• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 추계 학술대회논문집
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• pp.20-30
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• 2001

A multigrid DADI method for low Mach number preconditioning method is presented. The eigenvalues of governing equations are modified by A low Mach number preconditioner developed by Choi & Merkle, and it results in an accurate solution and fast convergence In the low Mach number region. The convergence of numerical method is further accelerated by multigrid method. The efficient and accuracy of present method is shown by comparison with conventional solution method for the compressible flows.

• East Asian mathematical journal
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• 제15권1호
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• pp.121-133
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• 1999

• 자연과학논문집
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• 제8권2호
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• pp.9-11
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• 1996

Dirichlet 경계조건을 갖는 Laplace 고유치방정식의 고유치를 구하는 데 복합마디방법을 이용하였다. 유한차분법을 적용하여 행렬 고유치방정식을 만들고 이 방정식의 고유치를 구하기 위하여 역거듭제곱방법과 전체복합마디법을 사용하였다. 그 결과 고유치를 기존의 방법보다 더욱 빠르게 구할 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권2호
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• pp.69-79
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• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1998년도 춘계학술발표회논문집(2)
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• pp.705-710
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• 1998

We describe a multigrid wavelet-based natural pixel (WNP) method for image reconstruction in emission computed tomography (ECT). The ECT is used to identify the tagged radioactive material's position in the body for detection of abnormal tissue such as tumor or cancer, as in SPECT and PET. With ECT methodology in parallel beam mode, we formulate a matrix-based reconstruction method for radionuclide sources in the human body. The resulting matrix for a practical problem is very large and nearly singular. To overcome this ill-conditioning, wavelet transform is considered in this study. Wavelets have inherent de-noising and multiscale resolution properties. Therefore, the multigrid wavelet-based natural pixel (WNP) method is very efficient to reconstruct image from projection data that is noisy and incomplete. We test this multigrid wavelet natural pixel (WNP) reconstruction method with the MCNP generated projection data for diagnosis of the simulated cancerous tumor.

• Journal of information and communication convergence engineering
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• 제9권3호
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• pp.319-324
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• 2011

In computing the optical flow. Horn and Schunck's method which is a representative algorithm is based on differentiation. But it is difficult to estimate the velocity for a large displacement by this algorithm. To cope with this problem multigrid method has been proposed. In this paper, we have proposed a scaled multigrid algorithm which the initial flow for a level is calculated by the summation of the optimally scaled flow and error flow. The optimally scaled flow is the scaled expanded flow of the previous level, which can generate an estimated second image having the least RMS error with respect to the original second image, and the error flow is the flow between the estimated second image (generated by the optimally scaled flow) and the original second image. The flow for this level is then estimated using the original first and second images and the initial flow for that level. From among the various coarsest starting levels of the multigrid algorithm, we select the one that finally gives the best estimated flow. Better results were achieved using our proposed method compared with Horn and Schunck's method and a conventional multigrid algorithm.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 춘계 학술대회논문집
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• pp.29-34
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• 1998

An efficient 3-dimensional compressible solver is developed using the second-order upwind TVD scheme and the multigrid diagonalized ADI method. The multigrid method is improved so that the present DADI algorithm obtains better convergence rates. Results are computed on Cray C90 computer for transonic unsaperated flows past ONERA-M6 wing to demonstrate the accuracy and efficiency. The results show good agreement with experimetal data. A reduction of four orders of residual for 3-dimensional transonic flow is obtained about 99 seconds.

• East Asian mathematical journal
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• 제14권2호
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• pp.399-410
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• 1998

In [3], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated-linear systems. In this work, we present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.31-34
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• 2002

An efficient implicit multigrid method is presented for the Navier-Stokes and $k-{\omega}$ turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. The eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.35-38
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• 2002

The convergence acceleration methods for the compressible Wavier-Stokes equations are studied ,which are multigrid method and implicit preconditioned multistage time stepping method. In this paper, the performance of implicit preconditioning methods are studied for the full-coarsening multigrid methods on the high Reynolds number compressible flow computations. The effect of numerical flux on the convergence are investigated for the inviscid and viscous calculations.