Schur complement domain decomposition methods for the solution of multiple scattering problems

A preconditioner for the Schur complement domain decomposition method

The condition number of the Schur complement in domain decomposition

In the nonoverlapping approach to domain decomposition (cf. [10], [21] and the references therein) the nite element equation for an elliptic boundary value problem is reduced, after parallel subdomain solves, to its Schur complement which involves only the nodal variables (degrees of freedom) on the subdomain boundaries. The condition number of the Schur complement has been investigated for sec...

Schur Complement based domain decomposition preconditioners with Low-rank corrections

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this “Schur Low Rank” (SLR) preconditioning approach, the coefficient matrix is first decoupled by DD, and then a low-rank correction is exploited to compute an approximate inverse of the Schur compleme...

Domain Decomposition Methods for Inverse Problems

Inverse problems related to the estimation of coeecients of partial diierential equations are illposed. Practical applications often use the t-to-data output-least-square's method to recover the coeecients. In this work, we develop parallel nonoverlapping domain decomposition algorithms to estimate the diiusion coeecient associated with elliptic diierential equations. In order to realize the do...

Domain decomposition methods for welding problems

The welding of metals and alloys is a widely used industrial process. Many types of analysis have been carried out on such problems [MUB67]. The numerical thermal analysis of welding is required to take into account such features as temperature dependent material properties, phase change, non-uniform distribution of energy from heat source etc. In this paper, a 2-D non-linear electric arc-weldi...