Abstract

We realize fast collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels on a polyhedral domain in Rd with d ≥ 3. A polyhedral domain is subdivided into a finite number of simplices. We construct a uniform self-similar partition of a simplex for the purpose of constructing multi-scale bases and their corresponding collocation functionals. The multi-scale bases and the collocation functionals lead to a compression of the matrix representation of the weakly singular integral operator and thus to a fast collocation scheme for solving the integral equation. We develop a quadrature rule for computing the weakly singular integrals appearing in the matrix. 2000 AMS Mathematics subject classification. Primary 65B05, 45L10.

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