TY - JOUR
T1 - Planewave Density Interpolation Methods for 3D Helmholtz Boundary Integral Equations
AU - Pérez Arancibia, Carlos Andrés
AU - Turc, Catalin
AU - Faria, Luiz M.
N1 - Funding Information:
\ast Submitted to the journal's Methods and Algorithms for Scientific Computing section January 22, 2019; accepted for publication (in revised form) May 9, 2019; published electronically July 2, 2019. https://doi.org/10.1137/19M1239866 Funding: This work was supported by FONDECYT grant 11181032. \dagger Institute for Mathematical and Computational Engineering, School of Engineering and Faculty of Mathematics, Pontificia Universidad Cat\o'lica de Chile, Santiago, Region Metropolitana, 7820436, Chile ([email protected], http://cperezar.sitios.ing.uc.cl/). \ddagger Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102 ([email protected]). \S Laboratoire POEMS, INRIA, 91762 Palaiseau Cedex, France ([email protected]). 1This technique has also been referred to as singularity extraction by some authors.
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.
PY - 2019/7/2
Y1 - 2019/7/2
N2 - This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular, and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated integral operators. Relying on Green's third identity and pointwise interpolation of density functions in the form of planewaves, these methods allow layer potentials and integral operators to be expressed in terms of integrand functions that remain bounded or even more regular regardless of the location of the target point relative to the surface sources. Common challenging integrals that arise in both Nyström and boundary element discretization of boundary integral equations can then be numerically evaluated by standard quadrature rules irrespective of the kernel singularity. Closed-form and purely numerical planewave density interpolation procedures are presented in this paper, which are used in conjunction with Chebyshev-based Nyström and Galerkin boundary element methods. A variety of numerical examples, including problems of acoustic scattering involving multiple touching and even intersecting obstacles, demonstrate the capabilities of the proposed technique.
Read More: https://epubs.siam.org/doi/10.1137/19M1239866
AB - This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular, and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated integral operators. Relying on Green's third identity and pointwise interpolation of density functions in the form of planewaves, these methods allow layer potentials and integral operators to be expressed in terms of integrand functions that remain bounded or even more regular regardless of the location of the target point relative to the surface sources. Common challenging integrals that arise in both Nyström and boundary element discretization of boundary integral equations can then be numerically evaluated by standard quadrature rules irrespective of the kernel singularity. Closed-form and purely numerical planewave density interpolation procedures are presented in this paper, which are used in conjunction with Chebyshev-based Nyström and Galerkin boundary element methods. A variety of numerical examples, including problems of acoustic scattering involving multiple touching and even intersecting obstacles, demonstrate the capabilities of the proposed technique.
Read More: https://epubs.siam.org/doi/10.1137/19M1239866
KW - Boundary element methods
KW - Helmholtz equation
KW - Integral equations
KW - Nystrom methods
UR - https://www.scopus.com/pages/publications/85071930161
U2 - 10.1137/19m1239866
DO - 10.1137/19m1239866
M3 - Article
SN - 1064-8275
VL - 41
SP - A2088-A2116
JO - SIAM journal on scientific computing
JF - SIAM journal on scientific computing
IS - 4
ER -