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Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory. (English) Zbl 0801.65131
The paper is concerned with the fast solution of the first-kind integral equation of potential theory in a three-dimensional domain. It presents an overlapping-block preconditioned Krylov-subspace iterative algorithm for solving the dense matrix problem generated by Galerkin or collocation schemes. A modified multipole algorithm with a novel adoption scheme is used to compute the iterates and is proved to require order $$N$$ computation and order $$N$$ storage. Furthermore, experimental evidence is given to demonstrate that the combined algorithm is nearly order $$N$$ in practice, and the method is shown to be effective for several engineering applications.

##### MSC:
 65R20 Numerical methods for integral equations 65N38 Boundary element methods for boundary value problems involving PDEs 65Y20 Complexity and performance of numerical algorithms 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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