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1,369
Efficient Sampling on Coarse Grids in Tomography
, 1993
"... In tomography we have to give an estimate of a function from a finite number of its intergrals along straight lines or on strips. Under very reasonable conditions, the interlaced sampling is well known to be the most efficient scheme for this problem. In this paper we examine some pertubations on th ..."
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Cited by 3 (0 self)
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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
COARSE GRID APPROXIMATION GOVERNED BY LOCAL FOURIER ANALYSIS
"... Abstract. Solving discrete boundary value problems with the help of an appropriate 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 are the ..."
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Abstract. Solving discrete boundary value problems with the help of an appropriate 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
Simulation of separation using coarse grid
"... 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 staircaselike representation of the surface object, it was found that the added surf ..."
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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 staircaselike 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 NavierStokes equations are carried out in a uniform Cartesian coordinates using a multidirectional finite difference scheme with a thirdorder upwinding. No explicit turbulence model is incorporated into the model, and the dependence of the solution on the blvr parameter is investigated.
The optimized Schwarz method with a coarse grid correction
, 2009
"... 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 cy ..."
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Cited by 12 (3 self)
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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
A New Coarse Grid Correction for RAS/AS
"... 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 proce ..."
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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
Coarsegrid Selection for Parallel Algebraic Multigrid
 Held at Lawrence Berkeley National Laboratory
, 1998
"... . 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 coarsegrid poin ..."
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Cited by 25 (3 self)
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. 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 coarsegrid
Coarse grid acceleration of a parallel block preconditioner
"... A block preconditioner is considered in a parallel computing environment. This preconditioner has good parallel properties, however, the convergence deteriorates when the number of blocks increases. Two different techniques are studied to accelerate the convergence: overlapping at the interfaces and ..."
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Cited by 9 (4 self)
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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.
Fast Parallel Direct Solvers For Coarse Grid Problems
 J. Parallel and Distributed Computing
, 1997
"... 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 of the inver ..."
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Cited by 23 (4 self)
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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
A comparison of Deflation and Coarse Grid Correction applied to porous media flow
, 2003
"... 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 socalled de
ation preconditioner. We prove that the eective condition number of the deflated pr ..."
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Cited by 48 (22 self)
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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 socalled de
ation preconditioner. We prove that the eective condition number of the deflated
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