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Fast direct solution of the Helmholtz equation with a perfectly matched layer or an absorbing boundary condition
Author(s) -
Heikkola Erkki,
Rossi Tuomo,
Toivanen Jari
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.752
Subject(s) - perfectly matched layer , helmholtz equation , discretization , solver , mathematics , mathematical analysis , reflection (computer programming) , bilinear interpolation , finite element method , boundary value problem , boundary (topology) , reduction (mathematics) , helmholtz free energy , boundary layer , geometry , physics , computer science , mathematical optimization , mechanics , statistics , quantum mechanics , thermodynamics , programming language
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 (ABC). 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. Copyright © 2003 John Wiley & Sons, Ltd.