Titlebook: Domain Decomposition Methods in Science and Engineering XVI; Olof B. Widlund,David E. Keyes Conference proceedings 2007 Springer-Verlag Be

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MINISYMPOSIUM 1: Domain Decomposition Methods for Simulation-constrained Optimizationgorithms and hardware have provided the framework for high fidelity simulations, to the point that it is now practical to consider complex optimization problems. In such problems we wish to determine various parameters that typically consist the data of a simulation: boundary and initial conditions,

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Robust Multilevel Restricted Schwarz Preconditioners and Applicationsner works extremely well for some difficult large systems of linear equations arising from some optimization problems constrained by the incompressible Navier-Stokes equations. Performance of the preconditioner is reported for parameters including number of processors, mesh sizes and Reynolds number

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Erdressourcen: Die Herausforderungens. In order to retain as much flexibility as possible, we do not require the subdomain grids to match along their common interfaces. Dual Lagrange multipliers are employed to generate efficient and robust transmission operators between the subdomains. Various numerical examples are presented to illustrate the applicability of the approach.

COLIC

https://doi.org/10.1007/978-3-031-57176-3the Cahn-Hilliard equation with an obstacle potential. We present a new class of preconditioners based on linear Schur complements associated with successive approximations of the coincidence set. In numerical experiments, we found superlinear convergence and finite termination.

COLIC

Penicillin and Beta-Lactam Drug Allergy,coarse level consists of the lowest order finite element space. On the fine level, we investigate several decompositions with large or small overlap leading to optimal or close to optimal condition numbers. The analysis is confirmed by numerical experiments for a model problem.