On high order methods for the heterogeneous Helmholtz equation

DOI10.1016/j.camwa.2016.08.026zbMath1368.78131OpenAlexW2522648897MaRDI QIDQ2012695

T. Chaumont-Frelet

Publication date: 3 August 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.08.026

zbMATH Keywords

finite element methodHelmholtz equationmultiscale methodhigh order methodpollution effecthighly heterogeneous media

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (17)

Wavenumber-explicit convergence of the \(hp\)-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients ⋮ A coercive heterogeneous media Helmholtz model: formulation, wavenumber-explicit analysis, and preconditioned high-order FEM ⋮ Finite Element Approximation of Electromagnetic Fields Using Nonfitting Meshes for Geophysics ⋮ A simple proof that the \textit{hp}-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation ⋮ Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization ⋮ High-order compact finite difference methods for solving the high-dimensional Helmholtz equations ⋮ Does the Helmholtz Boundary Element Method Suffer from the Pollution Effect? ⋮ Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method ⋮ Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification ⋮ The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances ⋮ An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation ⋮ Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions ⋮ Quasi-Monte Carlo Finite Element Analysis for Wave Propagation in Heterogeneous Random Media ⋮ An efficient high-order multiscale finite element method for frequency-domain elastic wave modeling ⋮ Optimal constants in nontrapping resolvent estimates and applications in numerical analysis ⋮ Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes

Uses Software

• Triangle

Cites Work

• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• Stability estimates for a class of Helmholtz problems
• Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
• FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?

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