A Geometric Multigrid Preconditioner for the Solution of the Helmholtz Equation in Three-Dimensional Heterogeneous Media on Massively Parallel Computers

DOI10.1007/978-3-319-28832-1_6zbMath1364.86008OpenAlexW2593182373MaRDI QIDQ5266546

Serge Gratton, Henri Calandra, Xavier Vasseur

Publication date: 16 June 2017

Published in: Modern Solvers for Helmholtz Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-28832-1_6

Mathematics Subject Classification ID

Related Items (3)

Preconditioners for Krylov subspace methods: An overview ⋮ A matrix-free parallel solution method for the three-dimensional heterogeneous Helmholtz equation ⋮ Parallel controllability methods for the Helmholtz equation

Uses Software

• MPI
• PSP
• clique
• FWT2D

Cites Work

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• A rapidly converging domain decomposition method for the Helmholtz equation
• Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
• An iterative method for the Helmholtz equation
• On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning
• Acoustic inverse scattering via Helmholtz operator factorization and optimization
• A high-performance, portable implementation of the MPI message passing interface standard
• The method of polarized traces for the 2D Helmholtz equation
• A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
• Advances in iterative methods and preconditioners for the Helmholtz equation
• On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian
• A perfectly matched layer for the absorption of electromagnetic waves
• Wave-ray multigrid method for standing wave equations
• Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
• On a class of preconditioners for solving the Helmholtz equation
• Accurate finite difference methods for time-harmonic wave propagation
• A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• A parallel evolution strategy for an Earth imaging problem in geophysics
• A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation
• Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
• A Modified Block Flexible GMRES Method with Deflation at Each Iteration for the Solution of Non-Hermitian Linear Systems with Multiple Right-Hand Sides
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
• On the convergence of shifted Laplace preconditioner combined with multilevel deflation
• An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media
• A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
• Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeneous Media
• Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
• Recent computational developments in Krylov subspace methods for linear systems
• Multilevel Block Factorization Preconditioners
• Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
• Algebraic Multigrid Solvers for Complex-Valued Matrices
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Flexible Inner-Outer Krylov Subspace Methods
• Inverse Problem Theory and Methods for Model Parameter Estimation
• A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections
• Improving Multifrontal Methods by Means of Block Low-Rank Representations
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Two-Level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

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