On Trefftz and weak Trefftz discontinuous Galerkin approaches for medium-frequency acoustics

DOI10.1016/j.cma.2014.05.024zbMath1423.74899OpenAlexW2046974883MaRDI QIDQ1667355

Hervé Riou, Pierre Ladevèze

Publication date: 28 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.cma.2014.05.024

zbMATH Keywords

discontinuous Galerkin methodsacousticshybrid methodsTrefftz methodsvtcr

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Extended variational theory of complex rays in heterogeneous Helmholtz problem, A Survey of Trefftz Methods for the Helmholtz Equation, Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems, A plane wave virtual element method for the Helmholtz problem, On wave based weak Trefftz discontinuous Galerkin approach for medium-frequency heterogeneous Helmholtz problem

Cites Work

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• Plane wave basis in Galerkin BEM for bidimensional wave scattering
• The Fourier version of the variational theory of complex rays for medium-frequency acoustics
• Partition of unity method for Helmholtz equation: \(q\)-convergence for plane-wave and wave-band local bases.
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• Element-free Galerkin solutions for Helmholtz problems: Formulation and numerical assessment of the pollution effect
• Wave boundary elements: a theoretical overview presenting applications in scattering of short waves
• An efficient wave based method for solving Helmholtz problems in three-dimensional bounded domains
• A least-squares method for the Helmholtz equation
• An ultra-weak method for acoustic fluid-solid interaction
• The variational theory of complex rays for the calculation of medium‐frequency vibrations
• A priori error estimate for the Baumann–Oden version of the discontinuous Galerkin method
• THE VARIATIONAL THEORY OF COMPLEX RAYS FOR THREE-DIMENSIONAL HELMHOLTZ PROBLEMS
• A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers
• A new computational method for transient dynamics including the low- and the medium-frequency ranges
• Plane wave discontinuous Galerkin methods: Analysis of theh-version
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• THE MULTISCALE VTCR APPROACH APPLIED TO ACOUSTICS PROBLEMS
• AN ADAPTIVE NUMERICAL STRATEGY FOR THE MEDIUM-FREQUENCY ANALYSIS OF HELMHOLTZ'S PROBLEM
• The discontinuous enrichment method