Browsing by Author "Huang, Yin-Liang"

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A NULL SPACE FREE JACOBI-DAVIDSON ITERATION FOR MAXWELL'S OPERATOR
(2015-01-01)
Huang, Yin-Liang
;
Huang, Tsung-Ming
;
Lin, Wen-Wei
;
Wang, Wei-Cheng
;
應用數學系
We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of time harmonic Maxwell's equations. We focus on a class of spatial discretizations that guarantee the existence of discrete vector potentials, such as Yee's scheme and the edge elements. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential instead. The correction equation is solved approximately as in the standard Jacobi-Davidson approach. The computational cost of the transformation from the vector potential to the corrector is negligible. As a consequence, the expanding subspace automatically stays out of the null space and no extra projection step is needed. Numerical evidence confirms that the proposed scheme indeed outperforms the standard and projection-based Jacobi-Davidson methods by a significant margin.
SEMI-EXACT SOLUTIONS AND PULSATING FRONTS FOR LOTKA-VOLTERRA SYSTEMS OF TWO COMPETING SPECIES IN SPATIALLY PERIODIC HABITATS
(2020-01-01)
Chen, Chiun-Chuan
;
Huang, Yin-Liang
;
Hung, Li-Chang
;
Wu, Chang-Hong
;
應用數學系
We are concerned with the coexistence states of the diffusive Lotka-Volterra system of two competing species when the growth rates of the two species depend periodically on the spacial variable. For the one-dimensional problem, we employ the generalized Jacobi elliptic function method to find semi-exact solutions under certain conditions on the parameters. In addition, we use the sine function to construct a pair of upper and lower solutions and obtain a solution of the above-mentioned system. Next, we provide a sufficient condition for the existence of pulsating fronts connecting two semi-trivial states by applying the abstract theory regarding monotone semiflows. Some numerical simulations are also included.