Why it is difficult to solve Helmholtz problems with classical iterative methods

OG Ernst, MJ Gander - Numerical analysis of multiscale problems, 2011 - Springer
In contrast to the positive definite Helmholtz equation, the deceivingly similar looking
indefinite Helmholtz equation is difficult to solve using classical iterative methods. Simply …

A review of finite-element methods for time-harmonic acoustics

LL Thompson - The Journal of the Acoustical Society of America, 2006 - pubs.aip.org
State-of-the-art finite-element methods for time-harmonic acoustics governed by the
Helmholtz equation are reviewed. Four major current challenges in the field are specifically …

[图书][B] Numerical simulation of mechatronic sensors and actuators

M Kaltenbacher - 2007 - Springer
Each modern industrial process environment needs sensors to detect the physical quantities
involved (eg, electric current, mechanical torque, temperature, etc.), a signal-conditioning …

Finite element prediction of wave motion in structural waveguides

BR Mace, D Duhamel, MJ Brennan… - The Journal of the …, 2005 - pubs.aip.org
A method is presented by which the wavenumbers for a one-dimensional waveguide can be
predicted from a finite element (FE) model. The method involves postprocessing a …

Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems

TJR Hughes, JA Evans, A Reali - Computer Methods in Applied Mechanics …, 2014 - Elsevier
We study the spectral approximation properties of finite element and NURBS spaces from a
global perspective. We focus on eigenfunction approximations and discover that the L 2 …

Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS

TJR Hughes, A Reali, G Sangalli - Computer methods in applied …, 2008 - Elsevier
We study the discretization behavior of classical finite element and NURBS approximations
on problems of structural vibrations and wave propagation. We find that, on the basis of …

Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods

M Ainsworth - Journal of Computational Physics, 2004 - Elsevier
The dispersive and dissipative properties of hp version discontinuous Galerkin finite element
approximation are studied in three different limits. For the small wave-number limit hk→ 0 …

Simulation methods for guided wave-based structural health monitoring: a review

C Willberg, S Duczek… - Applied …, 2015 - asmedigitalcollection.asme.org
This paper reviews the state-of-the-art in numerical wave propagation analysis. The main
focus in that regard is on guided wave-based structural health monitoring (SHM) …

Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation

JM Melenk, S Sauter - SIAM Journal on Numerical Analysis, 2011 - SIAM
We develop a stability and convergence theory for a class of highly indefinite elliptic
boundary value problems (bvps) by considering the Helmholtz equation at high …

Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions

J Melenk, S Sauter - Mathematics of Computation, 2010 - ams.org
A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in
${\mathbb {R}}^{d} $, $ d\in\{1, 2, 3\} $ is presented. General conditions on the approximation …