A fast boundary element method for the two-dimensional Helmholtz Equation

Abstract In this paper, we present a fast method for solving boundary integral equations arising from the exterior Dirichlet problem for the two-dimensional Helmholtz equation. This method combines a quadrature method for discretizing the boundary integral equations with a preconditioned iterative method for solving the resulting dense, nonsymmetric linear systems. Using this method, a polynomial rate of convergence can be obtained by performing a finite number of iterations, which yields high computational efficiency. Various numerical examples are presented.

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