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Conjugate direction methods for helmholtz problems with complex‐valued wavenumbers
Author(s) -
Paulsen Keith D.,
Lynch Daniel R.,
Liu Weiping
Publication year - 1992
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.1620350311
Subject(s) - helmholtz equation , wavenumber , mathematics , discretization , scalar (mathematics) , helmholtz free energy , mathematical analysis , conjugate gradient method , algebraic equation , galerkin method , algebraic number , geometry , finite element method , algorithm , physics , boundary value problem , quantum mechanics , nonlinear system , optics , thermodynamics
The convergence behaviour of conjugate direction methods for Helmholtz problems with complex‐valued wavenumbers is studied. The model problem is a Galerkin discretization of the scalar Helmholtz equation on square arrays of 2D and 3D, C ° linear elements. A series of controlled experiments is performed which use the dimensionless wavenumber and the algebraic size of the system of equations to completely characterize the iterative performance of the solvers. The effects of algebraic size are examined as functions of both mesh refinement and mesh extension within the limits of present‐day workstation computing environments. A comparison is drawn between the conjugate direction methods investigated and the equivalent time‐domain solution obtained through explicit time‐stepping.