A summary of infinite element formulations for exterior Helmholtz problems

DOI10.1016/S0045-7825(98)00048-6zbMath0943.65126OpenAlexW2020385406MaRDI QIDQ1971150

K. Gerdes

Publication date: 22 March 2000

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

Full work available at URL: https://doi.org/10.1016/s0045-7825(98)00048-6

zbMATH Keywords

numerical resultscomputational efficiencyexterior domainsinfinite element methodHelmholtz problems\(hp\)-adaptive refinements

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Complexity and performance of numerical algorithms (65Y20)

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Uses Software

• HP90

Cites Work

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• Solution of the 3D-Helmholtz equation in exterior domains of arbitrary shape using \(hp\)-finite-infinite elements
• HP90: A general and flexible Fortran 90 \(hp\)-FE code
• Solution of 3D-Laplace and Helmholtz equations in exterior domains using \(hp\)-infinite elements
• Convergence of the infinite element methods for the Helmholtz equation in separable domains
• Special finite elements for use with high-order boundary conditions
• The conjugated vs. the unconjugated infinite element method for the Helmholtz equation in exterior domains
• A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems
• Mapped Wave Envelope Elements for Acoustical Radiation and Scattering
• A Variable Order Infinite Acoustic Wave Envelope Element
• An analysis of the coupling of finite-element and Nyström methods in acoustic scattering
• Recent progress on application of hp‐adaptive BE/FE methods to elastic scattering