Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems

DOI10.1137/15M1011755zbMath1382.65401OpenAlexW2389633190MaRDI QIDQ2807282

Martin Halla

Publication date: 20 May 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1011755

zbMATH Keywords

Helmholtz equationtransparent boundary conditionpole conditionHardy space infinite elements

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Laplace transform (44A10) Resonance in context of PDEs (35B34)

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Cites Work

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• Hardy space infinite elements for time harmonic wave equations with phase and group velocities of different signs
• Two scale Hardy space infinite elements for scalar waveguide problems
• Linear integral equations.
• A perfectly matched layer for the absorption of electromagnetic waves
• Inverse acoustic and electromagnetic scattering theory.
• Convergence of infinite element methods for scalar waveguide problems
• High-order local non-reflecting boundary conditions: a review
• Approximation von Eigenwertproblemen bei nichtlinearer Parameterabhängigkeit
• Convergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem
• The computation of resonances in open systems using a perfectly matched layer
• Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems
• Hardy Space Infinite Elements for Scattering and Resonance Problems
• Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory
• Approximation in eigenvalue problems for holomorphic fredholm operator functions I
• Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate)
• Exact Sequences of High Order Hardy Space Infinite Elements for Exterior Maxwell Problems