Numerical integration over n-dimensional cubes using generalized Gaussian quadrature

참고문헌 (20)

1. A. H. Stroud, "Approximate Calculation of Multiple Integrals" (1971), Prentice-Hall
2. A. H. Stroud, "Gaussian Quadrature Formulas" (1966), Prentice Hall
3. A. Sommariva, "Product Gauss cubature over polygons based on Green's integration Formula", BIT Numerical Mathematics, 47, pp.441~453 (2007)
4. D Holdych, "Quadrature rules for triangular and tetrahedral elements with generalized functions", International Jour-nal for Numerical Methods in Engineering, 73, pp.1310~1327 (2008)
5. Ethan J. Kubatko, "New com-putationally effcient quadrature formulas for pyramidal elements", Finite Elements in Analysis and Design, 65, pp.63~75 (2013)
6. Ethan J. Kubatko, "New com-putationally effcient quadrature formulas for triangular prism ele-ments", Computers & Fluids, 73, pp.187~201 (2013)
7. Hans Minnebo, "Three-dimensional integration strategies of singu-lar functions introduced by the XFEM in the LEFM", International Journal for Numerical Methods in Engineering, 92, pp.1117~1138 (2012)
8. J. Ma, "Generalized Gaussian Quadrature rules for systems of arbitrary functions", SIAM J. Numer. Anal, 33, pp.971~996 (1996)
9. Jayan Sarada, "Generalized Gaussian Quadrature rules over two-dimensional regions with linear edges", Applied Math-ematics and Computation, 217, pp.5612~5621 (2011)
10. K. V. Nagaraja, "Generalized Gaussian quadrature rules over regions with parabolic edges", International Journal of Computer Mathematics, 89, pp.1631~1640 (2012)
11. Marc Lenoir, "Evaluation of 3-D Singular and Nearly Singular Integrals in Galerkin BEM for Thin Layers", SIAM Journal on Scientic Computing, 34, pp.A3057~A3078 (2012)
12. Michael G. Duffy, "Quadrature Over a Pyramid or Cube of Inte-grands with a Singularity at a Vertex", SIAM J. Numer. Anal, 19, pp.1260~1262 (1982)
13. P. J. Davis, "Methods of Numerical Integration" (2007), Courier Dover Publications
14. P.V. Dooren, "An adaptive algorithm for numerical integration over an n-dimensional cube", Journal of Computational and Applied Mathematics, 2, pp.207~210 (1976)
15. R. Cools, "An encyclopedia of Cubature formulas", Journal of com-plexity, 19, pp.445~453 (2003)
16. R. Cools, "Constructing cubature formulae: the science behind the art", Acta Numerica, 6, pp.1~54 (1997)
17. R. Cools, "Monomial cubature rules since Stroud: A compilation", Journal of Computational and Applied Mathematics, 48, pp.309~326 (1993)
18. S. E. Mousavi, "Generalized Gaussian Quad-rature Rules on Arbitrary Polygons", International Journal for Nu-merical Methods in Engineering, 82, pp.99~113 (2010)
19. S. E. Mousavi, "Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended nite ele-ment method", Computer Methods in Applied Mechanics and Engi-neering, 199, pp.3237~3249 (2010)
20. T. W. Sag, "Numerical Evaluation of High-Dimensional Integrals", Math. Comp., 18, pp.245~253 (1964)

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