TY - JOUR
T1 - General-purpose kernel regularization of boundary integral equations via density interpolation
AU - Faria, Luiz M.
AU - Pérez-Arancibia, Carlos
AU - Bonnet, Marc
N1 - Funding Information:
C. Pérez-Arancibia would like to acknowledge the support of FONDECYT (Fondo Nacional de Desarrollo Científico y Tecnológico), Chile through Grant No. 11181032 .
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/5/1
Y1 - 2021/5/1
N2 - This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed technique relies on interpolating the density function around the kernel singularity in terms of solutions of the underlying homogeneous PDE, so as to recast singular and nearly singular integrals in terms of bounded (or more regular) integrands. We present here a simple interpolation strategy which, unlike previous approaches, does not entail explicit computation of high-order derivatives of the density function along the surface. Furthermore, the proposed approach is kernel- and dimension-independent in the sense that the sought density interpolant is constructed as a linear combination of point-source fields, given by the same Green's function used in the integral equation formulation, thus making the procedure applicable, in principle, to any PDE with known Green's function. For the sake of definiteness, we focus here on Nystr‘̀om methods for the (scalar) Laplace and Helmholtz equations and the (vector) elastostatic and time-harmonic elastodynamic equations. The method's accuracy, flexibility, efficiency, and compatibility with fast solvers are demonstrated by means of a variety of large-scale three-dimensional numerical examples.
AB - This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed technique relies on interpolating the density function around the kernel singularity in terms of solutions of the underlying homogeneous PDE, so as to recast singular and nearly singular integrals in terms of bounded (or more regular) integrands. We present here a simple interpolation strategy which, unlike previous approaches, does not entail explicit computation of high-order derivatives of the density function along the surface. Furthermore, the proposed approach is kernel- and dimension-independent in the sense that the sought density interpolant is constructed as a linear combination of point-source fields, given by the same Green's function used in the integral equation formulation, thus making the procedure applicable, in principle, to any PDE with known Green's function. For the sake of definiteness, we focus here on Nystr‘̀om methods for the (scalar) Laplace and Helmholtz equations and the (vector) elastostatic and time-harmonic elastodynamic equations. The method's accuracy, flexibility, efficiency, and compatibility with fast solvers are demonstrated by means of a variety of large-scale three-dimensional numerical examples.
KW - Boundary integral equations
KW - Nyström methods
KW - Singular integrals
UR - http://www.scopus.com/inward/record.url?scp=85101372684&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.113703
DO - 10.1016/j.cma.2021.113703
M3 - Article
AN - SCOPUS:85101372684
VL - 378
JO - Computer methods in applied mechanics and engineering
JF - Computer methods in applied mechanics and engineering
SN - 0045-7825
M1 - 113703
ER -