Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves

DOI10.1051/m2an/2016067zbMath1378.65179arXiv1511.08251OpenAlexW3105211260MaRDI QIDQ5367327

Lise-Marie Imbert-Gérard, Peter B. Monk

Publication date: 13 October 2017

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.08251

zbMATH Keywords

numerical examplesdiscontinuous Galerkin methodHelmholtz equationorder of convergencegeneralized plane wavesTrefftz based method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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)

Related Items (12)

A Trefftz method with reconstruction of the normal derivative applied to elliptic equations ⋮ A space-time DG method for the Schrödinger equation with variable potential ⋮ A Novel Least Squares Method for Helmholtz Equations with Large Wave Numbers ⋮ A roadmap for generalized plane waves and their interpolation properties ⋮ Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number ⋮ A comparison of high-order polynomial and wave-based methods for Helmholtz problems ⋮ A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation ⋮ Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations ⋮ A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential ⋮ Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions ⋮ Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers ⋮ A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

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