Dispersion Analysis of Finite-element Schemes for a First-order Formulation of the Wave Equation

2015 ◽  
Author(s):  
R. Shamasundar ◽  
R. Al Khoury ◽  
W.A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Dispersion Analysis ◽  
First Order ◽  
Finite Element Schemes

scholarly journals Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping

2007 ◽  
Vol 17 (3) ◽  
pp. 375-393 ◽  
Author(s):  
Sébastien Jund ◽  
Stéphanie Salmon
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Elements ◽  
Taylor Expansion ◽  
High Order ◽  
Computational Time ◽  
Mass Lumping ◽  
Stiffness Matrices ◽  
High Order Time ◽  
Finite Element Schemes

Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of orderkand show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up toP5elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

Beyond first-order finite element schemes in micromagnetics

2014 ◽  
Vol 256 ◽  
pp. 357-366 ◽  
Author(s):  
E. Kritsikis ◽  
A. Vaysset ◽  
L.D. Buda-Prejbeanu ◽  
F. Alouges ◽  
J.-C. Toussaint
Keyword(s):  
Finite Element ◽  
First Order ◽  
Finite Element Schemes

scholarly journals A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation

2015 ◽  
Vol 20 (2) ◽  
pp. 31
Author(s):  
Samir Karaa
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Mixed Finite Element ◽  
A Priori ◽  
Energy Estimation ◽  
Time Stepping ◽  
Space Discretization ◽  
Priori Error Estimates ◽  
Sharp Stability ◽  
Finite Element Schemes

A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. A convergence analysis is carried out and optimal a priorierror estimates for both displacement and pressure are derived.      

Exact First Order Finite Element Modeling for Eddy Current NDE

1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Eddy Current ◽  
Element Modeling ◽  
First Order ◽  
Eddy Current Nde
Sign in / Sign up

Export Citation Format

Share Document