Nystrom's Method and Iterative Solvers for the Solution of the Double-Layer Potential Equation over Polyhedral Boundaries

In this paper we consider a quadrature method for the solution of the double-layer potential equation corresponding to Laplace's equation in a three-dimensional polyhedron. We prove the stability for our method in the case of special triangulations over the boundary of the polyhedron. For the s...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1995-06, Vol.32 (3), p.924-951
Main Author: Rathsfeld, A.
Format: Article
Language:English
Subjects:
Differential equations
Eigenvalues
Error rates
Gaussian elimination
Integral equations
Interpolation
Iterative solutions
Linear equations
Linear systems
Methods
Polyhedrons
Triangulation
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Summary:In this paper we consider a quadrature method for the solution of the double-layer potential equation corresponding to Laplace's equation in a three-dimensional polyhedron. We prove the stability for our method in the case of special triangulations over the boundary of the polyhedron. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and a further simple iteration procedure. Finally, we establish the rates of convergence and complexity and discuss the effect of mesh refinement near the corners and edges of the polyhedron.
ISSN:0036-1429
1095-7170
DOI:10.1137/0732043