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Parallel Numerical Integration Methods For Nonlinear Dynamics (Supercomputers)


Ou, Rongfu (1990) Doctoral Thesis, Georgia Institute of Technology, Atlanta.


Recent advances in computer technology indicate that significant increases in effective calculation speed will be achieved through parallel supercomputers. However, this potential increase in speed cannot be effectively realized without the development and implementation of appropriate parallel numerical algorithms. The research in this thesis investigates parallel numerical integration methods for nonlinear dynamics especially relevant to finite element type methods.

The goal of this research is to advance the state of the art in parallel numerical integration methods for finite element nonlinear dynamics and to establish the concepts for the design strategy of a new generation of parallel nonlinear finite element code. To attain this goal, this study investigated the strategic approach to numerically integrate nonlinear dynamic finite element equations on parallel computers. Several numerical integration methods were studied and implemented in parallel including the explicit and implicit methods for finite element nonlinear dynamics and some related methods of solving simultaneous algebraic equations. The features and performance of the methods were examined and compared from the standpoint of parallel computation. The study also includes a discussion of related issues associated with parallel computer architectures, e.g. moderately and massively parallel computer architectures. Based on the research results, an approach to massively parallel finite element nonlinear dynamic analysis was proposed. This approach is based on the concept of using the explicit central difference method with a diagonal mass matrix and a diagonal (or neglected) damping matrix. By this approach the parallel computations decouple for both the element and force vector generation steps and the parallelism is high. This proposed approach has been tested by implementation of the approach within a production level finite element system--DYNA3D on the Butterfly GP1000. The parallel performance results are encouraging and indicate that the basic approach has high potential.

Other results and finding from this research include an extension of the parallel cyclic reduction method for solving equations together with its comparison with parallel decomposition methods, the development of a parallel modified Jacobi/Gauss-Seidel method, and the evaluation of several parallel numerical integration methods.

Manuscript: order via UMI