Browsing by Author "Tseng, Yu-Hou"

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An efficient semi-coarsening multigrid method for variable diffusion problems in cylindrical coordinates
(2007-05-01)
Lai, Ming-Chih
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Wu, Chin-Tien
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Tseng, Yu-Hou
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應用數學系
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Department of Applied Mathematics
In this paper, we present an efficient multigrid (MG) algorithm for solving the three-dimensional variable coefficient diffusion equation in cylindrical coordinates. The multigrid V-cycle combines a semi-coarsening in azimuthal direction with the red-black Gauss-Seidel plane (radial-axial plane) relaxation. On each plane relaxation, we further semi-coarsen the axial direction with red-black line relaxation in the radial direction. We also prove the convergence of two-level MG with plane Jacobi relaxation. Numerical results show that the present multigrid method indeed is scalable with the mesh size. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
New Numerical Results for the Surface Quasi-Geostrophic Equation
(2012-01-01)
Constantin, Peter
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Lai, Ming-Chih
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Sharma, Ramjee
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Tseng, Yu-Hou
;
Wu, Jiahong
The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.