Abstract
An iterative quadrature method is presented and analyzed for a second kind Fredholm integral equation with a logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two-dimensional Helmholtz equation. The method combines a quadrature method for discretizing the integral equation with a preconditioned iterative method for solving the resulting dense and nonsymmetric linear system. The quadrature method has a polynomial or exponential rate of convergence, which can be retained by the preconditioned iterative method with only $O(N^2 )$ arithmetic operations.
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