4.551914400963142e-15 6 1.000000000000002 2.220446049250313e-15 7 0.999999999999998 1.998401444325282e-15 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999978 2.220446049250313e-15 10 0.9999999999999967 3.33066907387547e-15 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 0.5761316872427947 0.4238683127572053 2 0.8191872427983579 0.1808127572016421 3 0.9499259259259274 0.05007407407407261 4 0.9584343448152447 0.0415656551847553 5 0.9629629629629586 0.03703703703704142 6 1.000000000000001 6.661338147750939e-16 7 1 4.440892098500626e-16 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999968 3.219646771412954e-15 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 0.5761316872427941 0.4238683127572059 2 0.4816100823045301 0.5183899176954699 3 0.5915259259259279 0.4084740740740721 4 1.057370444436664 0.05737044443666361 5 1.053665910808764 0.05366591080876359 6 0.9995049020691392 0.0004950979308607772 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999989 1.110223024625157e-15 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 0.4801097393689945 0.5198902606310054 2 0.3206983024691386 0.6793016975308614 3 0.4145382716049402 0.5854617283950598 4 1.129906973064206 0.1299069730642055 5 1.137746103732494 0.1377461037324936 6 0.9835924220110452 0.01640757798895476 7 0.9854550876925737 0.01454491230742627 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000002 1.998401444325282e-15 10 0.999999999999998 1.998401444325282e-15 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 0.3520804755372623 0.6479195244627377 2 0.293629615340652 0.706370384659348 3 0.4025547325102896 0.5974452674897104 4 1.106104831351558 0.1061048313515578 5 1.14249035467046 0.1424903546704603 6 0.98274090555801 0.01725909444199003 7 0.9855046352465319 0.01449536475346813 8 0.9990653931110697 0.0009346068889303227 9 1.000000000000003 2.886579864025407e-15 10 0.9999999999999973 2.664535259100376e-15 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 0.2347203170248413 0.7652796829751587 2 0.3325968554717301 0.66740314452827 3 0.4674610216735265 0.5325389783264736 4 0.9988283998579236 0.001171600142076401 5 1.069173199520118 0.06917319952011813 6 1.007858145127857 0.00785814512785743 7 1.01024311940511 0.01024311940511025 8 0.9978902668857511 0.002109733114248891 9 0.9966912366912396 0.003308763308760398 10 0.9999999999999971 2.886579864025407e-15 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 0.0864197530864193 0.9135802469135808 2 0.9236111111111122 0.07638888888888784 3 0.8088888888888883 0.1911111111111117 4 1.005273934867111 0.005273934867110919 5 0.9999999999999967 3.33066907387547e-15 6 1.000000000000006 5.773159728050814e-15 7 0.9999999999999937 6.328271240363392e-15 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999966 3.441691376337985e-15 10 1.000000000000001 8.881784197001252e-16 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 0.2304526748971179 0.7695473251028822 2 1.235082304526753 0.2350823045267527 3 1.25357037037037 0.25357037037037 4 0.9822472551723104 0.01775274482768963 5 1.013756613756608 0.0137566137566083 6 1.000000000000003 3.33066907387547e-15 7 0.9999999999999972 2.775557561562891e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999979 2.109423746787797e-15 10 0.9999999999999962 3.774758283725532e-15 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 0.3456790123456766 0.6543209876543234 2 0.9371141975308689 0.06288580246913111 3 1.080675555555556 0.08067555555555628 4 0.8815019770050568 0.1184980229949432 5 0.9097505668934188 0.09024943310658118 6 1.000891176275551 0.0008911762755507979 7 1 2.220446049250313e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999999 1.110223024625157e-16 10 0.999999999999996 3.996802888650564e-15 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 0.3840877914951957 0.6159122085048043 2 0.5446244855967117 0.4553755144032883 3 0.6945106172839519 0.3054893827160481 4 0.9721305594358866 0.02786944056411345 5 0.9924774142461172 0.00752258575388276 6 1.011536773794916 0.01153677379491613 7 1.011657611348051 0.01165761134805088 8 0.9999999999999987 1.332267629550188e-15 9 1.000000000000001 1.110223024625157e-15 10 0.9999999999999971 2.886579864025407e-15 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 0.3520804755372623 0.6479195244627377 2 0.293629615340652 0.706370384659348 3 0.4025547325102897 0.5974452674897104 4 1.106104831351558 0.1061048313515578 5 1.14249035467046 0.1424903546704603 6 0.9827409055580097 0.01725909444199025 7 0.985504635246532 0.01449536475346802 8 0.9990653931110695 0.0009346068889305448 9 1.000000000000003 2.664535259100376e-15 10 0.9999999999999976 2.442490654175344e-15 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 0.2816643804298096 0.7183356195701904 2 0.1878679412437149 0.812132058756285 3 0.2735522660082318 0.7264477339917681 4 1.166184510418822 0.1661845104188222 5 1.239578844891442 0.2395788448914415 6 0.9503256832693606 0.04967431673063938 7 0.9555740437777276 0.04442595622227241 8 0.9976843973853773 0.002315602614622714 9 1.003977067977072 0.003977067977071869 10 0.9999999999999979 2.109423746787797e-15 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 0.03840877914951964 0.9615912208504803 2 0.8197873799725665 0.1802126200274335 3 0.6606617283950613 0.3393382716049387 4 1.012949494765379 0.01294949476537877 5 0.9954144620811249 0.00458553791887506 6 1.000000000000006 6.439293542825908e-15 7 0.9999999999999923 7.66053886991358e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999974 2.55351295663786e-15 10 1.000000000000002 2.220446049250313e-15 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 0.1152263374485588 0.8847736625514412 2 1.230581275720169 0.2305812757201688 3 1.166625185185185 0.1666251851851845 4 0.9991170406072903 0.0008829593927096591 5 1.043386243386237 0.04338624338623687 6 0.9993068628967994 0.000693137103200625 7 0.9999999999999966 3.441691376337985e-15 8 0.9999999999999994 5.551115123125783e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999961 3.885780586188048e-15 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 0.1920438957475978 0.8079561042524022 2 1.028485082304533 0.02848508230453262 3 1.133495308641975 0.1334953086419755 4 0.8113921072273262 0.1886078927726738 5 0.8665010977936088 0.1334989022063912 6 0.996224442869723 0.003775557130276996 7 0.9941169905707085 0.005883009429291541 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999953 4.662936703425657e-15 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 0.2347203170248415 0.7652796829751585 2 0.635853671315353 0.364146328684647 3 0.8005938216735261 0.1994061783264739 4 0.8463179268812918 0.1536820731187082 5 0.8963880504750773 0.1036119495249227 6 1.030392324808048 0.03039232480804799 7 1.028932067888712 0.02893206788871172 8 1.001551556719631 0.001551556719631142 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999959 4.107825191113079e-15 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 0.2347203170248413 0.7652796829751587 2 0.33259685547173 0.66740314452827 3 0.4674610216735264 0.5325389783264736 4 0.9988283998579234 0.001171600142076623 5 1.069173199520118 0.06917319952011836 6 1.007858145127857 0.007858145127857208 7 1.01024311940511 0.0102431194051098 8 0.9978902668857512 0.00210973311424878 9 0.9966912366912396 0.003308763308760398 10 0.999999999999997 2.997602166487923e-15 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 0.01646090534979412 0.9835390946502058 2 0.7024176954732525 0.2975823045267475 3 0.5161007407407404 0.4838992592592596 4 1.016901624524834 0.0169016245248339 5 0.9817082388510918 0.01829176114890818 6 1.000198039172351 0.0001980391723512831 7 0.9999999999999913 8.659739592076221e-15 8 0.9999999999999983 1.665334536937735e-15 9 0.9999999999999978 2.220446049250313e-15 10 1.000000000000004 3.552713678800501e-15 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 0.05486968449931366 0.9451303155006864 2 1.170910493827165 0.1709104938271653 3 1.020815802469135 0.02081580246913539 4 1.035862570339427 0.03586257033942686 5 1.082131416436559 0.08213141643655941 6 0.9992326879833251 0.0007673120166749037 7 1.001711833411374 0.001711833411374153 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999983 1.665334536937735e-15 10 0.9999999999999963 3.663735981263017e-15 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 0.100594421582075 0.899405578417925 2 1.07412051326018 0.0741205132601801 3 1.103431637860082 0.1034316378600824 4 0.7696828411439617 0.2303171588560383 5 0.8460902411571046 0.1539097588428954 6 0.9816781406020066 0.01832185939799336 7 0.9792225441811702 0.02077745581882984 8 0.9992094022584866 0.0007905977415133547 9 0.9999999999999991 8.881784197001252e-16 10 0.9999999999999949 5.10702591327572e-15 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 0.1341258954427665 0.8658741045572336 2 0.718176059289748 0.281823940710252 3 0.8601701838134435 0.1398298161865565 4 0.7204965241704401 0.2795034758295599 5 0.7970803762944992 0.2029196237055008 6 1.042706234947614 0.04270623494761439 7 1.039343367901023 0.03934336790102289 8 1.006133549344604 0.006133549344603972 9 1.001881361881363 0.001881361881362675 10 0.999999999999995 4.996003610813204e-15 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 0.006858710562414208 0.9931412894375858 2 0.5852944958847751 0.4147055041152249 3 0.3899219753086416 0.6100780246913584 4 1.012161388071187 0.01216138807118705 5 0.9566024444547238 0.04339755554527625 6 1.000439376969608 0.0004393769696078298 7 0.9995720416471456 0.0004279583528543629 8 0.999999999999998 1.998401444325282e-15 9 0.999999999999998 1.998401444325282e-15 10 1.000000000000005 4.662936703425657e-15 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 0.02514860539551873 0.9748513946044812 2 1.073089027492003 0.07308902749200308 3 0.85243390946502 0.14756609053498 4 1.083738321283062 0.0837383212830618 5 1.120935304978982 0.1209353049789819 6 1.002030401021518 0.002030401021517969 7 1.007157358084734 0.007157358084733723 8 1.000260471866212 0.0002604718662118088 9 0.9999999999999987 1.332267629550188e-15 10 0.9999999999999966 3.441691376337985e-15 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 0.05029721079103742 0.9497027892089626 2 1.073285500971658 0.07328550097165776 3 1.01255421893004 0.01255421893004049 4 0.7613180219665323 0.2386819780334677 5 0.8495227503643231 0.1504772496356769 6 0.9579452617335612 0.0420547382664388 7 0.9567540055313337 0.04324599446866628 8 0.9963061209271792 0.003693879072820816 9 0.9993026793026781 0.0006973206973218682 10 0.9999999999999947 5.329070518200751e-15 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 0.002794289488390971 0.997205710511609 2 0.4768957110831695 0.5231042889168305 3 0.2871415454961132 0.7128584545038867 4 0.9962554029129936 0.003744597087006363 5 0.9200840310048877 0.07991596899511233 6 1.000085816069183 8.581606918345308e-05 7 0.9978864157721261 0.002113584227873888 8 0.9999421173630616 5.788263693840001e-05 9 0.9999999999999989 1.110223024625157e-15 10 1.000000000000006 5.773159728050814e-15 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 0.01117715795356387 0.9888228420464361 2 0.9538023373596551 0.04619766264034486 3 0.6866952486511199 0.3133047513488801 4 1.132942216937082 0.1329422169370815 5 1.152148228008733 0.1521482280087325 6 1.009418068376315 0.009418068376315203 7 1.017443906148548 0.01744390614854807 8 1.001344321726166 0.00134432172616572 9 1.000151320151319 0.0001513201513194673 10 0.9999999999999972 2.775557561562891e-15 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 0.001117715795356387 0.9988822842046436 2 0.3815143858278731 0.6184856141721269 3 0.2072308048651118 0.7927691951348882 4 0.9689180401081772 0.03108195989182283 5 0.8736711916041175 0.1263288083958825 6 0.998219365607757 0.001780634392242963 7 0.9939749176968417 0.006025082303158347 8 0.9996616764904409 0.0003383235095590909 9 0.9999697359697352 3.026403026484825e-05 10 1.000000000000007 6.883382752675971e-15 TEST05 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 0 2 1 0 3 0 1 Rule 2 for reference triangle with area = 0.5 X Y W 0 0.666666666666667 0.166666666666667 0.333333333333333 1 0.166666666666667 0.166666666666667 0.333333333333333 2 0.166666666666667 0.666666666666667 0.333333333333333 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 2 for physical triangle with area = 1 X Y W 0 1.333333333333334 1.333333333333333 0.333333333333333 1 1.333333333333334 1.833333333333333 0.333333333333333 2 2.333333333333334 1.833333333333333 0.333333333333333 TRIANGLE_DUNAVANT_RULE_TEST: Normal end of execution. 03 March 2022 09:19:26 AM