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Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation. (English) Zbl 0907.65118
The paper considers the iterative solution of fully populated complex valued non-Hermitian linear systems by preconditioned Krylov subspace methods arising in the boundary element solution of two-dimensional exterior Helmholtz problems. The authors discretize the uniquely solvable integral equation of Burton/Miller which involves a hypersingular operator, study the spectral properties of the boundary integral operators for the Helmholtz equation and report on numerical experiments with different iterative methods of Krylov type. As preconditioner the periodic tridiagonal band of the system matrix is chosen.
Reviewer: G.Schmidt (Berlin)

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