Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis

DOI10.1016/j.cam.2011.04.020zbMath1226.65090OpenAlexW2010002946MaRDI QIDQ633949

Liwei Xu, Nilima Nigam, George C. Hsiao, Joseph E. Pasciak

Publication date: 2 August 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.04.020

zbMATH Keywords

finite element methoderror analysisHelmholtz equationDirichlet-to-Neumann mappingseparation of variables techniqueacoustic scattering problemexterior Neumann boundary value problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (26)

An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures ⋮ An adaptive finite element DtN method for the elastic wave scattering problem ⋮ A priori error estimates of the dtn-FEM for the transmission problem in acoustics ⋮ An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition ⋮ A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics ⋮ Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structures ⋮ A High Order Numerical Method for Scattering from Locally Perturbed Periodic Surfaces ⋮ An adaptive finite element method for the wave scattering with transparent boundary condition ⋮ A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet--Bloch Transform ⋮ Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics ⋮ Complete radiation boundary conditions for the Helmholtz equation. II: Domains with corners ⋮ A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity ⋮ An Adaptive Finite Element DtN Method for Maxwell’s Equations ⋮ A coupled BEM and FEM for the interior transmission problem in acoustics ⋮ Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition ⋮ Nonsingular kernel boundary integral and finite element coupling method ⋮ A Bayesian level set method for an inverse medium scattering problem in acoustics ⋮ An efficient iterative method for solving multiple scattering in locally inhomogeneous media ⋮ Dirichlet-to-Neumann boundary conditions for multiple scattering in waveguides ⋮ Coupling of boundary integral equation and finite element methods for transmission problems in acoustics ⋮ Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods ⋮ A stable node-based smoothed finite element method with PML technique for the elastic wave obstacle scattering ⋮ A Bayesian level set method for the shape reconstruction of inverse scattering problems in elasticity ⋮ A weak-form meshfree coupled with infinite element method for predicting acoustic radiation ⋮ Unnamed Item ⋮ An Adaptive Finite Element DtN Method for the Elastic Wave Scattering Problem in Three Dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact non-reflecting boundary conditions on perturbed domains and \(hp\)-finite elements
• Error analysis of an enhanced DtN-FE method for exterior scattering problems
• Error estimates of the DtN finite element method for the exterior Helmholtz problem
• Error analysis and preconditioning for an enhanced DtN-FE algorithm for exterior scattering problems
• Boundary integral equations
• Exact non-reflecting boundary conditions
• A finite element method for exterior interface problems
• Analysis of continuous formulations underlying the computation of time- harmonic acoustics in exterior domains
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• Finite element analysis of acoustic scattering
• A finite-element capacitance matrix method for exterior Helmholtz problems
• Exact non-reflecting boundary conditions on general domains.
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• On nonreflecting boundary conditions
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Plenary Lectures
• Radiation boundary conditions for wave-like equations
• On the Coupling of Boundary Integral and Finite Element Methods
• A Finite Element Method for Solving Helmholtz Type Equations in Waveguides and Other Unbounded Domains
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions

This page was built for publication: Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis