Efficient Parallel Adaptive Finite Element Methods Using Self-Scheduling Data and Computations

Parallel adaptive hp finite element methods (FEM), in which both grid size h and local polynomial order p are dynamically altered, are the most effective discretization schemes for a large class of problems. The greatest difficulty in using these methods on parallel computers is the design of efficient schemes for data storage, access and distribution. We describe here the development of a comprehensive infrastructureAdaptive Finite Elements Application Programmers Interface (AFEAPI), that addresses these concerns. AFEAPI provides a simple base for users to develop their own parallel adaptive hp finite element codes. It is responsible for the parallel mesh database, mesh partitioning and redistribution and optionally solution of the large irregularly sparse systems of linear equations generated in these schemes. Dynamic hashing schemes and B-trees are used to store and access the distributed unstructured data efficiently.