Search results for "Algebraic multigrid method"

showing 3 items of 3 documents

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

2009

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed

Algebraic multigrid methodPhysics and Astronomy (miscellaneous)Helmholtz equationGMRESNavier equationMathematics::Numerical AnalysisMultigrid methodHelmholtz equationäärellisten elementtien menetelmäMathematicsElastic scatteringNumerical AnalysisNavierin yhtälöPreconditionerApplied MathematicsMathematical analysispohjustinAcoustic waveWave equationAlgebrallinen multigrid-menetelmäHelmholzin yhtälöGeneralized minimal residual methodComputer Science::Numerical AnalysisFinite element methodComputer Science ApplicationselementtimenetelmäComputational MathematicsClassical mechanicsModeling and SimulationPreconditioner
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An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

2007

A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…

Algebraic multigrid methodPhysics and Astronomy (miscellaneous)Helmholtz equationGMRESMathematics::Numerical Analysissymbols.namesakeMultigrid methodQuadratic equationHelmholtz equationäärellisten elementtien menetelmäMathematicsNumerical AnalysisPreconditionerApplied MathematicspohjustinMathematical analysisAlgebrallinen multigrid-menetelmäHelmholzin yhtälöComputer Science::Numerical AnalysisGeneralized minimal residual methodFinite element methodComputer Science ApplicationselementtimenetelmäComputational MathematicsModeling and SimulationHelmholtz free energysymbolsPreconditionerLaplace operatorJournal of Computational Physics
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Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

2010

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…

Algebraic multigrid methodFinite element methodHelmholtz equationPreconditionerSpectral element methodApplied MathematicsSpectral element methodMathematical analysisExact controllabilityComputational acousticsFinite element methodControllabilitysymbols.namesakeComputational MathematicsMultigrid methodHelmholtz free energysymbolsHelmholtz equationPreconditionerLaplace operatorMathematicsJournal of Computational and Applied Mathematics
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