Domain Decomposition Methods: Algorithms and Theory

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Large scale continuum mechanics simulations routinely requirethe efficient solution of very large linear or nonlinear systemsof algebraic equations as well as powerful computer systems.Such problems are increasingly solved on parallel or distributedcomputing systems which provide access to a large amount of memoryas well as a substantial number of fast processors. The goal ofthis project is to further develop solvers of domain decompositiontype, algorithms which respect the memory hierarchy of modern computing systems and allow for a performance which approaches peak floating pointperformance. There already exists a well developed mathematical theory and a good understanding of how to adjust these algorithms to problemsarising in different applications but there is also a real needto further extend our understanding and to improve and numericallytest new algorithms especially in view of emergence of parallelcomputing systems with very many powerful processors. A maingoal of this project is the further understanding of theFETI-DP and BDDC families of domain decomposition methods.The direction of the work in this field is strongly influencedby the interaction between academic computational scientistsand scientists at the US national laboratories and inthe engineering software industry. The connection to the SANDIA-Albuquerque laboratories is particularly strong. Domain decompositionmethods are used extensively in very large and important applicationsat these laboratories and the domain decomposition methods arealso making significant inroads in software systems that are usedby a large community of engineers for the design and checkingof machine parts and larger engineering structures. Particularly importantapplication areas are elasticity and electromagnetics. The latterfield helps create a foundation for improvements of cellularphone systems, other wire-less communication systems, as well asmicro electronics.