The Distributed Parallel Lanczos Algorithm For Eigenvalue Problems Of Large Complex Structures

Eigenvalue problems of super large systems has been an improtant work in engineering and scientific research. Parallel computing makes it possible to compute large numerical problems. With the generalization of PC computers and the development of the network, distributed parallel computing provides a good platform for scientific computing.Lanczos method is one of the best methods for large real symmetric matrices's eigenvalue problems. Under the distributed parallel environments, for vibration analysis of large structures with the element by element method, it is meaningfull to study the distributed parallel Lanczos algorithm.The thesis studies the Lanczos iteration for generalized eigenvalue problems, gives the full reorthogonalization method, which modifies the orthogonalization of Lanczos vectors, eliminates spurious eigenvalues and makes Lanczos algorithm efficient. Restart Lanczos methods are generalized, which improves the computing efficiency of generalized eigenvalues. The block Lanczos method for structures's eigenvalues is also researched and numerical tests are given.The thesis also studies parallel computing environments. The interface between Matlab and C is researched deeply. Based on the message passing interface(MPI), take two PC computers for example, the thesis studies the construction of the distributed parallel computing environments.Based on the substructure parallel algorithm, take full reorthogonalization method into consideration, under the parallel substructure algorithm, the thesis gives the distributed parallel Lanczos algorithm and a numerical test for structures's eigenvalues.