Preconditioning techniques for the solution of the Helmholtz equation by the finite element method

Riyad Kechroud; Azzeddine Soulaimani; Yousef Saad; Shivaraju Gowda

doi:10.1016/j.matcom.2004.01.004

Preconditioning techniques for the solution of the Helmholtz equation by the finite element method

Riyad Kechroud, Azzeddine Soulaimani, Yousef Saad, Shivaraju Gowda

Computer Science and Engineering

Research output: Contribution to journal › Conference article › peer-review

24 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	303-321
Number of pages	19
Journal	Mathematics and Computers in Simulation
Volume	65
Issue number	4-5
DOIs	https://doi.org/10.1016/j.matcom.2004.01.004
State	Published - May 11 2004
Event	Wave Phenomena in Physisc and Engineering: New Models - Montreal, Canada Duration: May 1 2003 → May 1 2003

Keywords

Acoustic scattering
DtN technique
Finite element method
GMRES iterative method
Helmholtz equation
ILU0
ILUT
ILUTC
Incomplete factorization

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title = "Preconditioning techniques for the solution of the Helmholtz equation by the finite element method",

abstract = "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.",

keywords = "Acoustic scattering, DtN technique, Finite element method, GMRES iterative method, Helmholtz equation, ILU0, ILUT, ILUTC, Incomplete factorization",

author = "Riyad Kechroud and Azzeddine Soulaimani and Yousef Saad and Shivaraju Gowda",

year = "2004",

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doi = "10.1016/j.matcom.2004.01.004",

language = "English (US)",

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journal = "Mathematics and Computers in Simulation",

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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

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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DO - 10.1016/j.matcom.2004.01.004

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EP - 321

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

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T2 - Wave Phenomena in Physisc and Engineering: New Models

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