Search results for "GMRES"

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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Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach

2009

This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the p…

Hierarchical ApproachLarge scale problemHigh frequency range.Rapid Acoustic Boundary Element Method Adaptive Cross ApproximationGMRES
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