Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 252, Issue -, Pages 332-349Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.06.027
Keywords
Layer potentials; Singular integrals; Quadrature; High-order accuracy; Integral equations
Funding
- AFOSR/NSSEFF [FA9550-10-1-0180]
- NSF [DMS-0811005]
- Department of Energy [DEFG0288ER25053]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1216656] Funding Source: National Science Foundation
Ask authors/readers for more resources
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior domains. The practical application of these methods, however, requires the accurate evaluation of boundary integrals with singular, weakly singular or nearly singular kernels. Historically, these issues have been handled either by low-order product integration rules (computed semi-analytically), by singularity subtraction/cancellation, by kernel regularization and asymptotic analysis, or by the construction of special purpose generalized Gaussian quadrature rules. In this paper, we present a systematic, high-order approach that works for any singularity (including hypersingular kernels), based only on the assumption that the field induced by the integral operator is locally smooth when restricted to either the interior or the exterior. Discontinuities in the field across the boundary are permitted. The scheme, denoted QBX (quadrature by expansion), is easy to implement and compatible with fast hierarchical algorithms such as the fast multipole method. We include accuracy tests for a variety of integral operators in two dimensions on smooth and corner domains. (C) 2013 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available