| Title | On the evaluation of layer potentials close to their sources |
| Authors | Johan Helsing, Rikard Ojala |
| Alternative Location | http://www.maths.lth.se/na/... |
| Alternative Location | http://dx.doi.org/10.1016/j... |
| Publication | Journal of Computational Physics |
| Year | 2008 |
| Volume | 227 |
| Issue | 5 |
| Pages | 2899 - 2921 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Inc. |
| Abstract English | When solving elliptic boundary value problems using integral<br> equation methods one may need to evaluate potentials represented by<br> a convolution of discretized layer density sources against a kernel.<br> Standard quadrature accelerated with a fast hierarchical method for<br> potential field evaluation gives accurate results far away from the<br> sources. Close to the sources this is not so. Cancellation and<br> nearly singular kernels may cause serious degradation. This paper<br> presents a new scheme based on a mix of composite polynomial<br> quadrature, layer density interpolation, kernel approximation,<br> rational quadrature, high polynomial order corrected interpolation<br> and differentiation, temporary panel mergers and splits, and a<br> particular implementation of the GMRES solver. Criteria for which<br> mix is fastest and most accurate in various situations are also<br> supplied. The paper focuses on the solution of the Dirichlet problem<br> for Laplace's equation in the plane. In a series of examples we<br> demonstrate the efficiency of the new scheme for interior domains<br> and domains exterior to up to 2000 close-to-touching contours.<br> Densities are computed and potentials are evaluated, rapidly and<br> accurate to almost machine precision, at points that lie arbitrarily<br> close to the boundaries. |
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