Accelerated simultaneous iterations for large finite element eigenproblems
Journal of Computational Physics
Solving sparse triangular linear systems on parallel computers
International Journal of High Speed Computing
SIAM Journal on Scientific and Statistical Computing
Solution of large, sparse systems of linear equations in massively parallel applications
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
SIAM Journal on Scientific Computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
ICS '01 Proceedings of the 15th international conference on Supercomputing
Parallel preconditioning of a sparse eigensolver
Parallel Computing - Linear systems and associated problems
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
International Journal of High Performance Computing Applications
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Parallel solution of sparse linear systems arising in advection–diffusion problems
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
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The Jacobi-Davidson (JD) algorithm was recently proposed for evaluating a number of the eigenvalues of a matrix. JD goes beyond pure Krylov-space techniques; it cleverly expands its search space, by solving the so-called correction equation, thus in principle providing a more powerful method. Preconditioning the Jacobi-Davidson correction equation is mandatory when large, sparse matrices are analyzed. We considered several preconditioners: Classical block-Jacobi, and IC(0), together with approximate inverse (AINV or FSAI) preconditioners. The rationale for using approximate inverse preconditioners is their high parallelization potential, combined with their efficiency in accelerating the iterative solution of the correction equation. Analysis was carried on the sequential performance of preconditioned JD for the spectral decomposition of large, sparse matrices, which originate in the numerical integration of partial differential equations arising in physical and engineering problems. It was found that JD is highly sensitive to preconditioning, and it can display an irregular convergence behavior. We parallelized JD by data-splitting techniques, combining them with techniques to reduce the amount of communication data. Our own parallel, preconditioned code was executed on a dedicated parallel machine, and we present the results of our experiments. Our JD code provides an appreciable parallel degree of computation. Its performance was also compared with those of PARPACK and parallel DACG.