Some Schwarz Methods for Symmetric And Nonsymmetric Elliptic Problems
Some Schwarz Methods for Symmetric And Nonsymmetric Elliptic Problems
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' Courant Institute of Mathematical Science, New York University, 251 Mercer Street, New York, N. Y. 10012. This work was supported in part by the National Science Foundation under Grant NSF- CCR-8903003 and in part by the U. S. Department of Energy under contract DE-FG02-88ER250553 at the Courant Mathematics and Computing Laboratory.
1 This paper is organized as follows. In Section 2, we first briefly review the theory for the positive definite, symmetric case and then, to provide an example, ...turn to a special case already discussed in our first papers on Schwarz methods, cf. Dryja and Widlund [15], [16]. This additive method uses two levels of discretization corre- sponding to a coarse space and a number of local finite element spaces. The former plays a role similar to the coarse mesh solver in a multigrid method; it provides global transportation of information across the region.
In our original proof that the condition number for this Schwarz method is inde- pendent of the number of subspaces and the mesh size, it is important to assume that there is a relatively generous overlap between the subregions.
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To quickly assess the difficulty of the text, read a short excerpt:
' Courant Institute of Mathematical Science, New York University, 251 Mercer Street, New York, N. Y. 10012. This work was supported in part by the National Science Foundation under Grant NSF- CCR-8903003 and in part by the U. S. Department of Energy under contract DE-FG02-88ER250553 at the Courant Mathematics and Computing Laboratory.
1 This paper is organized as follows. In Section 2, we first briefly review the theory for the positive definite, symmetric case and then, to provide an example, ...turn to a special case already discussed in our first papers on Schwarz methods, cf. Dryja and Widlund [15], [16]. This additive method uses two levels of discretization corre- sponding to a coarse space and a number of local finite element spaces. The former plays a role similar to the coarse mesh solver in a multigrid method; it provides global transportation of information across the region.
In our original proof that the condition number for this Schwarz method is inde- pendent of the number of subspaces and the mesh size, it is important to assume that there is a relatively generous overlap between the subregions.
What to read after Some Schwarz Methods for Symmetric And Nonsymmetric Elliptic Problems?
You can find similar books in the "Read Also" column, or choose other free books by Olof B Widlund to read onlineMoreLess
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