Many scientific and engineering problems involve complex boundary value problems for partial differential equations. Especially higher level simulations put up considerable demands on the flexibility, accuracy, and efficiency of the underlying numerical model. Among the most attractive approaches having the potential to meet these requirements are finite element methods combined with adaptive local grid refinement, multigrid solvers, and parallelization techniques.
Within this paper, we present the parallel multilevel system PML. The intention of PML is to provide a light, but efficient interface for implementing parallel, adaptive finite element methods. Based on a distributed multilevel data structure, it supplies methods for the generation and adaption of local multigrids consisting of tetrahedral cells. Curved boundary surfaces are approximated by an unique rational point normal interpolation. To optimize performance on parallel computer systems, PML offers predictive load balancing using either METIS or CHACO for mesh partitioning. A special feature of PML is the support for periodic boundaries. This is of particular importance for our primary target application - the large eddy simulation of complex turbulent flows.
A major part of the paper is devoted to the basic design principles of PML. Further, the scalability of parallel mesh adaption is analysed. This is done theoretically as well as experimentally, using the visualization tool VAMPIR. Finally, we discuss our experiences with first applications including diffusion problems, and - as far as completed - compressible flows.