Asymptotic analysis for close evaluation of layer potentials

JOURNAL OF COMPUTATIONAL PHYSICS

卷:355

Article

Carvalho, Camille¹  Khatri, Shilpa¹  Kim, Arnold D.¹ 

[1] Univ Calif Merced, Appl Math Unit, Sch Nat Sci, 5200 North Lake Rd, Merced, CA 95343 USA

关键词: Boundary integral equations;    Laplace's equation;    Layer potentials;    Nearly singular integrals;    Close evaluations;   

DOI  :  10.1016/j.jcp.2017.11.015

来源: Elsevier

【 摘 要 】

We study the evaluation of layer potentials close to the domain boundary. Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in nano-optics. When numerically evaluating layer potentials, it is natural to use the same quadrature rule as the one used in the Nystrom method to solve the underlying boundary integral equation. However, this method is problematic for evaluation points close to boundaries. For a fixed number of quadrature points, N, this method incurs O(1) errors in a boundary layer of thickness O(1/N). Using an asymptotic expansion for the kernel of the layer potential, we remove this O(1) error. We demonstrate the effectiveness of this method for interior and exterior problems for Laplace's equation in two dimensions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free