COMPUTING WEAKLY SINGULAR AND NEAR-SINGULAR INTEGRALS OVER CURVED BOUNDARY ELEMENTS

被引：5
作者：
Montanelli, Hadrien [1 ]
Aussal, Matthieu [1 ]
Haddar, Houssem [1 ]
机构：
[1] Inria, CMAP, École Polytechnique, IP Paris, Palaiseau
来源：
SIAM Journal on Scientific Computing | 2022年 / 44卷 / 06期
关键词：
boundary element method; continuation approach; Gauss quadrature; Helmholtz equation; homogeneous functions; integral equations; near-singular integrals; singular integrals; Taylor series;
D O I：
10.1137/21M1462027
中图分类号：
学科分类号：
摘要：
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the reference element's space using Newton's method, singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy of our method for quadratic basis functions and quadratic triangles with several numerical experiments, including the scattering by two half-spheres. © 2022 Society for Industrial and Applied Mathematics.
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页码：A3728 / A3753
页数：25
相关论文
共 52 条
[11]  
Colton D., Kress R., Inverse Acoustic and Electromagnetic Scattering Theory, (2013)
[12]  
Delourme B., Haddar H., Joly P., Approximate models for wave propagation across thin periodic interfaces, J. Math. Pures Appl, 98, pp. 28-71, (2012)
[13]  
Duffy M. G., Quadrature over a pyramid or cube of integrands with a singularity at a vertex, SIAM J. Numer. Anal, 19, pp. 1260-1262, (1982)
[14]  
Geuzaine C., Remacle J.-F., Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Internat. J. Numer. Methods Engrg, 79, pp. 1309-1331, (2009)
[15]  
Graglia R. D., Lombardi G., Machine precision evaluation of singular and nearly singular potential integrals by use of Gauss quadrature formulas for rational functions, IEEE Trans. Antennas and Propagation, 56, pp. 981-998, (2008)
[16]  
Greengard L., Rokhlin V., A fast algorithm for particle simulations, J. Comput. Phys, 73, pp. 325-238, (1987)
[17]  
Guiggiani M., Gigante A., A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method, ASME J. Appl. Mech, 57, pp. 906-915, (1990)
[18]  
Guiggiani M., Krishnasamy G., Rudolphi T. J., Rizzo F. J., A general algorithm for the numerical solution of hypersingular boundary integral equations, ASME J. Appl. Mech, 59, pp. 603-614, (1992)
[19]  
Hackbusch W., Hierarchical Matrices: Algorithms and Analysis, (2015)
[20]  
Hackbusch W., Sauter S. A., On the efficient use of the Galerkin-method to solve Fredholm integral equations, Appl. Math, 38, pp. 301-322, (1993)
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