scholarly journals A Fast Optimization Algorithm of FEM/BEM Simulation for Periodic Surface Acoustic Wave Structures

Information ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 90
Author(s):  
Honglang Li ◽  
Zixiao Lu ◽  
Yabing Ke ◽  
Yahui Tian ◽  
Wei Luo
Keyword(s):  
Acoustic Wave ◽  
Surface Acoustic Wave ◽  
Toeplitz Matrix ◽  
Recursive Algorithm ◽  
Coefficient Matrix ◽  
Time Cost ◽  
Accurate Analysis ◽  
Periodic Surface ◽  
Speed Up ◽  
Element Method

The accurate analysis of periodic surface acoustic wave (SAW) structures by combined finite element method and boundary element method (FEM/BEM) is important for SAW design, especially in the extraction of couple-of-mode (COM) parameters. However, the time cost is very large. With the aim to accelerate the calculation of SAW FEM/BEM analysis, some optimization algorithms for the FEM and BEM calculation have been reported, while the optimization for the solution to the final FEM/BEM equations which is also with a large amount of calculation is hardly reported. In this paper, it was observed that the coefficient matrix of the final FEM/BEM equations for the periodic SAW structures was similar to a Toeplitz matrix. A fast algorithm based on the Trench recursive algorithm for the Toeplitz matrix inversion was proposed to speed up the solution of the final FEM/BEM equations. The result showed that both the time and memory cost of FEM/BEM was reduced furtherly.

scholarly journals Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

The Recursive Algorithms of Yule-Walker Equation in Generalized Stationary Prediction

2013 ◽  
Vol 756-759 ◽  
pp. 3070-3073 ◽  
Author(s):  
Er Yan Zhang ◽  
Xiao Feng Zhu
Keyword(s):  
Toeplitz Matrix ◽  
Gaussian Elimination ◽  
Recursive Algorithm ◽  
Toeplitz Matrices ◽  
Recursive Formula ◽  
Coefficient Matrix ◽  
Recursive Algorithms ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Order Of Magnitude

Toeplitz matrix arises in a remarkable variety of applications such as signal processing, time series analysis, image processing. Yule-Walker equation in generalized stationary prediction is linear algebraic equations that use Toeplitz matrix as coefficient matrix. Making better use of the structure of Toeplitz matrix, we present a recursive algorithm of linear algebraic equations from by using Toeplitz matrix as coefficient matrix , and also offer the proof of the recursive formula. The algorithm, making better use of the structure of Toeplitz matrices, effectively reduces calculation cost. For n-order Toeplitz coefficient matrix, the computational complexity of usual Gaussian elimination is about , while this algorithm is about , decreasing of one order of magnitude.

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