GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method

DOI10.1016/j.cam.2011.07.021zbMath1228.65208OpenAlexW2107095846MaRDI QIDQ645714

H. Knibbe, Cornelis W. Oosterlee, Kees Vuik

Publication date: 10 November 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.07.021

zbMATH Keywords

convergencenumerical examplesfinite difference schemeconjugate gradient methodHelmholtz equationGPUKrylov solversshifted Laplace multigrid preconditioner

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Preconditioners for iterative methods (65F08)

Related Items (9)

Reduction of computing time for least-squares migration based on the Helmholtz equation by graphics processing units ⋮ Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs ⋮ A matrix-free parallel solution method for the three-dimensional heterogeneous Helmholtz equation ⋮ Full Waveform Inversion Guided by Travel Time Tomography ⋮ A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme ⋮ How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid? ⋮ Numerical methods to solve PDE models for pricing business companies in different regimes and implementation in GPUs ⋮ A geometric full multigrid method and fourth-order compact scheme for the 3D Helmholtz equation on nonuniform grid discretization ⋮ Optimal Complex Relaxation Parameters in Multigrid for Complex-Shifted Linear Systems

Uses Software

• CUDA
• BiCGstab
• ITER-REF
• Algorithm 913

Cites Work

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• A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization
• Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

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