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Ph.D. Theses

A Hierarchical Partition Model for Parallel Adaptive Finite Element Computation

By James D. Teresco
Advisor: Joseph E. Flaherty
July 25, 2000

Software tools for the solution of partial differential equations using parallel adaptive finite element methods have been developed. We describe the design and implementation of the parallel mesh structures within an adaptive framework. In a parallel adaptive computation, the mesh changes during the computation, necessitating a dynamic redistribution of data. Mesh structures must not only support the adaptivity, but this dynamic redistribution. The distributed mesh structures are built upon a serial mesh database, and our enhancements to that system are described. This work began with several enhancements to a parallel mesh database developed previously. Our redesigned distributed mesh structures are based on the object-oriented and generic programming paradigms. The most fundamental concept is that of a hierarchical partition model used to distribute finite element meshes and associated data on a parallel computer. The hierarchical model represents heterogeneous processor and network speeds, and may be used to represent processes in any parallel computing environment, including an SMP, a distributed-memory computer, a network of workstations, or some combination of these. We describe several example applications, examining both the solution properties and the effectiveness of several algorithms for dynamic load balancing. We present experiments which show that the information about different processor speeds, memory sizes, and the corresponding interconnection network can be useful in a dynamic load balancing algorithm which seeks to achieve a good balance with minimal interprocessor communication penalties when a slow interconnection network is involved. Examples of how such architecture-dependent load balancing can be applied are also given.

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