scholarly journals Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Yidu Yang ◽  
Yu Zhang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Adaptive Algorithm ◽  
Variational Formulation ◽  
High Efficiency ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.

scholarly journals Highly Efficient Calculation Schemes of Finite-Element Filter Approach for the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yu Zhang ◽  
Yidu Yang ◽  
Jie Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
High Efficiency ◽  
Numerical Results ◽  
Linear Algebraic System ◽  
Highly Efficient ◽  
Efficient Calculation ◽  
Interpolation Postprocessing ◽  
Filter Approach

This paper discusses finite-element highly efficient calculation schemes for solving eigenvalue problem of electric field. Multigrid discretization is extended to the filter approach for eigenvalue problem of electric field. With this scheme one solves an eigenvalue problem on a coarse grid just at the first step, and then always solves a linear algebraic system on finer and finer grids. Theoretical analysis and numerical results show that the scheme has high efficiency. Besides, we use interpolation postprocessing technique to improve the accuracy of solutions, and numerical results show that the scheme is an efficient and significant method for eigenvalue problem of electric field.

Numerical Simulations of a Building-Acoustic Volume Interaction System Excited by Multiple Human Footfall Impacts

2008 ◽  
Author(s):  
Jing Tang Xing ◽  
Ye Ping Xiong
Keyword(s):  
Finite Element ◽  
Variational Formulation ◽  
Impact Load ◽  
Mixed Finite Element ◽  
Moving Load ◽  
Mixed Finite Element Method ◽  
Dynamic Responses ◽  
Experimental Result ◽  
Structure Interaction ◽  
Interaction System

A mixed finite element method is used to simulate a building structure-acoustic volume interaction system subject to multiple human footfall impacts. The pressure in the acoustic volume and the displacement of the structure are chosen as the fundamental variables to describe air-structure interaction dynamics. The governing equations and the corresponding variational formulation for generalised air-structure interaction systems are presented. From the variational formulation, the finite element and substructure-subdomain equations are derived. The available experimental results of footfall impact load histories are described and discussed. Based on an experimental result, an approximate footfall load time function is proposed to model the footfall loads in two successive human foot-steps. This approximate footfall load is applied at each structure point at which a left or right foot contacts at the corresponding time instant. Therefore, this footfall load is a moving load with a speed equalling the human walking speed. Following a generalised description of the developed numerical approach and footfall loads, an example is given. In this example, three cases involving two people walking along two perpendicular directions on the top floor of the structure are simulated, respectively. The dynamic responses of the displacement of the structure and the acoustic pressure in the acoustic volume are obtained. The calculated results are compared and discussed to illustrate the developed method and to reveal the mechanism of low-frequency vibration produced by human footfall impacts. The advantages of the proposed method are summarised to provide some guidelines to house designs.

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