A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems

DOI10.1016/S0045-7825(98)00050-4zbMath0962.76055OpenAlexW2016701910MaRDI QIDQ1971153

Joseph J. Shirron, Ivo M. Babuška

Publication date: 13 June 2001

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)00050-4

zbMATH Keywords

weak formulationconvergence rateapproximate boundary conditionsexterior Helmholtz problemsinfinite element methodtest functionsconjugated elementunconjugated element

Mathematics Subject Classification ID

Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (40)

Three-dimensional infinite elements utilizing basis functions with compact support ⋮ An optimal high-order non-reflecting finite element scheme for wave scattering problems ⋮ A survey of finite element methods for time-harmonic acoustics ⋮ Unnamed Item ⋮ Trefftz-based methods for time-harmonic acoustics ⋮ A mapped finite and infinite partition of unity method for convected acoustic radiation in axisymmetric domains ⋮ The stability of infinite element schemes for transient wave problems ⋮ Effectiveness and robustness of improved infinite elements for exterior acoustics ⋮ The performance of local absorbing boundary conditions for acoustic scattering from elliptical shapes ⋮ Parallel iterative solution for the Helmholtz equation with exact non-reflecting boundary conditions ⋮ Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering ⋮ An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems ⋮ Analytical and numerical investigation of the performance of the BGT2 condition for low-frequency acoustic scattering problems ⋮ The performance of spheroidal infinite elements ⋮ A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies. ⋮ A REVIEW OF INFINITE ELEMENT METHODS FOR EXTERIOR HELMHOLTZ PROBLEMS ⋮ FINITE ELEMENT SOLUTION OF TWO-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS USING ARBITRARILY SHAPED CONVEX ARTIFICIAL BOUNDARIES ⋮ ON FUNDAMENTAL ASPECTS OF EXTERIOR APPROXIMATIONS WITH INFINITE ELEMENTS ⋮ NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION ⋮ Scattering from targets in three-dimensional littoral and surf-zone environments with multi-layered elastic sediments based on an interior-transmission formulation ⋮ The conjugated vs. the unconjugated infinite element method for the Helmholtz equation in exterior domains ⋮ An ellipsoidal acoustic infinite element ⋮ An infinite element for Maxwell's equations ⋮ A summary of infinite element formulations for exterior Helmholtz problems ⋮ A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems ⋮ Improvement of the performance of the BGT2 condition for low frequency acoustic scattering problems ⋮ A novel ellipsoidal acoustic infinite element ⋮ Local absorbing boundary conditions for elliptical shaped boundaries ⋮ Connection and comparison between frequency shift time integration and a spectral transformation preconditioner ⋮ Enhanced conformal perfectly matched layers for Bernstein-Bézier finite element modelling of short wave scattering ⋮ Unnamed Item ⋮ Perfectly matched layers for time-harmonic second order elliptic problems ⋮ A fast method for solving acoustic scattering problems in frequency bands ⋮ Solving two dimensional second order elliptic equations in exterior domains using the inverted finite elements method ⋮ A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers ⋮ The ill-conditioning of infinite element stiffness matrices ⋮ On two-dimensional infinite elements utilizing basis functions with compact support ⋮ Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains ⋮ Higher order finite and infinite elements for the solution of Helmholtz problems ⋮ Isogeometric analysis of acoustic scattering using infinite elements

Uses Software

• LAPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-reflecting boundary conditions
• Exact non-reflecting boundary conditions
• A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics
• Solution of 3D-Laplace and Helmholtz equations in exterior domains using \(hp\)-infinite elements
• High-order boundary conditions and finite elements for infinite domains
• Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm
• Convergence of the infinite element methods for the Helmholtz equation in separable domains
• On nonreflecting boundary conditions
• Special finite elements for use with high-order boundary conditions
• An ellipsoidal acoustic infinite element
• A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems
• Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung
• Error-bounds for finite element method
• Non-Reflecting Finite Element Schemes for Three-Dimensional Acoustic Waves
• High-Order Finite Element Methods for Acoustic Problems
• A simple wave envelope element example
• Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets
• An expansion theorem for electromagnetic fields
• A Generalization of Theorems of Rellich and Atkinson
• Finite element formulations for acoustical radiation
• Wave envelope and infinite elements for acoustical radiation
• Radiation boundary conditions for wave-like equations
• More on infinite elements
• Operation counts for boundary integral and finite element methods
• Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
• Infinite elements
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• Diffraction and refraction of surface waves using finite and infinite elements
• Radiation boundary conditions for acoustic and elastic wave calculations
• Mapped Wave Envelope Elements for Acoustical Radiation and Scattering
• A Variable Order Infinite Acoustic Wave Envelope Element
• Application of the finite element method to acoustic scattering problems
• INTEGRAL EQUATIONS FOR THE EXTERIOR ACOUSTIC PROBLEM
• Solution of unbounded domain problems using elliptic artificial boundaries
• Improved Integral Formulation for Acoustic Radiation Problems
• The application of integral equation methods to the numerical solution of some exterior boundary-value problems
• A convergent ‘farfield’ expansion for two‐dimensional radiation functions
• Analysis of a coupled finite-infinite element method for exterior Helmholtz problems

This page was built for publication: A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems