A survey of finite element methods for time-harmonic acoustics

2006 ◽  
Vol 195 (13-16) ◽  
pp. 1594-1607 ◽  
Author(s):  
Isaac Harari
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Time Harmonic

scholarly journals Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

2011 ◽  
Vol 81 (278) ◽  
pp. 623-642 ◽  
Author(s):  
Liuqiang Zhong ◽  
Long Chen ◽  
Shi Shu ◽  
Gabriel Wittum ◽  
Jinchao Xu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Maxwell Equations ◽  
Time Harmonic ◽  
Convergence And Optimality

scholarly journals A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Boniface Nkemzi ◽  
Jake Léonard Nkeck
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
A Priori ◽  
Electric Boundary Condition ◽  
Polygonal Domains ◽  
Time Harmonic ◽  
Predictor Corrector ◽  
Mesh Refinements

The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution. In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains. The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions. A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces. Numerical experiments that validate the theoretical results are presented.

ANALYSIS AND FINITE ELEMENT METHODS FOR A FLUID-SOLID INTERACTION PROBLEM IN ONE DIMENSION

1996 ◽  
Vol 06 (08) ◽  
pp. 1119-1141 ◽  
Author(s):  
CH. MAKRIDAKIS ◽  
F. IHLENBURG ◽  
I. BABUŠKA
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Model Problem ◽  
Type System ◽  
Interaction Model ◽  
One Dimension ◽  
Regularity Properties ◽  
Time Harmonic ◽  
Fluid Solid Interaction ◽  
Interaction Problem

In this paper we study a time-harmonic fluid-solid interaction model problem in one dimension. This is a Helmholtz-type system equipped with boundary and transmission conditions. We show the existence of a unique solution to this problem and study its stability and regularity properties. We analyze the convergence of finite element methods with respect to appropriate energy norms. Computational results are also presented.

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

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