Why it is difficult to solve Helmholtz problems with classical iterative methods
In contrast to the positive definite Helmholtz equation, the deceivingly similar looking
indefinite Helmholtz equation is difficult to solve using classical iterative methods. Simply …
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 …
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 …
involved (eg, electric current, mechanical torque, temperature, etc.), a signal-conditioning …
Finite element prediction of wave motion in structural waveguides
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 …
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
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 …
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
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 …
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 …
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) …
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 …
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 …
${\mathbb {R}}^{d} $, $ d\in\{1, 2, 3\} $ is presented. General conditions on the approximation …