Nested parallelism: Allocation of threads to tasks and OpenMP implementation

In this paper we discuss the use of nested parallelism. Our claim is that if the problem naturally possesses multiple levels of parallelism, then applying parallelism to all levels may significantly enhance the scalability of your algorithm. This claim is sustained by numerical experiments. We also discuss how to implement multi-level parallelism using OpenMP. We find current OpenMP implementation, based on version 1.0, to have severe limitation for implementing nested parallelization. We then show how this can be circumvented by explicitly assign task to threads. Load balancing issues become more complicated with two (or more) levels of parallelism. To handle this problem, we have designed a distribution algorithm which groups threads into teams, each team being responsible for one course grain outer-level task. This algorithm is proven to produce the optimal load balance, under given assumptions.