A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation

DOI10.1016/j.jcp.2014.01.042zbMath1349.65613arXiv1306.5942OpenAlexW1986479605MaRDI QIDQ348948

Huangxin Chen, Xuejun Xu, Peipei Lu

Publication date: 5 December 2016

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

Full work available at URL: https://arxiv.org/abs/1306.5942

zbMATH Keywords

Helmholtz equationGMRES methodmultilevel methodlocal Fourier analysishybridizable discontinuous Galerkin methodhigh wave number

Mathematics Subject Classification ID

Related Items (21)

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Uses Software

• LFA

Cites Work

• Unnamed Item
• Advances in iterative methods and preconditioners for the Helmholtz equation
• Wave-ray multigrid method for standing wave equations
• On a class of preconditioners for solving the Helmholtz equation
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
• A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• A convergent multigrid cycle for the hybridized mixed method
• ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
• Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
• Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• A projection-based error analysis of HDG methods
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• A Schwarz Preconditioner for a Hybridized Mixed Method
• Finite Element Methods for Maxwell's Equations
• Accuracy Properties of the Wave‐Ray Multigrid Algorithm for Helmholtz Equations
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

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