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CubatureData2D.m
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% Purpose: script to set the nodes and weights of
% multidimensional quadrature (cubature) rules
% Cubature formulae from:
%
% Cools, R. "Monomial Cubature Rules Since "Stroud": A Compilation--Part 2."
% J. Comput. Appl. Math. 112, 21-27, 1999.
%
% Cools, R. "Encyclopaedia of Cubature Formulas."
% http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html
cub2D{1} = [...
[-0.333333333333333 -0.333333333333333 2.000000000000000];...
];
cub2D{2} = [...
[-0.666666666666667 -0.666666666666667 0.666666666666667];...
[0.333333333333333 -0.666666666666667 0.666666666666667];...
[-0.666666666666667 0.333333333333333 0.666666666666667];...
];
cub2D{3} = [...
[-0.816847572980458 -0.816847572980458 0.219903487310644];...
[0.633695145960917 -0.816847572980459 0.219903487310644];...
[-0.816847572980459 0.633695145960917 0.219903487310644];...
[-0.108103018168070 -0.108103018168070 0.446763179356023];...
[-0.783793963663860 -0.108103018168070 0.446763179356023];...
[-0.108103018168070 -0.783793963663860 0.446763179356023];...
];
cub2D{4} = [...
[-0.816847572980458 -0.816847572980458 0.219903487310644];...
[0.633695145960917 -0.816847572980459 0.219903487310644];...
[-0.816847572980459 0.633695145960917 0.219903487310644];...
[-0.108103018168070 -0.108103018168070 0.446763179356023];...
[-0.783793963663860 -0.108103018168070 0.446763179356023];...
[-0.108103018168070 -0.783793963663860 0.446763179356023];...
];
cub2D{5} = [...
[-0.333333333333333 -0.333333333333333 0.450000000000000];...
[-0.059715871789770 -0.059715871789770 0.264788305577012];...
[-0.880568256420460 -0.059715871789770 0.264788305577012];...
[-0.059715871789770 -0.880568256420460 0.264788305577012];...
[-0.797426985353087 -0.797426985353087 0.251878361089654];...
[0.594853970706175 -0.797426985353087 0.251878361089654];...
[-0.797426985353087 0.594853970706175 0.251878361089654];...
];
cub2D{6} = [...
[-0.501426509658179 -0.501426509658179 0.233572551452759];...
[0.002853019316358 -0.501426509658179 0.233572551452759];...
[-0.501426509658179 0.002853019316358 0.233572551452759];...
[-0.873821971016996 -0.873821971016996 0.101689812740414];...
[0.747643942033991 -0.873821971016996 0.101689812740414];...
[-0.873821971016996 0.747643942033991 0.101689812740414];...
[-0.379295097932431 -0.893709900310366 0.165702151236747];...
[-0.893709900310366 -0.379295097932431 0.165702151236747];...
[0.273004998242797 -0.893709900310366 0.165702151236747];...
[-0.893709900310366 0.273004998242797 0.165702151236747];...
[0.273004998242797 -0.379295097932431 0.165702151236747];...
[-0.379295097932431 0.273004998242797 0.165702151236747];...
];
cub2D{7} = [...
[-0.158765070723907 -0.158765070723907 0.278402959350494];...
[-0.682469858552186 -0.158765070723907 0.278402959350494];...
[-0.158765070723907 -0.682469858552186 0.278402959350494];...
[-0.901937632421608 -0.901937632421608 0.063653882657145];...
[0.803875264843215 -0.901937632421608 0.063653882657145];...
[-0.901937632421608 0.803875264843215 0.063653882657145];...
[-0.696696002590528 -0.696696002590528 0.168642646759703];...
[0.393392005181056 -0.696696002590528 0.168642646759703];...
[-0.696696002590528 0.393392005181056 0.168642646759703];...
[0.348275575962283 -0.375762055856278 0.077983588949662];...
[-0.375762055856278 0.348275575962283 0.077983588949662];...
[-0.972513520106005 -0.375762055856278 0.077983588949662];...
[-0.375762055856278 -0.972513520106005 0.077983588949662];...
[-0.972513520106005 0.348275575962283 0.077983588949662];...
[0.348275575962283 -0.972513520106005 0.077983588949662];...
];
cub2D{8} = [...
[-0.333333333333333 -0.333333333333333 0.288631215355574];...
[-0.081414823414554 -0.081414823414554 0.190183268534569];...
[-0.837170353170893 -0.081414823414554 0.190183268534569];...
[-0.081414823414554 -0.837170353170893 0.190183268534569];...
[-0.658861384496480 -0.658861384496480 0.206434741069437];...
[0.317722768992959 -0.658861384496480 0.206434741069437];...
[-0.658861384496480 0.317722768992959 0.206434741069437];...
[-0.898905543365938 -0.898905543365938 0.064916995246396];...
[0.797811086731876 -0.898905543365938 0.064916995246396];...
[-0.898905543365938 0.797811086731876 0.064916995246396];...
[-0.473774340730724 0.456984785910809 0.054460628348870];...
[0.456984785910809 -0.473774340730724 0.054460628348870];...
[-0.983210445180085 0.456984785910809 0.054460628348870];...
[0.456984785910809 -0.983210445180085 0.054460628348870];...
[-0.983210445180085 -0.473774340730724 0.054460628348870];...
[-0.473774340730724 -0.983210445180085 0.054460628348870];...
];
cub2D{9} = [...
[-0.333333333333333 -0.333333333333333 0.194271592565598];...
[-0.020634961602525 -0.020634961602525 0.062669400454278];...
[-0.958730076794950 -0.020634961602525 0.062669400454278];...
[-0.020634961602525 -0.958730076794950 0.062669400454278];...
[-0.125820817014127 -0.125820817014127 0.155655082009549];...
[-0.748358365971746 -0.125820817014127 0.155655082009549];...
[-0.125820817014127 -0.748358365971746 0.155655082009549];...
[-0.623592928761935 -0.623592928761935 0.159295477854420];...
[0.247185857523869 -0.623592928761935 0.159295477854420];...
[-0.623592928761935 0.247185857523869 0.159295477854420];...
[-0.910540973211095 -0.910540973211095 0.051155351317396];...
[0.821081946422189 -0.910540973211095 0.051155351317396];...
[-0.910540973211095 0.821081946422189 0.051155351317396];...
[0.482397197568996 -0.556074021678469 0.086567078754579];...
[-0.556074021678469 0.482397197568996 0.086567078754579];...
[-0.926323175890527 -0.556074021678469 0.086567078754579];...
[-0.556074021678469 -0.926323175890527 0.086567078754579];...
[-0.926323175890527 0.482397197568996 0.086567078754579];...
[0.482397197568996 -0.926323175890527 0.086567078754579];...
];
cub2D{10} = [...
[-0.333333333333333 -0.333333333333333 0.167046799610393];...
[-0.004269134091050 -0.004269134091050 0.014459701184113];...
[-0.991461731817899 -0.004269134091050 0.014459701184113];...
[-0.004269134091050 -0.991461731817899 0.014459701184113];...
[-0.143975100541888 -0.143975100541888 0.148984355841961];...
[-0.712049798916225 -0.143975100541888 0.148984355841961];...
[-0.143975100541888 -0.712049798916225 0.148984355841961];...
[-0.630487174513551 -0.630487174513551 0.157292946806217];...
[0.260974349027102 -0.630487174513551 0.157292946806217];...
[-0.630487174513551 0.260974349027102 0.157292946806217];...
[-0.959037562856645 -0.959037562856645 0.013856646174215];...
[0.918075125713290 -0.959037562856645 0.013856646174215];...
[-0.959037562856645 0.918075125713290 0.013856646174215];...
[-0.726852847487933 0.656846867693389 0.059036640669559];...
[0.656846867693389 -0.726852847487933 0.059036640669559];...
[-0.929994020205456 0.656846867693389 0.059036640669559];...
[0.656846867693389 -0.929994020205456 0.059036640669559];...
[-0.929994020205456 -0.726852847487933 0.059036640669559];...
[-0.726852847487933 -0.929994020205456 0.059036640669559];...
[-0.334512798822723 0.259414658305837 0.079158734392122];...
[0.259414658305837 -0.334512798822723 0.079158734392122];...
[-0.924901859483115 0.259414658305837 0.079158734392122];...
[0.259414658305837 -0.924901859483115 0.079158734392122];...
[-0.924901859483115 -0.334512798822723 0.079158734392122];...
[-0.334512798822723 -0.924901859483115 0.079158734392122];...
];
cub2D{11} = [...
[-0.333333333333333 -0.333333333333333 0.171542269659139];...
[-0.008227986519701 -0.008227986519701 0.033232309648099];...
[-0.983544026960598 -0.008227986519701 0.033232309648099];...
[-0.008227986519701 -0.983544026960598 0.033232309648099];...
[-0.123062767323470 -0.123062767323470 0.134650934561697];...
[-0.753874465353061 -0.123062767323470 0.134650934561697];...
[-0.123062767323470 -0.753874465353061 0.134650934561697];...
[-0.579583807314522 -0.579583807314522 0.141045284213931];...
[0.159167614629044 -0.579583807314522 0.141045284213931];...
[-0.579583807314522 0.159167614629044 0.141045284213931];...
[-0.794793191450311 -0.794793191450311 0.077255352409353];...
[0.589586382900622 -0.794793191450311 0.077255352409353];...
[-0.794793191450311 0.589586382900622 0.077255352409353];...
[-0.943045809035533 -0.943045809035533 0.020851693311810];...
[0.886091618071066 -0.943045809035533 0.020851693311810];...
[-0.943045809035533 0.886091618071066 0.020851693311810];...
[-0.701412405190965 0.686811031831200 0.020556454130106];...
[0.686811031831200 -0.701412405190965 0.020556454130106];...
[-0.985398626640235 0.686811031831200 0.020556454130106];...
[0.686811031831200 -0.985398626640235 0.020556454130106];...
[-0.985398626640235 -0.701412405190966 0.020556454130106];...
[-0.701412405190966 -0.985398626640235 0.020556454130106];...
[-0.420944470627256 0.328932876191794 0.080668713854259];...
[0.328932876191794 -0.420944470627256 0.080668713854259];...
[-0.907988405564538 0.328932876191794 0.080668713854259];...
[0.328932876191794 -0.907988405564538 0.080668713854259];...
[-0.907988405564538 -0.420944470627256 0.080668713854259];...
[-0.420944470627256 -0.907988405564538 0.080668713854259];...
];
cub2D{12} = [...
[-0.115127288420454 -0.115127288420454 0.088694050812375];...
[-0.769745423159092 -0.115127288420454 0.088694050812375];...
[-0.115127288420454 -0.769745423159092 0.088694050812375];...
[-0.241326933740970 -0.241326933740970 0.083486638970495];...
[-0.517346132518060 -0.241326933740970 0.083486638970495];...
[-0.241326933740970 -0.517346132518060 0.083486638970495];...
[-0.773435586772427 -0.773435586772427 0.061949370456958];...
[0.546871173544855 -0.773435586772427 0.061949370456958];...
[-0.773435586772427 0.546871173544855 0.061949370456958];...
[-0.550360151853422 -0.550360151853422 0.096926744607805];...
[0.100720303706844 -0.550360151853422 0.096926744607805];...
[-0.550360151853422 0.100720303706844 0.096926744607805];...
[-0.949850839686919 -0.949850839686919 0.016284715813394];...
[0.899701679373837 -0.949850839686919 0.016284715813394];...
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