General-purpose kernel regularization of boundary integral equations via density interpolation

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dc.contributor.authorFaria, Luiz M.
dc.contributor.authorPerez-Arancibia, Carlos
dc.contributor.authorBonnet, Marc
dc.date.accessioned2025-01-20T22:21:37Z
dc.date.available2025-01-20T22:21:37Z
dc.date.issued2021
dc.description.abstractThis paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderon 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. (C) 2021 Elsevier B.V. All rights reserved.
dc.description.funderFONDECYT (Fondo Nacional de Desarrollo Cient'ifico y Tecnologico), Chile
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.cma.2021.113703
dc.identifier.eissn1879-2138
dc.identifier.issn0045-7825
dc.identifier.urihttps://doi.org/10.1016/j.cma.2021.113703
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/94655
dc.identifier.wosidWOS:000653170700005
dc.language.isoen
dc.revistaComputer methods in applied mechanics and engineering
dc.rightsacceso restringido
dc.subjectBoundary integral equations
dc.subjectNystrom methods
dc.subjectSingular integrals
dc.titleGeneral-purpose kernel regularization of boundary integral equations via density interpolation
dc.typeartículo
dc.volumen378
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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