Advanced Iterative Solvers for High Order Finite Elements

这个项目是研究一类新的非常有前途的高度并行迭代方法，用于求解具有板、壳和接缝结构的三维弹性中由高阶单元（p-版本有限元法）产生的大规模系统。我们所关心的问题的大小现在决定着我们的直接解法，但高阶元素，特别是薄元素，会产生条件非常恶劣的方程组，这就需要新的特定的先决条件。第一阶段的计划是研究预处理薄固体高阶单元的新方法，并研究它们在高达一百万自由度的三维问题上的性能。设计和开发将以理论分析和广泛的实验为指导。阶段1将产生在CRAY-YMP上运行的粗粒度并行原型代码。第二阶段将关注消除非常大问题的瓶颈，扩展该方法的能力，以包括复杂的几何结构，并为CRAY-YMP和IBM SP-1开发生产级软件。该项目将进一步了解并行超级计算机上的多层次和领域分解计算方法。所提出的方法的有效性将对机械工程实践产生重大影响。

9360015 Mandel This project is to study a new class of very promising highly parallel iterative methods for the solution of large scale systems which arise from high order elements (the p- version finite element method) in three-dimensional elasticity for structures with plates, shells and junctures. The size of problems on interest now rules our direct solvers, but high order elements, particularly thin elements, give rise to very ill-conditioned systems of equations, which necessitate new specific preconditioners. The plan in Phase I is to investigate new methods for preconditioning thin solid high order elements and to study their performance on three-dimensional problems with up to over one million degrees of freedom. The design and development will be guided by theoretical analyses as well as extensive experimentation. Phase I will result in a coarse grained parallel prototype code running on CRAY-YMP. Phase II will be concerned with eliminating bottlenecks for very large problems, extending the capabilities of the method to include complicated goemetries and development of production level software for CRAY-YMP and IBM SP-1. The project will further knowledge in the areas of multilevel and domain decomposition computational methods on parallel supercomputers. The availability of the proposed methods will have a significant impact on mechanical engineering practice.