Numerical solution of a first kind integral equation of potential theory

Abstract

A boundary integral equation reformulation of the exterior Dirichlet problem for Laplace's equation yields an integral equation of the first kind, in which the unknown is the normal derivative on the boundary of the unknown harmonic function. The integral equation is solved with a collocation method based on piecewise quadratic interpolation. The discretized linear system is solved by using iterative Krylov-subspace methods such as Conjugate Gradient-like methods. Numerical examples are presented.

Keywords:

• Numerical analysis
• Laplace's equations
• Integral equations
• Iterative methods

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Notes

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