Domain Decomposition Methods for Partial Differential Equations

Domain decomposition methods are designed to allow the effective numerical solution of partial differential equations on parallel computer architectures. They comprise a relatively new field of study, but have already found important applications in many branches of physics and engineering. In this book the authors illustrate the basic mathematical concepts behind domain decomposition, looking at a large variety of boundary value problems. Contents include; symmetric elliptic equations; advection-diffusion equations; the elasticity problem; the Stokes problem for incompressible and compressible fluids; the time-harmonic Maxwell equations; parabolic and hyperbolic equations; and suitable couplings of heterogeneous equations.

1 - Mathematical foundation of domain decomposition methods
2 - Discretized equations and domain decomposition
3 - Iterative domain decomposition methods at the discrete level
4 - Convergence analysis for iterative domain decomposition
5 - Other boundary value problems
6 - Advection-diffusion equations
7 - Time-dependent problems
8 - Heterogeneous domain decomposition methods

Professor Alfio Quarteroni, Via Agostino da Lodi, 7 26900 Lodi, ITALY. Tel: +39 371 410148; Fax: +39 2399 4588; email: aq@mate.polimi.it Professor Alberto Valli, Department of Mathematics, University of Trento, 38050 Povo (TN), ITALY. Tel: +39 461 881580; Fax: +39 461 881624; email: valli@science.unitn.it