Efficient allocation of computational resources for finite element applications

This thesis deals with two topics: (1) Adaptive finite element analysis; (2) Finite element analysis on the CONNECTION Machine, a massively parallel SIMD computer. Both topics focus on the efficient allocation of computational resources but in different environments. Whereas the thrust of the adaptive algorithm is towards achieving the best solution with a specified amount of computer resources in a SISD environment through h-method reallocation, the parallel algorithm seeks to attain peak performance in a SIMD environment through a computation versus communication tradeoff. The adaptive procedure is developed for the transient analysis of nonlinear shells. The scheme is an h-method which employs fission and fusion of elements to adaptively refine and coarsen the mesh. Incremental work and deviation of the bilinear finite element approximation to the shell from a Kirchhoff-Love surface are used as error criteria for adaptivity. The example problems show that the adaptive schemes are capable of achieving substantial improvements in accuracy for a given computational effort. They include both material and geometric nonlinearities and local and global buckling. The adaptation of a finite element program with explicit time integration to a massively parallel SIMD computer, the CONNECTION Machine, required the standard gather and assembly to be replaced by an exchange of nodal forces at each time step. In addition, the data was reconfigured so that all nodal variables associated with an element are stored in a processor along with other element data. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY X-MP/14 by a factor of about 10. The implementation of an explicit transient program for the three-dimensional nonlinear finite element analysis of shells on the CONNECTION Machine is described. Particular emphasis is placed on interprocessor communication using router and NEWS schemes. A hybrid communication scheme, where NEWS is used within structured subdomains and the router is used to exchange nodal forces between subdomains is examined. It is shown that the "homogeneity index" of most large meshes is sufficient to make hybrid schemes effective and this is verified by computer runs.