國立臺南大學專任教師基本資料
姓名黃印良
系所應用數學系
校內分機531
EMAILliang@mail.nutn.edu.tw
辦公室C211-1
網址 
專長/研究領域數值分析、科學計算、計算流體力學
學位畢業學校國別主修學門修業期間
碩士交通大學中華民國應用數學1998/09~2000/06
博士清華大學中華民國數學2000/09~2004/10
服務機關部門系所職稱服務期間
臺南大學應用數學系助理教授2010/08~2015/07
臺南大學應用數學系副教授2015/08~
著作名稱:SEMI-EXACT SOLUTIONS AND PULSATING FRONTS FOR LOTKA-VOLTERRA SYSTEMS OF TWO COMPETING SPECIES IN SPATIALLY PERIODIC HABITATS
年度:2020
類別: 期刊論文 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
摘要: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.
關鍵字:Semi-exact solutions;traveling wave solutions;reaction-diffusion equations
著作名稱:Positive steady states of reaction–diffusion–advection competition models in periodic environment
年度:2017
類別: 期刊論文 Journal of Mathematical Analysis and Applications
摘要:In this paper, we consider the positive steady states for reaction–diffusion–advection competition models in the whole space with a spatially periodic structure. Under the spatially periodic setting, we establish sufficient conditions for the existence of positive steady states of this model, respectively, by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems. As an application, a Lotka–Volterra reaction–diffusion–advection model for two competing species in a spatially periodic environment is considered. Finally, some numerical simulations are presented to seek dynamical behaviors.
關鍵字:Positive steady states, Reaction–diffusion–advection, Population dynamics, Periodic environment
著作名稱:A Null Space Free Jacobi-Davidson Iteration for Maxwells Operator
年度:2015
類別: 期刊論文 SIAM Journal on Scientific Computing
摘要: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.
關鍵字:time harmonic Maxwell’s equations, Yee’s scheme, edge elements, generalized eigenvalue problem, discrete vector potential, discrete deRham complex, Poincar’e Lemma, Jacobi– Davidson method
著作名稱:A GENERALIZED MAC SCHEME ON CURVILINEAR DOMAINS
年度:2013
類別: 期刊論文 SIAM Journal on Scientific Computing
摘要:We propose a simple finite difference scheme for Navier–Stokes equations in primitive formulation on curvilinear domains. With proper boundary treatment and interplay between covariant and contravariant components, the spatial discretization admits exact Hodge decomposition and energy identity. As a result, the pressure can be decoupled from the momentum equation with explicit time stepping. No artificial pressure boundary condition is needed. In addition, it can be shown that this spatially compatible discretization leads to uniform inf-sup condition, which plays a crucial role in the pressure approximation of both dynamic and steady state calculations. Numerical experiments demonstrate the robustness and efficiency of our scheme.
關鍵字:Navier–Stokes equations, inf-sup condition, Mark-And-Cell scheme, incompressible flow, pressure boundary condition, pressure Poisson equation
著作名稱:Preconditioning bandgap eigenvalue problems in three-Dimensional photonic crystals simulations
年度:2010
類別: 期刊論文 Journal of Computational Physics
摘要:To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yees scheme as examples, we propose using Krylov–Schur method and Jacobi-Davidson method to solve the resulting eigenvalue problems. For preconditioning, we derive several novel preconditioning schemes based on various preconditioners, including a preconditioner that can be solved by Fast Fourier Transform efficiently. We then conduct intensive numerical experiments for various combinations of eigenvalue solvers and preconditioning schemes. We find that the Krylov-Schur method associated with the Fast Fourier Transform based preconditioner is very efficient. It remarkably outperforms all other eigenvalue solvers with common preconditioners like Jacobi, Symmetric Successive Over Relaxation, and incomplete factorizations. This promising solver can benefit applications like photonic crystal structure optimization.
關鍵字:Three-dimensional photonic crystals, Maxwells equations, Eigenvalue problems, Preconditioning, Fast Fourier transform, Krylov-Schur method, Jacobi-Davidson method, Harmonic extraction
著作名稱:An FFT Based Fast Poisson Solver on Spherical Shells
年度:2011
類別: 期刊論文 Communications in Computational Physic
摘要:We present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with O(N^3 log N) operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.
關鍵字:Poisson equation, spherical coordinate, FFT, spectral-finite difference method, fast diagonalization, high order accuracy, error estimate, trapezoidal rule, Euler-Maclaurin formula, Bernoulli numbers.