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Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz equation. (English) Zbl 0979.65107
The authors solve the Helmholtz equation in a region exterior to some closed, simply connected domains, subject to a Neumann boundary condition on the boundary of the domains and to the Sommerfeld radiation condition at infinity by the boundary element method. In order to solve the resulted dense algebraic system, the authors develop two preconditioners . The first is based on operator splitting, and the second on the idea of constructing approximate sparse inverses which admit an implicit operator splitting. Numerical experiments on the above problem confirm their effectivness.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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