A Scalable Balancing Domain Decomposition Based Preconditioner for Large Scale Heat Transfer Problems A Scalable Balancing Domain Decomposition Based Preconditioner for Large Scale Heat Transfer Problems

An efficient and scalable Balancing Domain Decomposition (BDD) type preconditionerfor large scale linear systems arising from 3-dimensional heat transfer problems ispresented. The new method improves parallel scalability of BDD by employing anincomplete balancing technique to approximate a coarse space problem and a diagonalscaling to precondition the local fine space problems instead of the Neumann-Neumannpreconditioner. It may increase the number of iterations but reduces the computationcosts of the precondition process for each iteration. Consequently, total computationtime and required memory are expected to be reduced. The convergence estimates mayalso be independent of the number of subdomains. We have implemented thisalgorithm on the parallel processors and have succeeded in solving some illconditionedlarge scale heat transfer problems.

An efficient and scalable Balancing Domain Decomposition (BDD) type preconditioner for large scale linear systems arising from 3-dimensional heat transfer problems is presented. The new method improves parallel scalability of BDD by employing an incomplete balancing technique to approximate a coarse space problem and a diagonal scaling to precondition the local fine space problems instead of the Neumann-Neumann preconditioner. It may increase the number of iterations but reduces the computation costs of the precondition process for each iteration. Consequently, total computation time and required memory are expected to be reduced. The convergence estimates may also be independent of the number of subdomains. We have implemented this algorithm on the parallel processors and have succeeded in solving some ill-conditioned large scale heat transfer problems.