A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations

DOI10.1016/j.jcp.2023.112622arXiv1806.11277OpenAlexW4388576132MaRDI QIDQ6119247

Eran Treister, Rachel Yovel

Publication date: 29 February 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.11277

zbMATH Keywords

domain decomposition methodsparallel computationselasticity equationelastic wave modelingshifted Laplacian multigridelastic Helmholtz equation

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

• Unnamed Item
• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• A rapidly converging domain decomposition method for the Helmholtz equation
• A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
• Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
• A fast method for the solution of the Helmholtz equation
• A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
• Optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling
• A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media
• On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian
• A damping preconditioner for time-harmonic wave equations in fluid and elastic material
• Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
• On accuracy conditions for the numerical computation of waves
• The use of local mode analysis in the design and comparison of multigrid methods
• A domain decomposition method for the Helmholtz equation and related optimal control problems
• Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
• High-order finite difference methods for the Helmholtz equation
• A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems
• L-sweeps: a scalable, parallel preconditioner for the high-frequency Helmholtz equation
• Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: algorithms and convergence analysis
• Multidirectional sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems
• Full waveform inversion through double-sweeping solver
• Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• Multigrid-based `shifted-Laplacian' preconditioning for the time-harmonic elastic wave equation
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• A robust domain decomposition method for the Helmholtz equation with high wave number
• A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
• Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs
• Local Fourier analysis of the complex shifted Laplacian preconditioner for Helmholtz problems
• An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media
• A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems
• Julia: A Fresh Approach to Numerical Computing
• Full Waveform Inversion and the Truncated Newton Method
• A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization
• SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION
• Smoothed aggregation for Helmholtz problems
• A multigrid solver to the Helmholtz equation with a point source based on travel time and amplitude
• Complex Additive Geometric Multilevel Solvers for Helmholtz Equations on Spacetrees
• Shifted-Laplacian Preconditioners for Heterogeneous Helmholtz Problems
• Monolithic Multigrid Methods for Two-Dimensional Resistive Magnetohydrodynamics
• An Introduction to Domain Decomposition Methods
• Distributive smoothers in multigrid for problems with dominating grad-div operators
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Absorbing boundary conditions for numerical simulation of waves
• Radiation boundary conditions for acoustic and elastic wave calculations
• A Multigrid Tutorial, Second Edition
• A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
• A local Fourier analysis of additive Vanka relaxation for the Stokes equations
• Domain Decomposition with Local Impedance Conditions for the Helmholtz Equation with Absorption
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Full Waveform Inversion Guided by Travel Time Tomography
• jInv--a Flexible Julia Package for PDE Parameter Estimation
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
• A scalable multigrid method for solving indefinite Helmholtz equations with constant wave numbers
• Augmented AMG‐shifted Laplacian preconditioners for indefinite Helmholtz problems

This page was built for publication: A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations