Advanced Iterative Solvers for High Order Finite Elements

高阶有限元的高级迭代求解器

• 批准号: 9360015
• 负责人: Jan Mandel
• 金额: $ 6.49万
• 依托单位: Solvers International Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-05-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9360015&HistoricalAwards=false
• 关键词: Advanced; Iterative; Solvers; Order; Finite

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.

9360015曼德尔该项目是为了研究带有板，壳体和关联的结构的三维弹性，研究了一类新的非常有希望的高度平行迭代方法，该方法是由三维弹性中的高阶元素（P版本有限元法）中产生的。 现在，利息问题的大小统治了我们的直接解决者，但是高阶元素（尤其是薄元素）会产生非常不良的方程式系统，这需要新的特定预处理。 第一阶段的计划是调查预处理薄固体高阶元素的新方法，并研究其在三维问题上具有多达一百万个自由度的三维问题的表现。 设计和开发将由理论分析以及广泛的实验来指导。 第一阶段将导致在Cray-ymp上运行的粗粒粒状并行原型代码。 第二阶段将关注消除非常大问题的瓶颈，从而扩展了该方法的功能，包括复杂的goemorties和为Cray-ymp和IBM SP-1开发生产水平软件。 该项目将进一步了解并行超级计算机上的多级和域分解计算方法。 所提出的方法的可用性将对机械工程实践产生重大影响。