Taking Advantage of Symmetry in the Finite Strip Formulation for Dynamic Plate-Bending Problems
by
Hsin-Chu Chen
Department of Computer and Infomation Science, Clark Atlanta University, Atlanta, GA
Coauthors: Shinn-Yih Tzeng (Department of Computer and Infomation Science, Clark Atlanta University, Atlanta, GA)

In this presentation, we propose an approach to further decomposing the decoupled dynamic subsystems induced by the finite strip method (FSM) for the dynamic analysis of plate-bending problems with reflexive symmetry. FSM is a semi-analytical finite element process that approximates the solution using harmonic functions in one direction and piecewise interpolation polynomials in the other. It discretizes the domain of the problem into finite strips and decomposes a single problem into m smaller and independent subproblems when m harmonic functions are employed, yielding natural parallelism at a very high level. For problems with reflexive symmetry across strips, however, FSM alone does not take full advantage of all parallelism offered by the problem. In this presentation, we show that further decomposition is possible for such type of problems by exploiting a special reflexivity property possessed by both the stiffness matrix and the mass matrix derived from FSM. We then use the exploited special property to increase large-grain parallelism by decomposing each of the m subsystems into 2 independent subsystems via an orthogonal transformation, resulting in a total of 2m smaller and independent subsystems to solve in parallel. The computational cost for the decomposition is extremely cheap, making the approach an attractive one. Furthermore, since the decomposition is performed via an orthogonal transformation, this approach is applicable to both linear systems and eigenvalue problems.

Date received: March 30, 2003