Wavenumber-explicit convergence of the \(hp\)-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
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Publication:2122632
DOI10.1016/j.camwa.2022.03.007zbMath1504.65257arXiv2010.00585OpenAlexW3091748925MaRDI QIDQ2122632
David Lafontaine, Jared Wunsch, Euan A. Spence
Publication date: 7 April 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.00585
Related Items (11)
A simple proof that the \textit{hp}-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation ⋮ Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems ⋮ Does the Helmholtz Boundary Element Method Suffer from the Pollution Effect? ⋮ At the interface between semiclassical analysis and numerical analysis of wave scattering problems. Abstracts from the workshop held September 25 -- October 1, 2022 ⋮ Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method ⋮ Asymptotic Dispersion Correction in General Finite Difference Schemes for Helmholtz Problems ⋮ Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations ⋮ Comparison of approximate and numerical methods for solving the homogeneous Dirichlet problem for the Helmholtz operator in a two-dimensional domain ⋮ Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition ⋮ Higher-order finite element methods for the nonlinear Helmholtz equation ⋮ Decompositions of high-frequency Helmholtz solutions and application to the finite element method
Cites Work
- Unnamed Item
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- Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
- A refined finite element convergence theory for highly indefinite Helmholtz problems
- Boundary integral equations
- Autour de l'approximation semi-classique. (Around semiclassical approximation)
- A two-point boundary value problem with a rapidly oscillating solution
- Local energy decay of the wave equation in an exterior problem and without resonance in the neighborhood of the real line
- The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- Partial differential equations. 2: Qualitative studies of linear equations
- On high order methods for the heterogeneous Helmholtz equation
- A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency
- Optimal constants in nontrapping resolvent estimates and applications in numerical analysis
- General DG-methods for highly indefinite Helmholtz problems
- Fourier integral operators. II
- Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
- On Stability of Discretizations of the Helmholtz Equation
- Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
- Wave-Number-Explicit Bounds in Time-Harmonic Scattering
- Complex Scaling and the Distribution of Scattering Poles
- ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation
- High-frequency behaviour of corner singularities in Helmholtz problems
- Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation
- Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems
- For Most Frequencies, Strong Trapping Has a Weak Effect in Frequency‐Domain Scattering
- Stability and finite element error analysis for the Helmholtz equation with variable coefficients
- Mathematical Theory of Scattering Resonances
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
- Trapped rays in spherically symmetric media and poles of the scattering matrix
- Acoustic and electromagnetic equations. Integral representations for harmonic problems
- An introduction to semiclassical and microlocal analysis
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