The Use of a Hypercube in the Solution of Some Free Boundary Problems

将在Intel IPPSC-D5 Hypercube上开发并行算法，用于使用非结构网格对自由边界渗流问题进行有限元数值求解，并确定处理器之间的负载平衡和通信结构。目标是开发负载平衡策略，在处理器之间分配任务，以优化整体计算效率。将使用和评估几种域分裂技术，包括帕维亚大学的意大利研究人员开发的一种相对较新的技术。此外，将在加州大学圣巴巴拉大学和帕维亚大学的各种系统上进行扩大性能实验。所开发的知识和工具将提供有效解决自由边界问题以及使用有限元方案的技术。

Parallel algorithms will be developed, on a Intel iPPSC-D5 Hypercube, for the finite element numerical solution of free-boundary seepage problems using unstructured meshes and for the determination of the load balance and communication structure among the processors. The goal will be to develop load balancing strategies which will assign tasks among the processors to optimize the overall computational efficiency. Several domain splitting techniques will be used and evaluated including a relatively recent one developed by Italian researchers at the University of Pavia. Furthermore, scale up performance experiments will be performed on various systems both at University California Santa Barbara as well as at the University of Pavia. The knowledge and tools developed will provide techniques for the efficient solution of both free- boundary problems as well as the use of finite- element schemes.