Petter E. Bjrstad, Randi Moe, and Morten Skogen. Parallel domain decomposition and iterative refinement algorithms. In Wolfgang Hackbusch, editor, Parallel Algorithms for PDEs, Proceedings of the 6th GAMM-Seminar held in Kiel, Germany, January 19--21, 1990, Braunschweig, Wiesbaden, 1990. Vieweg-Verlag. Home/Search Document Details and Download
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Domain Decomposition Algorithms With Small Overlap - Dryja, Widlund (1994) (46 citations) (Correct)
....A general theory has evolved and a substantial number of new algorithms has been designed, analyzed and tested numerically. Among them are two level, additive Schwarz methods first introduced in 1987; cf. Dryja and Widlund [28,25,29,30,55] For related work see also Bjrstad, Moe, and Skogen [1,2,3], Cai [10,11,12] Mathew [40,42,41] Matsokin and Nepomnyaschikh [43] Nepomnyaschikh [44] Skogen [47] Smith [48,52,49,50,51] and Zhang [59,60] As shown in Dryja and Widlund [30] a number of other domain decomposition methods, in particular those of Bramble, Pasciak, and Schatz [5,6] can ....
....programs is often the smallest when the overlap is at a minimum. The number of conjugate gradient iterations is typically higher in such a case but this can be compensated for by the fact that the local problems are smaller and therefore cheaper to solve; cf. in particular Bjrstad, Moe, and Skogen [2], Bjrstad and Skogen [3] Cai [10,11] Cai, Gropp, and Keyes [13] and Skogen [47] If the local problems are themselves solved by an iterative method, then a smaller overlap will give better conditioned local problems and therefore a higher rate of convergence; see Skogen [47] for a detailed ....
Petter E. Bjrstad, Randi Moe, and Morten Skogen. Parallel domain decomposition and iterative refinement algorithms. In Wolfgang Hackbusch, editor, Parallel Algorithms for PDEs, Proceedings of the 6th GAMM-Seminar held in Kiel, Germany, January 19--21, 1990, Braunschweig, Wiesbaden, 1990. Vieweg-Verlag.
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