Dr. Maciej Woźniak

AGH University of Science and Technology in Kraków, Poland.

We analyze the integration for 3D isogeometric finite element method solvers and its effective scheduling on hierarchical computer architecture. Data necessary for concurrency over elements is independent, so computation on this level is trivially concurrent.

However, constructing several layers of concurrency for the integration algorithm is challenging. We propose a multilevel concurrent integration algorithm associated with scheduling that brings one extra degree of possible speedup. Because of one extra degree of possible speedup, we analyze the concurrent integration inside elements. The scheduling algorithm is intended for strongly related hierarchical

architectures of a GPU. Using trace theory and Foata Normal Form, we verify integrity of the

proposed solution. Summing up, we propose a general method for analyzing concurrency of the integration algorithm.

We instantiate this method on a classical element-based integration algorithm, however, this methodology is possible to apply for other integration algorithms, including sum factorization, fast numerical quadrature, or row-wise integration methods.