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Boundary Integral Equations

2001
In Chapter 10, we examined finite element methods for the numerical solution of Laplace's equation. In this chapter, we propose an alternative approach. We introduce the idea of reformulating Laplace's equation as a boundary integral equation (BIE), and then we consider the numerical solution of Laplace's equation by numerically solving its ...
Kendall Atkinson, Weimin Han
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Preconditioning for Boundary Integral Equations

SIAM Journal on Matrix Analysis and Applications, 1992
This paper discusses three alternative preconditioning techniques to solve 3-D, mixed boundary conditions, Laplace equation problems. The direct boundary element equations are tested in conjunction with three iterative solution methods; namely, conjugate gradient on the normal equations, CGS of \textit{P. Sonneveld} [SIAM J. Sci. Stat. Comput.
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