Abstract
Fast methods are developed for the numerical solution of Laplace’s equation on irregular regions with smooth boundaries. The methods use an integral equation formulation in a small carefully chosen region near the boundary, and use fast solvers to extend the solution to the rest of the region. Our experiments show the method works well for problems on interior, multiconnected and exterior regions. Moreover, we have found the computation of fourth order accurate solutions to be only slightly more expensive than those of second order. In addition, since we use integral equations we find that when we compute a harmonic function its conjugate can be computed at small additional cost.
Published Version
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