Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D

Document Type

Article

Publication Date

1-1-2019

Abstract

We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on the use of Green's third identity and local Taylor-like interpolations of density functions in terms of harmonic polynomials. The proposed technique effectively regularizes the singularities present in boundary integral operators and layer potentials, and recasts the latter in terms of integrands that are bounded or even more regular, depending on the order of the density interpolation. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. A variety of numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule (to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type quadrature rule (to integrate over surfaces given as unions of non-overlapping quadrilateral patches) in three-dimensions.

Identifier

85054423469 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2018.10.002

e-ISSN

10902716

ISSN

00219991

First Page

411

Last Page

434

Volume

376

Grant

CMMI-1727565

Fund Ref

National Stroke Foundation

This document is currently not available here.

Share

COinS