Preconditioning for Domain Decomposition through Function Approximation

Preconditioning for Domain Decomposition through Function Approximation

A new approach was presented in [11] for construcling preconditioners through a function approximation for the domain decomposi~ion-basedpreconditioned conjugate gradient method. This work extends the approach to more general cases where grids may be nonuniform; elliptic operatoI'B may have variable coefficients (but are separable and self-adjoint); and geometric domains may be nonrectangular. ...

Wavelet Stabilization and Preconditioning for Domain Decomposition

The aim of this paper is to propose a stabilization technique in order to circumvent the two inf{sup conditions needed for stability of the discretization of the Three Fields Formulation for domain decomposition methods BM93, BM94]. Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is shown to admit an asymptotically optimal preconditio...

Domain Decomposition Preconditioning for Parallel PDE Software

Domain decomposition methods have been applied to the solution of engineering problems for many years. Over the past two decades however the growth in the use of parallel computing platforms has ensured that interest in these methods, which offer the possibility of parallelism in a very natural manner, has become greater than ever. This interest has led to research that has yielded significant ...

Domain decomposition preconditioning for elliptic problems with jumps in coefficients

In this paper, we propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without ‘cross points’ on interfaces between subdomains and the second is the ‘cross points’ case. In both cases the main computational cost is an implementatio...

Parallel Domain-Decomposition Preconditioning for Computational Fluid Dynamics