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Fast direct solution of the Helmholtz equation with a perfectly matched layer or an absorbing boundary condition. (English) Zbl 1035.65127
Summary: We consider the efficient numerical solution of the Helmholtz equation in a rectangular domain with a perfectly matched layer (PML) or an absorbing boundary condition. Standard bilinear (trilinear) finite-element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction-type fast direct solver. We present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a PML, and we optimize certain parameters of the layer to minimize the reflection.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F05 Direct numerical methods for linear systems and matrix inversion
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