TY - JOUR
T1 - Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
AU - Kechroud, Riyad
AU - Soulaimani, Azzeddine
AU - Saad, Yousef
AU - Gowda, Shivaraju
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2004/5/11
Y1 - 2004/5/11
N2 - This paper discusses 2D and 3D solutions of the harmonic Helmholtz equation by finite elements. It begins with a short survey of the absorbing and transparent boundary conditions associated with the DtN technique. The solution of the discretized system by means of a standard Galerkin or Galerkin least-squares (GLS) scheme is obtained by a preconditioned Krylov subspace technique, specifically a preconditioned GMRES iteration. The stabilization parameter associated to GLS is computed using a new formula. Three types of preconditioners: ILUT, ILUTC and ILU0, are tested to enhance convergence.
AB - This paper discusses 2D and 3D solutions of the harmonic Helmholtz equation by finite elements. It begins with a short survey of the absorbing and transparent boundary conditions associated with the DtN technique. The solution of the discretized system by means of a standard Galerkin or Galerkin least-squares (GLS) scheme is obtained by a preconditioned Krylov subspace technique, specifically a preconditioned GMRES iteration. The stabilization parameter associated to GLS is computed using a new formula. Three types of preconditioners: ILUT, ILUTC and ILU0, are tested to enhance convergence.
KW - Acoustic scattering
KW - DtN technique
KW - Finite element method
KW - GMRES iterative method
KW - Helmholtz equation
KW - ILU0
KW - ILUT
KW - ILUTC
KW - Incomplete factorization
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U2 - 10.1016/j.matcom.2004.01.004
DO - 10.1016/j.matcom.2004.01.004
M3 - Conference article
AN - SCOPUS:2342510323
VL - 65
SP - 303
EP - 321
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
SN - 0378-4754
IS - 4-5
T2 - Wave Phenomena in Physisc and Engineering: New Models
Y2 - 1 May 2003 through 1 May 2003
ER -