Numerical performance of preconditioning techniques for the solution of complex sparse linear systems

Mazzia, Annamaria; Pini, Giorgio

doi:10.1002/cnm.568

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…While solving the above real system by a preconditioned conjugate gradient solver shows acceptable convergence for this particular problem, it should be noted this does not necessarily hold for general complex systems arising from finite element discretizations of HelmholtzÕs equation because the resulting system is not always positive definite. Several iterative solvers for such complex systems have been developed and examined for different problems [28][29][30].…”

Section: The Finite Element Methodsmentioning

confidence: 99%

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

Mehdizadeh

Paraschivoiu

2005

Applied Acoustics

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A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption linings are modeled as a bulk media with a complex speed of sound and mean density. Domain decomposition and parallel processing techniques are applied to address the high computational and memory requirements. The comparison of the computationally predicted and the experimentally measured transmission loss shows a good agreement.

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Section: The Finite Element Methodsmentioning

confidence: 99%

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

Mehdizadeh

Paraschivoiu

2005

Applied Acoustics

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“…Suitable iterative solvers for sparse complex symmetric matrix systems other than GM-RES include BiCG-Stab, [170], QMR [67] and TF-QMR [68] methods. Some numerical comparisons of the alternative iterative solvers are reported in [128] and elsewhere. The best combination of iterative solver and preconditioner seems to be problem dependent.…”

Section: Iterative Solution Methodsmentioning

confidence: 99%

A review of finite-element methods for time-harmonic acoustics

Thompson

2006

The Journal of the Acoustical Society of America

302

196

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State-of-the-art finite element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the field are specifically addressed: the effective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, infinite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; efficient algebraic equation solving methods for the resulting complex-symmetric (non-Hermitian) matrix systems including sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite element methods are described. Stabilized, multiscale and other wavebased discretization methods developed to reduce this error are reviewed. A review of finite element methods for acoustic inverse problems and shape optimization is also given.Running Title: Finite element methods for acoustics

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“…those studied in Adams (2007), Elman et al (2001), Erlangga et al (2004), Haber & Ascher (2001), Howle & Vavasis (2005), Poirier (2000) and Reitzinger et al (2003), there has been some work on the use of generalpurpose techniques such as SSOR, polynomial preconditioning, incomplete factorizations and sparse approximate inverses (see, e.g. Freund, 1990;Horesh et al, 2006;Mazzia & Pini, 2003;Mazzia & McCoy, 1999). Somewhere in between, we mention the work of Magolu monga Made (2001, e.g.…”

Section: Previous Workmentioning

confidence: 99%

Block preconditioning of real-valued iterative algorithms for complex linear systems

Benzi

Bertaccini

2007

IMA Journal of Numerical Analysis

155

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We revisit real-valued preconditioned iterative methods for the solution of complex linear systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the real equivalent formulation are discussed, as well as different types of block preconditioners for Krylov subspace methods. We argue that if either the real or the symmetric part of the coefficient matrix is positive semidefinite, block preconditioners for real equivalent formulations may be a useful alternative to preconditioners for the original complex formulation. Numerical experiments illustrating the performance of the various approaches are presented.

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Numerical performance of preconditioning techniques for the solution of complex sparse linear systems

Cited by 11 publications

References 24 publications

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

A review of finite-element methods for time-harmonic acoustics

Block preconditioning of real-valued iterative algorithms for complex linear systems

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