Development and evaluation of a multiprocessing structural vibration algorithm
A new parallel algorithm utilizing the finite element method for free vibration analysis of large linear elastic models is developed, tested and evaluated herein. The concurrent solution of the generalized eigenproblem, KÖ = MÖÙ, is based on the classical frontal technique for the solution of linear simultaneous equations and the modified subspace method for the solution of the least dominant eigenpairs. Large structures are subdivided into independent domains containing an equal number of elements, i.e. a balanced load within each domain to avoid overhead; a common boundary (global front) exists between all domains. Using the multitasking library on the Cray X-MP/24 computer, each domain is assigned a separate processor to create the stiffness and mass matrices of the elements and perform the simul- taneous assembly/forward elimination and back-substitution completely independent of all other domains. Parallelism is also exploited in the modified subspace method by projecting the stiffness and mass matrices onto the required subspace in each iteration within each domain. In other words, a wave front sweeps across the domain and converges to the global front, upon reaching the boundary the domains communicate their interface matrices to all other domains and diverge from the global front. The parallel algorithm successfully uses a completely connected network to transmit the matrices needed by the other domains to continue execution. Following the back-substitution the specified eigenpairs are solved and tested against the required tolerance level, if tolerance is met the program ceases opera- tion. Computational speedup and efficiency is used to determine the effectiveness of parallel processing within domains on a number of rectangular plates. The investigation entails a number of factors affecting the assessment of the algorithm, e.g. number of domains, size of the global front, direction the wave front converges and the number of eigenpairs. In addition, a number of typical finite element problems in free vibration are analyzed to show the accuracy and speedup of the parallel numerical algorithm.
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:large linear elastic models multiprocessing structural vibration classical frontal technique
Date of Publication:01/01/1988