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Title: Modified Representations for the Close Evaluation Problem
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions.  more » « less
Award ID(s):
1819052
PAR ID:
10357848
Author(s) / Creator(s):
Date Published:
Journal Name:
Mathematical and Computational Applications
Volume:
26
Issue:
4
ISSN:
2297-8747
Page Range / eLocation ID:
69
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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