Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics

2013 ◽  
Vol 96 (1) ◽  
pp. 1-28 ◽  
Author(s):  
R. Kolman ◽  
J. Plešek ◽  
M. Okrouhlík ◽  
D. Gabriel
Keyword(s):  
Finite Elements ◽  
Dispersion Analysis ◽  
Grid Dispersion

ANALYTICAL AND NUMERICAL STUDIES OF A FINITE ELEMENT PML FOR THE HELMHOLTZ EQUATION

2000 ◽  
Vol 08 (01) ◽  
pp. 121-137 ◽  
Author(s):  
ISAAC HARARI ◽  
MICHAEL SLAVUTIN ◽  
ELI TURKEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Acoustic Waves ◽  
Dispersion Analysis ◽  
Exterior Domains ◽  
Stabilized Finite Elements ◽  
Numerical Studies ◽  
Time Harmonic ◽  
Element Computation ◽  
Finite Element Computation

A symmetric PML formulation that is suitable for finite element computation of time-harmonic acoustic waves in exterior domains is analyzed. Dispersion analysis displays the dependence of the discrete representation of the PML parameters on mesh refinement. Stabilization by modification of the coefficients is employed to improve PML performance, in conjunction with standard stabilized finite elements in the Helmholtz region. Numerical results validate the good performance of this finite element PML approach.

A FLUX-BASED CONSERVATION APPROACH FOR ACOUSTIC PROBLEMS

2008 ◽  
Vol 16 (01) ◽  
pp. 31-53
Author(s):  
NADIA MASSÉ ◽  
CHRISTIAN PRAX ◽  
EMMANUEL REDON
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Control Volume ◽  
Dispersion Analysis ◽  
Two Dimensional ◽  
Field Behavior ◽  
Determination Process ◽  
Spatial Convergence ◽  
Control Volume Finite Element

In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.

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