Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6929212 | Journal of Computational Physics | 2018 | 15 Pages |
Abstract
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 Nyström 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Camille Carvalho, Shilpa Khatri, Arnold D. Kim,