A multilevel N log N algorithm for solving boundary integral equation

Multilevel algorithms have been used to generate fast algorithms for Fourier transforms and inversion of matrices in finite element method. They usually involve nesting a smaller problem within a larger problem. Recently, multilevel algorithms have been used to solve integral equation by expediting matrix-vector multiplies or by finding the inverse of the integral operator. Interpolation multilevel algorithm has also been proposed. These algorithms could invert an integral operator in less than O(N/sup 3/) operations and expedite a matrix-vector multiply to require O(Nlog N) or O(N) operations. In this paper, we will describe a multilevel algorithm for expediting matrix-vector multiply in an iterative solution of boundary integral equation. The algorithm has O(N(log N)/sup 2/) complexity, and for very large problem, O(Nlog N) complexity.<>