The wave based method: An overview of 15 years of research
Abstract The Wave Based Method is a deterministic prediction technique to solve steady-
state dynamic problems and is developed to overcome some of the frequency limitations …
state dynamic problems and is developed to overcome some of the frequency limitations …
A survey of Trefftz methods for the Helmholtz equation
Trefftz methods are finite element-type schemes whose test and trial functions are (locally)
solutions of the targeted differential equation. They are particularly popular for time …
solutions of the targeted differential equation. They are particularly popular for time …
Modular bases for fluid dynamics
We present a new approach to fluid simulation that balances the speed of model reduction
with the flexibility of grid-based methods. We construct a set of composable reduced models …
with the flexibility of grid-based methods. We construct a set of composable reduced models …
Pollution studies for high order isogeometric analysis and finite element for acoustic problems
GC Diwan, MS Mohamed - Computer Methods in Applied Mechanics and …, 2019 - Elsevier
It is well known that Galerkin finite element methods suffer from pollution error when solving
wave problems. To reduce the pollution impact on the solution different approaches were …
wave problems. To reduce the pollution impact on the solution different approaches were …
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
The application of computational modelling to wave propagation problems is hindered by
the dispersion error introduced by the discretisation. Two common strategies to address this …
the dispersion error introduced by the discretisation. Two common strategies to address this …
A direct hybrid finite element–wave based modelling technique for efficient coupled vibro-acoustic analysis
B Van Genechten, D Vandepitte, W Desmet - Computer Methods in Applied …, 2011 - Elsevier
This paper presents a newly developed hybrid simulation technique for coupled structural–
acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or …
acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or …
Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method
A El Kacimi, O Laghrouche - International journal for numerical …, 2009 - Wiley Online Library
In this paper, we investigate a numerical approach based on the partition of unity finite
element method, for the time‐harmonic elastic wave equations. The aim of the proposed …
element method, for the time‐harmonic elastic wave equations. The aim of the proposed …
Overview of the discontinuous enrichment method, the ultra‐weak variational formulation, and the partition of unity method for acoustic scattering in the medium …
D Wang, R Tezaur, J Toivanen… - International Journal for …, 2012 - Wiley Online Library
The efficient finite element discretization of the Helmholtz equation becomes challenging in
the medium frequency regime because of numerical dispersion, or what is often referred to …
the medium frequency regime because of numerical dispersion, or what is often referred to …
A partition of unity FEM for time‐dependent diffusion problems using multiple enrichment functions
M Shadi Mohamed, M Seaid… - International Journal …, 2013 - Wiley Online Library
An enriched partition of unity FEM is developed to solve time‐dependent diffusion problems.
In the present formulation, multiple exponential functions describing the spatial and temporal …
In the present formulation, multiple exponential functions describing the spatial and temporal …
Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems
The Partition of Unity Finite Element Method is used to solve wave scattering problems
governed by the Helmholtz equation, involving one or more scatterers, in two dimensions …
governed by the Helmholtz equation, involving one or more scatterers, in two dimensions …