On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems
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Author(s)
Hochman, Amit
Leviatan, Yehuda
White, Jacob K.
Date Issued
April 2013
Journal
Journal of Computational Physics
Publisher
Elsevier B.V.
Citation
Hochman, Amit, Yehuda Leviatan, and Jacob K. White. “On the Use of Rational-Function Fitting Methods for the Solution of 2D Laplace Boundary-Value Problems.” Journal of Computational Physics 238 (April 2013): 337–358.
Version
Original manuscript
Abstract
A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context he 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss–Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary data. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nyström method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1016/j.jcp.2012.08.015
