• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.283-296
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• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• ETRI Journal
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• 제31권4호
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• pp.387-392
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• 2009

This paper introduces a novel parallel shift operator finite-difference time-domain (SO-FDTD) method for plasma in the dispersive media. We calculate the interaction between the electromagnetic wave of various frequencies and non-magnetized plasma by using the parallel SO-FDTD method. Then, we compare the results，which are calculated with serial and parallel SO-FDTD executions to obtain the speedup ratio and validate the parallel execution. We conclude that the parallel SO method has almost the same precision as the serial SO method, while the parallel approach expands the scope of memory and reduces the CPU time.

• 한국환경보건학회지
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• 제31권6호
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• pp.489-497
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• 2005

A numerical method for the mathematical water modeling in 2-dimensional flow has been developed. The model based on a split operator technique, in which, the advection term is calculated using the upwind scheme. The diffusion term is one- dimensionalized and calculated using Crank-Nicholson's implicit finite difference scheme to reduce the numerical errors from large time steps and variable spacings. It also provides a relatively simple and economic method for more accurate simulation of pollutant dispersion. Water depths and flow velocities in the Boreyong reservoir during the normal water periods were predicted by numerical experiments with a 2-dimensional flow model so as to provide current field data for the study of advection and diffusion of pollutants. Developed 2-dimensional water quality model is applied to Boreyong reservoir to simulate a spatial and periodical changes of water quality.

• 천문학회지
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• 제28권2호
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

• 대한수학회지
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• 제58권4호
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• pp.835-847
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• 2021

We study behavior of numerical solutions for a nonlinear eigenvalue problem on ℝⁿ that is reduced from a dispersion managed nonlinear Schrödinger equation. The solution operator of the free Schrödinger equation in the eigenvalue problem is implemented via the finite difference scheme, and the primary nonlinear eigenvalue problem is numerically solved via Picard iteration. Through numerical simulations, the results known only theoretically, for example the number of eigenpairs for one dimensional problem, are verified. Furthermore several new characteristics of the eigenpairs, including the existence of eigenpairs inherent in zero average dispersion two dimensional problem, are observed and analyzed.

• 대한기계학회논문집
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• 제19권8호
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• 한국지반공학회지:지반
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• 제1권1호
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• pp.5-12
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• 1985

압축성 흙에 대한 천밀침하의 수치해석 연구는 이제까지 Terzaghi의 정밀론을 간단히 확장하여 사용해 왔다. 그러나 비선형 응력-변형관계, 다층토, 큰 변형의 문제를 고려한 보다 복잡한 문제를 탄밀론에 적응한 예는 거의 없었다. 본 연구의 목적은 압축성 흙에서도 다층토를 중심으로 시간과 위치에 따른 추밀도와 과잉간극수압을 보다 실제적인 조건에 부합되도록 하기 위하여 유한차분법을 사용한 수치해석을 근거로 유용한 컴퓨터 알고리즘을 개발하는 데 있다. 압밀식을 해석하는 Explicit Scheme이 전체 깊이에 대한 최적분할 깊이율과 아울러 Operator의 변화에 따른 안정조건과 수고의 관점에서 연구되었다. 침하의 예측에 대해 전통적인 대석과 수식해법이 기초를 둔 개발된 알고리즘으로부터 새로운 알고리즘은 압축성 흙에 있어 전통적인 이론보다 우수한 것으로 판명되었다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1989년도 하계종합학술대회 논문집
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• pp.101-105
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• 1989

The iterative learning controller makes the system output follow the desired output over a finite time interval through iterating trials. In this paper, first we discuss that the design problem of learning controller is originally the design problem of the inverse model. Then we show that the tracking error which is the difference between the desired output and the system output is reduced monotonically by properly modeled inverse system if the magnitude of the learning operator being introduced is bounded within the unit circle in complex domain. Also it would be shown that the conventional learning control method is a kind of extremely simplified inverse model learning control method of the objective controlled system. Hence this control method can be considered as a generalization of the conventional learning control method. The more a designer model the objective controlled system precisely, the better the performance of the approximated inverse model learning controller would be. Finally we compare the performance of the conventional learning control method with that of the approximated inverse model learning control method by computer simulation.

• 물과 미래
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• 제27권2호
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• pp.155-166
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• 1994

Eulerian-Lagrangian 방법을 이용하여 1차원 종확산방정식의 수치모형을 비교·분석하였다. 본 연구에서서 비교·분석한 모형은 지배방정식을 연산자 분리방법에 의해서 이송만을 지배하는 이송방정식과 확산만을 지배하는 확산방정식으로 분리한다. 이송방정식은 특성곡선을 따라서 유체입자를 추적하는 특성곡선법을 사용하여 해를 구하고, 그 결과를 고정된 Eulerian 격자상에 보간하였고, 확산방정식은 상기 고정격자상에서 Crank-Nicholson 유한차분법을 사용하여 해를 구하였다. 이송방정식의 풀이에서 다양한 보간방법이 적용되었는데, 일반적으로 Hermite 보간다항식을 사용한 경우가 Lagrange 보간다항식을 사용한 경우보다 수치확산 및 수치진동 등의 오차를 최소화할 수 있어서 더욱 우수한 것으로 밝혀졌다.