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Parallel Computation of Eigenvalue Problems

Author: WangShunXu
Tutor: DaiHua
School: Nanjing University of Aeronautics and Astronautics
Course: General and Fundamental Mechanics
Keywords: Dynamic Analysis Parallel Processing Eigenvalue problem Generalized eigenvalue problems Quadratic eigenvalue problem Gyroscopic eigenvalue problem Subspace iteration method Davidson method Jacobi-Davidson method
CLC: O302
Type: PhD thesis
Year: 2008
Downloads: 468
Quote: 3
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Dynamic Analysis of vibration theory and its applications in fundamental problems, this paper studied the structural dynamic analysis of parallel algorithms eigenvalue problem given PVM and MPI environment PC network parallel computing environment construction method. First studied the rod - plate - shell combination of structural stiffness and mass matrices for parallel computing. Each node machine is responsible for part of the unit to the total stiffness matrix and the contribution of the total mass matrix obtained total stiffness matrix and the total mass matrix for structural dynamic analysis of parallel computing for preparation. Second, given the generalized eigenvalue problem concurrent subspace iterative algorithm. The first method is the generalized eigenvalue problem into a standard eigenvalue problem, using a standard eigenvalue problem subspace iterative algorithm for solving generalized eigenvalue problem; second method is generalized eigenvalue problem directly projected onto the subspace child space iterative algorithm, iterative algorithm gives two seed space parallel implementation, and were calculated using the two parallel algorithms and the J8-II missile wing pylons dynamic characteristics, in the computer network parallel computing environments and distributed parallel computing Environmental PAR2000 made a higher speedup and parallel efficiency. Third, given the generalized eigenvalue problem Parallel Block Davidson method, parallel refinement block Davidson method and the parallel Jacobi-Davidson method. Using Neumann series expansion method for Davidson, Davidson method and refined block Jacobi-Davidson correction equation pretreatment method in parallel computer IBM-P650 and PC network parallel environment for the numerical experiments, and use these methods of parallel computing J8-II missile wing pylons and dynamic characteristics. Fourth, the proposed parallel quadratic eigenvalue problem Jacobi-Davidson method, parallel refined Jacobi-Davidson method, and these methods are applied to the J8-II wing with proportional damping quadratic eigenvalue problem in parallel computing . Theoretical analysis and numerical experiments show that the quadratic eigenvalue problem Jacobi-Davidson parallel algorithms and parallel refined Jacobi-Davidson algorithm has good parallelism, and refined Jacobi-Davidson algorithm than non-precision approach on fewer iterations converge, using less computing time, and has a higher speedup and parallel efficiency. Finally, the proposed system for solving quadratic eigenvalue problem gyro parallel subspace iteration algorithm and parallel refined Jacobi-Davidson method. Using the steady state gyro eigenvalue problem is purely imaginary eigenvalues ??of the characteristics of the problem into a generalized symmetric matrix eigenvalue problem, using the parallel subspace iteration method, in the actual calculation process, will participate in the calculation of the matrix phase number reduced to the scale of the problem itself.

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CLC: > Mathematical sciences and chemical > Mechanics > Mathematical methods in mechanics
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