Browsing by Author "Chou, So-Hsiang"

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A finite element based fast eigensolver for three dimensional anisotropic photonic crystals
(2019-06-01)
Chou, So-Hsiang
;
Huang, Tsung-Ming
;
Li, Tiexiang
;
Lin, Jia-Wei
;
Lin, Wen-Wei
The standard Yee's scheme for the Maxwell eigenvalue problem places the discrete electric field variable at the midpoints of the edges of the grid cells. It performs well when the permittivity is a scalar field. However, when the permittivity is a Hermitian full tensor field it would generate un-physical complex eigenvalues or frequencies. In this paper, we propose a finite element method which can be interpreted as a modified Yee's scheme to overcome this difficulty. This interpretation enables us to create a fast FFT eigensolver that can compute very effectively the band structure of the anisotropic photonic crystal with SC and FCC lattices. Furthermore, we overcome the usual large null space associated with the Maxwell eigenvalue problem by deriving a null-space free discrete eigenvalue problem which involves a crucial Hermitian positive definite linear system to be solved in each of the iteration steps. It is demonstrated that the CG method without preconditioning converges in 37 iterations even when the dimension of a matrix is as large as 5, 184, 000. (C) 2019 Elsevier Inc. All rights reserved.
Efficient Arnoldi-type algorithms for rational eigenvalue problems arising in fluid-solid systems
(2011-03-01)
Chou, So-Hsiang
;
Huang, Tsung-Ming
;
Huang, Wei-Qiang
;
Lin, Wen-Wei
;
應用數學系
We develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy. The discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem. Numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on Raviart-Thomas finite elements for the displacement field. The trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem (GEP) of the form Ax = lambda"ss"x. For solving the GEP we apply Arnoldi algorithm to two different types of single matrices "ss"-1A and A"ss"-1. Numerical accuracy shows that the application of Arnoldi on A"ss"(-1) is better than that on "ss"(-1)A. (C) 2010 Elsevier Inc. All rights reserved.