Iterative solution applied to the Helmholtz equation: complex deflation on unstructured grids

DOI10.1016/j.cma.2012.06.007zbMath1354.65234OpenAlexW2071405486MaRDI QIDQ503303

Yong-Cai Geng, Sumit K. Garg

Publication date: 12 January 2017

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2012.06.007

zbMATH Keywords

Helmholtz equationdeflationiterative solverscomplex GMRESpollution effect

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (1)

A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator

Uses Software

• Matlab

Cites Work

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• An iterative method for the Helmholtz equation
• Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods
• An algebraic variational multiscale-multigrid method based on plain aggregation for convection-diffusion problems
• Advances in iterative methods and preconditioners for the Helmholtz equation
• Preconditioning Helmholtz linear systems
• The rate of convergence of conjugate gradients
• On accuracy conditions for the numerical computation of waves
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• Finite element analysis of acoustic scattering
• Stabilised vs. stable mixed methods for incompressible flow
• The partition of unity finite element method: basic theory and applications
• Wave-ray multigrid method for standing wave equations
• A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
• Analysis of acceleration strategies for restarted minimal residual methods
• On a class of preconditioners for solving the Helmholtz equation
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
• A least-squares method for the Helmholtz equation
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• Deflated preconditioned conjugate gradient solvers for the pressure-Poisson equation
• An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
• Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix
• On the Construction of Deflation-Based Preconditioners
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• Deflated preconditioned conjugate gradient solvers for the pressure-Poisson equation: Extensions and improvements
• Deflated preconditioned conjugate gradient solvers for linear elasticity
• Deflation of Conjugate Gradients with Applications to Boundary Value Problems
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeneous Media
• A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers
• Fast numerical solutions of patient-specific blood flows in 3D arterial systems
• An algebraic multigrid wave–ray algorithm to solve eigenvalue problems for the helmholtz operator
• Deflation and Balancing Preconditioners for Krylov Subspace Methods Applied to Nonsymmetric Matrices
• Multilevel Projection-Based Nested Krylov Iteration for Boundary Value Problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• Residual-free bubbles for the Helmholtz equation
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• Plane wave basis finite‐elements for wave scattering in three dimensions
• Numerical solution of the Helmholtz equation with high wavenumbers
• Global-basis two-level method for indefinite systems. Part 1: convergence studies
• A Deflated Version of the Conjugate Gradient Algorithm
• First-Order System Least-Squares for the Helmholtz Equation
• Multigrid Simulation for High-Frequency Solutions of the Helmholtz Problem in Heterogeneous Media
• Iterative Krylov Methods for Large Linear Systems
• A Restarted GMRES Method Augmented with Eigenvectors
• Any Nonincreasing Convergence Curve is Possible for GMRES
• Accuracy Properties of the Wave‐Ray Multigrid Algorithm for Helmholtz Equations
• Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering
• A parallel hp‐FEM infrastructure for three‐dimensional structural acoustics
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
• Methods of conjugate gradients for solving linear systems
• Matrix-based multigrid. Theory and applications

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