scholarly journals Finite Element Approximation of Time Harmonic Waves in Periodic Structures

1995 ◽  
Vol 32 (4) ◽  
pp. 1155-1169 ◽  
Author(s):  
Gang Bao
Keyword(s):  
Finite Element ◽  
Periodic Structures ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Harmonic Waves ◽  
Time Harmonic

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Finite Element Approximation of Wave Propagation in Composite Material With Asymptotic Homogenization

2014 ◽  
Author(s):  
Bhuiyan Shameem Mahmood Ebna Hai ◽  
Markus Bause
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Wave Propagation ◽  
Finite Element Approximation ◽  
Ultrasonic Waves ◽  
Element Approximation ◽  
Fiber Reinforced ◽  
Reinforced Plastics ◽  
Advanced Composite Materials ◽  
Time Harmonic

Advanced composite materials such as carbon fiber reinforced plastics are being applied to many aerospace or automotive structures in order to improve material performances and save weight. Most composites have strong, stiff fibres in a matrix which is weaker and less stiff. But these structures can be damaged due to fluid-structure interaction (FSI) oscillations or material fatigue. To design integrated structural health monitoring (SHM) systems in a lightweight structure, it is important to understand wave propagation phenomena in composite material, and the influence of the material properties of the structures. In non-destructive test (NDT), piezoelectric induced ultrasonic waves can be used for damage detection. In this work, we focus on mathematical modeling and numerical approximation of the propagation of time-harmonic elastic waves in a fiber-reinforced composite material. The fibers are assumed to be parallel to each other and statistically uniformly distributed. In this work we study higher order continuous finite element approximation of the elastic wave equation and the implementation is carried out by means of the FEM library deal.II. (Differential Equations Analysis Library)

An Angular Finite Element Method for the Solution of the Even-Parity Equation

2009 ◽  
Author(s):  
R. Becker ◽  
R. Koch ◽  
M. F. Modest ◽  
H.-J. Bauer
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Basis Functions ◽  
New Method ◽  
Discrete Ordinates ◽  
Test Case ◽  
Element Approximation ◽  
Promising Alternative ◽  
Element Discretization ◽  
Spatial Coordinates

The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.

Finite Element Approximation of the p-Laplacian

1993 ◽  
Vol 61 (204) ◽  
pp. 523 ◽  
Author(s):  
John W. Barrett ◽  
W. B. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation
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