Advanced Iterative Solvers for High Order Finite Elements

9360015 Mandel这个项目是研究一类新的非常有前途的高度并行的迭代方法，用于求解由板、壳和节点结构的三维弹性力学中的高阶单元(p-型有限元方法)产生的大规模系统。现在，感兴趣的问题的大小决定了我们的直接求解器，但高阶元素，特别是薄元素，导致了非常病态的方程组，这就需要新的特定预条件。第一阶段的计划是研究对薄固体高阶单元进行预处理的新方法，并研究其在多达一百万个自由度的三维问题中的性能。设计和开发将以理论分析和广泛的实验为指导。第一阶段将产生在Cray-YMP上运行的粗粒度并行原型代码。第二阶段将致力于消除非常大问题的瓶颈，将该方法的能力扩展到包括复杂的目标，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级和区域分解计算方法领域的知识。所提出的方法的可用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.