Simple data management, scheduling and solution strategies for managing the irregularities in parallel adaptive hp finite element simulations

Abstract

Adaptive hp finite element methods (FEM), in which both grid size h and local polynomial order p are dynamically altered, generate computations that require dynamic and irregular patterns of data storage, access and computation, making their parallelization very difficult. We show here that such applications can be parallelized easily if we use a good spatially local ordering of all data for organizing storage, distribution and access, and schedule computation using a “owner-computes” rule. This ordering results in a global index space which can be partitioned to distribute the data, locally used in hashing schemes and B-trees for the necessary dynamic memory management, and used in designing efficient solution schemes.