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.
