Application of partition matrix methods to solve large eigenproblems in structural dynamics
Louis H. Turcotte · PhDT · 1992
This dissertation addresses eigenvalue and eigenvector problems for large, sparse matrices resulting from the vibration analysis of complex structures. Problems of this type are computationally intensive and have traditionally been solved using supercomputers. Partitioned matrices are employed, herein, to produce a set of out-of-core algorithms which can be used for eigenproblems with several thousand degrees-of-freedom. The efficiency of a Rayleigh-Ritz iterative procedure, based on partitioned matrices, is compared with competing out-of-core eigensolution strategies. These results demonstrate that partition matrix algorithms are computationally competitive and may be implemented successfully across a wide range of computers to solve large eigenproblems. The partition matrix routines are implemented as extensions of the widely used commercial software system MATLAB. These extensions employ compiled fortran routines which are linked into MATLAB and provide a set of user friendly analysis tools that are easily employed to solve eigenproblems which were previously too large for this environment. Both workstations and supercomputers were used to evaluate the efficiency of the partition matrix algorithms. Additionally, a parallelized version of the software was implemented across a cluster of workstations. The parallelized code demonstrates the practicality of using a cluster of workstations to efficiently solve large eigenproblems typically requiring the use of a supercomputer.