Parallel adaptive finite element computations with hierarchical preconditioning

A parallel implementation of an adaptive finite element program is treated which is characterized by an underlying parallel dynamic data structure based on linked lists and tree structures. In conjunction with a conjugate gradient solver an efficient methodology for treating adaptive finite element systems is shown. This is achieved by preconditioning using hierarchical bases with and without a coarse grid solver and by new methods of quasi-optimal load balancing. The different levels of nested meshes needed for preconditioning are governed either by global or by adaptive refinements. A termination algorithm based on the vector method is implemented for the non deterministic adaptive mesh refinement procedure. The problems concerning load balancing due to adaptive refinement are solved by a dynamic load balancing for the nodes.This work has been supported by Deutsche Forschungsgemeinschaft under grant no. Ste238/26.