• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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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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• v.15 no.1
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• pp.121-133
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• 1999

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.9-11
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• 1996

We apply a full mutigrid scheme to computing eigenvalues of the Laplace eigenvalue problem with Dirichlet boundary condition. We use finite difference method to get an algebraic equation and apply inverse power method to estimating the smallest eigenvalue. Our result shows that combined method of inverse power method and full multigrid scheme is very effective in calculating eigenvalue of the eigenvalue problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05b
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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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• v.9 no.3
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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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• 1998.05a
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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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• v.14 no.2
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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.

• Proceedings of the KSME Conference
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• 2002.08a
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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.

• Proceedings of the KSME Conference
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• 2002.08a
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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.