Parallel interval Newton-like Schwarz methods for almost linear parabolic problems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Two-stage interval Krawczyk-Schwarz methods with applications to nonlinear parabolic PDE
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
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We develop a unified representation of two well-known approaches for the solution of linear systems of equations by partitioning the original system into overlapping subsystems. The representation generalizes the algebraic form of both the additive Schwarz and multisplitting methods. In the new formulation we obtain convergence results similar to those known for multisplittings, considering one- and two-stage variants. We report on some numerical experiments on a CRAY T3D which suggest a slight preference for algebraic additive Schwarz methods over multisplitting methods. These experiments also demonstrate the efficiency of our approach in a parallel computing environment.