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Efficient discretization of Laplace boundary integral equations on polygonal domains. (English) Zbl 1185.65219
Summary: We describe a numerical procedure for the construction of quadrature formulae suitable for the efficient discretization of boundary integral equations over very general curve segments. While the procedure has applications to the solution of boundary value problems on a wide class of complicated domains, we concentrate in this paper on a particularly simple case: the rapid solution of boundary value problems for Laplace’s equation on two-dimensional polygonal domains. We view this work as the first step toward the efficient solution of boundary value problems on very general singular domains in both two and three dimensions. The performance of the method is illustrated with several numerical examples.
MSC:
65N38Boundary element methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65D32Quadrature and cubature formulas (numerical methods)
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