Global-basis two-level method for indefinite systems. Part 1: convergence studies

DOI<439::AID-NME981>3.0.CO;2-A 10.1002/1097-0207(20000930)49:3<439::AID-NME981>3.0.CO;2-AzbMath0980.74060OpenAlexW2167267602MaRDI QIDQ4508277

Jacob Fish, Yong Qu

Publication date: 4 March 2002

Full work available at URL: https://doi.org/10.1002/1097-0207(20000930)49:3<439::aid-nme981>3.0.co;2-a

zbMATH Keywords

convergencefinite element discretizationHelmholtz equationstrain softeningLanczos vectorsglobal basis two-level methodglobal-basis prolongatorhigh-indefinite system of equationshighest eigenmodesoptimal coarse modelpredictor-corrector smoothingshear banding problemsmoothing iteration matrixsymmetric indefinite system of equationstwo-level feedback loop

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Classical linear elasticity (74B05) Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

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Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation, Fast Algorithms for High Frequency Wave Propagation, Advances in iterative methods and preconditioners for the Helmholtz equation, Iterative solution applied to the Helmholtz equation: complex deflation on unstructured grids, Discrete-to-continuum bridging based on multigrid principles, A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator, A comparison of coarse spaces for Helmholtz problems in the high frequency regime, Acceleration of the generalized global basis (GGB) method for nonlinear problems

Cites Work

• Preconditioning techniques for nonsymmetric and indefinite linear systems
• Algebraic spectral multigrid methods
• Experimental study of ILU preconditioners for indefinite matrices
• Automated adaptive multilevel solver
• Software for simplified Lanczos and QMR algorithms
• A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
• Towards robust two-level methods for indefinite systems
• Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems