A study of efficient concurrent integration methods of B-Spline basis functions in IGA-FEM

Based on trace theory, we study efficient methods for concurrent integration of B-spline basis functions in IGA-FEM. We motivate the discussion with the heat-equation problem discretized with the forward Euler time-marching scheme in time and the IGA-FEM in space, leading to the study of the cost associated with the assembling of the Mass matrix. We consider several scenarios of parallelization for two standard integration methods; the classical one and sum factorization. We aim to efficiently utilize hybrid memory machines, such as modern clusters, by focusing on the non-obvious layer of the shared memory part of concurrency. We estimate the performance of computations on a GPU and provide a strategy for performing such computations in practical implementations.