Recent Developments in Domain Decomposition Methods

The main goal of this book is to provide an overview of some of the most recent developments in the field of Domain Decomposition Methods. Domain decomposition relates to the construction of preconditioners for the large algebraic systems of equations which often arise in applications, by solving smaller instances of the same problem. It also relates to the construction of approximation methods built from different discretizations in different subdomains. The resulting methods are among the most successful parallel solvers for many large scale problems in computational science and engineering. The papers in this collection reflect some of the most active research areas in domain decomposition such as novel FETI, Neumann-Neumann, overlapping Schwarz and Mortar methods.

---

This volume collects some of the papers presented at the Workshop on Do main Decompositionheld at ETH, Zurich,on June 7-8th 2001. The Workshop was organized by Luca F. Pavarino (University of Milan), Christoph Schwab (ETH Zurich), Andrea Toselli (ETH Zurich), and OlofB. Widlund (Courant Institute of Mathematical Sciences). Our sponsors were the University of Milan, Department of Mathematics (MURST projects: "Calcolo Scientifico: modelli e metodi numerici innovativi" and "Simmetrie, forme geometriche, evoluzione e memoria nelle equazioni alle derivate parziali"), the Seminar for Applied Mathematics, ETH Zurich, and the Program on Computational Science and Engineering at ETH Zurich. The main goal ofthis meeting wasto provide a forum for the exchange of ideas on the most recent developmentsin the fieldof Domain Decomposition Methods. We broadly understand Domain Decomposition as relating to the construction of preconditioners for the large algebraic systems of equations which often arise in applications, by solving smaller instances of the same problem. In our planning, wealso wished to include studies of methods built from different discretizations in differentsubdomains such as in multi-physics models, mortar finite elements, wavelets, etc. Domain Decomposition meth ods are now fairly well understood for elliptic scalar and vector problems and are employed for the solution of large scale problems in computational sciencesand engineering. However they remain less wellunderstood for more general problems, such as scattering problems, mixed problems, wavepropa gation, and evolution problems.