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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:376

Article

Perez-Arancibia, Carlos^1,2,3  Faria, Luiz M.¹  Turc, Catalin⁴ 

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Pontificia Univ Catolica Chile, Sch Engn, Inst Math & Computat Engn, Santiago, Chile

[3] Pontificia Univ Catolica Chile, Fac Math, Santiago, Chile

[4] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

关键词: Laplace equation;    Layer potentials;    Boundary integral operators;    Taylor interpolation;    Harmonic polynomials;    Nystrom method;   

DOI  :  10.1016/j.jcp.2018.10.002

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free