Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems

DOI10.1142/S0218396X16500156zbMath1360.74138MaRDI QIDQ2981553

Pierre Ladevèze, Hervé Riou, Hao Li

Publication date: 9 May 2017

Published in: Journal of Computational Acoustics (Search for Journal in Brave)

zbMATH Keywords

FEMdiscontinuous Galerkin methodshybrid methodsTrefftz methodsVTCR

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) 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 (3)

A partition of unity finite element method for three-dimensional transient diffusion problems with sharp gradients ⋮ Pollution studies for high order isogeometric analysis and finite element for acoustic problems ⋮ A coupling scheme based on the partition of unity finite element method-finite element method for 3D vibro-acoustic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Plane wave basis in Galerkin BEM for bidimensional wave scattering
• Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains
• Partition of unity method for Helmholtz equation: \(q\)-convergence for plane-wave and wave-band local bases.
• The variational theory of complex rays: a predictive tool for medium-frequency vibrations.
• On Trefftz and weak Trefftz discontinuous Galerkin approaches for medium-frequency acoustics
• 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 comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems
• A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers
• 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
• THE MULTISCALE VTCR APPROACH APPLIED TO ACOUSTICS PROBLEMS

This page was built for publication: Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems