Scalability and performance analysis of a probabilistic domain decomposition method

Lecture Notes in Computer Science, 4967 (2008), 1257-1264
http://dx.doi.org/10.1007/978-3-540-68111-3_133

In this paper, we analyze the scalability and performance of a probabilistic domain decomposition strategy for solving linear elliptic boundary-value problems. Such a strategy consists of a hybrid numerical scheme based on a probabilistic method along with a domain decomposition, and full decoupling can be accomplished. It is shown that such a method performs well for an arbitrarily large number of processors, while the classical deterministic approach is strongly affected by intercommunications. Therefore, the overall performance degrades dramatically for rather large number of processors. Furthermore, we find that the probabilistic method is scalable as the number of subdomains, i.e., the number of processors involved, increases. This fact is clearly illustrated by an example.