An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems

DOI10.1016/j.laa.2009.03.024zbMath1166.65022OpenAlexW2159707849MaRDI QIDQ1025863

A. Sopaheluwakan, Gerard L. G. Sleijpen, Mikhail A. Botchev

Publication date: 23 June 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.03.024

zbMATH Keywords

algorithmnumerical examplesproper orthogonal decompositiontransparent boundary conditionsHelmholtz equationJacobi-Davidson methodabsorbing boundary conditionsprincipal component approximationperfectly matched layersnonlinear Helmholtz eigenvalue problemtruncated singular value decomposition (SVD)

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items

Detecting hyperbolic and definite matrix polynomials, A block Krylov subspace time-exact solution method for linear ordinary differential equation systems, A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations, The nonlinear eigenvalue problem, Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems, Iterative estimation of eigenmodes for acoustic cavities, Chebyshev interpolation for nonlinear eigenvalue problems, Resolvent sampling based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems, Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Uses Software

• ILUT

Cites Work

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