Large scale continuum mechanics simulations routinely require the efficient solution of very large linear or nonlinear systems of algebraic equations as well as powerful computer systems. Such problems are increasingly solved on parallel or distributed computing systems which provide access to a large amount of memory as well as a substantial number of fast processors. The goal of this project is to further develop solvers of domain decomposition type, algorithms which respect the memory hierarchy of modern computing systems and allow for a performance which approaches peak floating point performance. There already exists a well developed mathematical theory and a good understanding of how to adjust these algorithms to problems arising in different applications but there is also a real need to further extend our understanding and to improve and numerically test new algorithms especially in view of emergence of parallel computing systems with very many powerful processors. A main goal of this project is the further understanding of the FETI-DP and BDDC families of domain decomposition methods.
The direction of the work in this field is strongly influenced by the interaction between academic computational scientists and scientists at the US national laboratories and in the engineering software industry. The connection to the SANDIA- Albuquerque laboratories is particularly strong. Domain decomposition methods are used extensively in very large and important applications at these laboratories and the domain decomposition methods are also making significant inroads in software systems that are used by a large community of engineers for the design and checking of machine parts and larger engineering structures. Particularly important application areas are elasticity and electromagnetics. The latter field helps create a foundation for improvements of cellular phone systems, other wire-less communication systems, as well as micro electronics.
