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The optimized Schwarz method and the closely related 2-Lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations. Although these methods are known to work well in special cases (e.g., when the domain is a square and the two subdomains are rectangles), the problem has never… (More)

The 2-Lagrange multiplier method is a domain decomposition method which can be used to parallelize the solution of linear problems arising from partial differential equations. In order to scale to large numbers of subdomains and processors, domain decomposition methods require a coarse grid correction to transport low frequency information more rapidly… (More)

Optimized Schwarz methods (OSMs) 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 cylinder, together with the corresponding convergence factor… (More)

Domain decomposition methods are used to find the numerical solution of large boundary value problems in parallel. In optimized domain decomposition methods, one solves a Robin subproblem on each subdomain, where the Robin parameter a must be tuned (or optimized) for good performance. We show that the 2-Lagrange multiplier method can be analyzed using… (More)

Classical Schwarz methods and preconditioners subdivide the domain of a partial differential equation into subdomains and use Dirichlet transmission conditions at the artificial interfaces. Optimized Schwarz methods use Robin (or higher order) transmission conditions instead, and the Robin parameter can be optimized so that the resulting iterative method… (More)

The Robust Robust Generalized Methods of Moments (RGMM) and the Indirect Robust GMM (IRGMM) are algorithms for estimating parameter values in statistical models, such as diffusion models for interest rates, in a robust way. The long computation time is one of the main challenge facing these methods. In this paper, we introduce accelerated variants of RGMM… (More)

- Sébastien Loisel
- 2005