A parallel algorithm for computing eigenvalues of very large real symmetric matrices on message passing architectures

Balle, Susanne M.; Cullum, Jane

doi:10.1016/s0168-9274(98)00119-6

Cited by 3 publications

(1 citation statement)

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“…Supposing the number of processors is n p , and the overview of the parallel procedure, as discussed elsewhere [2,3], is as follows: processor reorders the submatrix. The data distribution is greatly effective for the efficiency of parallel computing and the load on each processor should be adjusted to best balance and minimum communication overhead.…”

Section: Parallel Numerical Solutionmentioning

confidence: 99%

A parallel solver for structural modal analysis based on commercial FEA code

Jin

et al. 2004

Int J Adv Manuf Technol

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This paper describes one promising parallel algorithm and software system for structural modal analysis. The supercomputer "ShenWei I" is taken as the parallel computing environment and the finite element code MSC.NASTRAN is taken as the development platform. The purpose of the research and development is to make the dominating computing work of modal analysis parallelized, and, moreover, make the parallel solver tightly coupled with original analysis code. The integrated software system includes a serial FEA (Finite Element Analysis) and parallel solver and has a friendly interface. It can significantly improve the scale and velocity of structural modal analysis. It contributes to dynamic performance analysis for massive structures.

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Section: Parallel Numerical Solutionmentioning

confidence: 99%

A parallel solver for structural modal analysis based on commercial FEA code

Jin

et al. 2004

Int J Adv Manuf Technol

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The Godunov-inverse iteration: A fast and accurate solution to the symmetric tridiagonal eigenvalue problem

Matsekh

2005

Applied Numerical Mathematics

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We present a new hybrid algorithm based on Godunov's method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov-Inverse Iteration. We use eigenvectors computed according to Godunov's method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of Godunov's eigenvectors with random uniform numbers. We use the right-hand bounds of the Ritz intervals found by the bisection method as Inverse Iteration shifts, while staying within guaranteed error bounds. In most test cases convergence is reached after only one step of the iteration, producing error estimates that are as good as or superior to those produced by standard Inverse Iteration implementations.

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