on the interlaced scheme. Using a theorem due to A. Faridani, we show that sampling on coarse grids leads to efficient schemes, allowing to consider a lot of different sampling geometries. Some of them could be in practice much more easily generated than the interlaced one. New efficient sampling schemes

Abstract. Solving discrete boundary value problems with the help of an appro-priate multigrid method [1, 4, 5, 6] necessitates the construction of a sequence of coarse grids with corresponding coarse grid approximations for the given fine grid discretization. Popular choices in this context

This paper introduces a computational technique to compensate for the added numerical diffusion that is generated when uniform Cartesian coordinates are used to describe the flow around bluff bodies. Because of the staircase-like representation of the surface object, it was found that the added surface ”roughness ” causes larger than expected separation region for some test cases (flow around a sphere, and flow around a cylindrical body). In order to control the velocity profile in the boundary layer, a new parameter blvr (boundary layer velocity ratio) is defined, and it is used to set the negative value of the viscosity along the surface. Extensive visualizations of flow past bluff bodies are performed using the present technique. Numerical solutions of the governing Navier-Stokes equations are carried out in a uniform Cartesian coordinates using a multi-directional finite difference scheme with a third-order upwinding. No explicit turbulence model is incorporated into the model, and the dependence of the solution on the blvr parameter is investigated.

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Optimized Schwarz Methods (OSM) use Robin transmission conditions across the subdomain interfaces. The Robin parameter can then be optimized to obtain the fastest convergence. A new formulation is presented with a coarse grid correction. The optimal parameter is computed for a model problem on a

It is well known that for elliptic problems, domain decomposition methods need a coarse grid in order to be scalable. One talks about strong scalability of an algorithm, if it permits to solve a problem of fixed size faster in the same proportion that one adds processors. For example if on one

. The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarse-grid

and using a coarse grid correction. It appears that the latter technique is indeed scalable, so the wall clock time is constant when the number of blocks increases. Furthermore, the method is easily added to an existing solution code. © 2001 Elsevier Science B.V. All rights reserved.

We develop a fast direct solver for parallel solution of “coarse grid ” problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial differential equations in d space dimensions. The approach is based upon a (quasi-) sparse factorization

In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called de ation preconditioner. We prove that the eective condition number of the deflated