A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations

Optimized Schwarz methods with nonoverlapping circular domain decomposition

While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interf...

Space-Time Domain Decomposition for Mixed Formulations of Diffusion Equations

Flow and transport problems in porous media are well-known for their high computational cost. In the far field simulation of an underground nuclear waste disposal site, one has to work with extremely different length and time scales, and highly variable coefficients while satisfying strict accuracy requirements. One strategy for tackling these difficulties is to apply a non-overlapping domain d...

Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms

In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always converge, while overlapping Schwarz methods with Robin transmission conditions only converge for semilinear parabolic equations, but the convergence is not g...

Some Recent Results on Schwarz Type Domain Decomposition Algorithms

Numerical experiments have shown that two-level Schwarz methods, for the solution of discrete elliptic problems, often perform very well even if the overlap between neighboring subregions is quite small. This is true to an even greater extent for a related algorithm, due to Barry Smith, where a Schwarz algorithm is applied to the reduced linear system of equations that remains after that the va...

A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz Equation