Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Modeling quantum structures with the boundary element method
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Parallel Jacobi-Davidson for Solving Generalized Eigenvalue Problems
VECPAR '98 Selected Papers and Invited Talks from the Third International Conference on Vector and Parallel Processing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational Physics
Numerical methods for semiconductor heterostructures with band nonparabolicity
Journal of Computational Physics
Numerical simulation of three dimensional pyramid quantum dot
Journal of Computational Physics
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
On a parallel multilevel preconditioned Maxwell eigensolver
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Iterative projection methods for computing relevant energy states of a quantum dot
Journal of Computational Physics
The use of bulk states to accelerate the band edge state calculation of a semiconductor quantum dot
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Jacobi-Davidson method for nonlinear and nonsymmetric eigenproblems
Computers and Structures
SIAM Journal on Scientific Computing
International Journal of Computational Science and Engineering
Reducing sparse nonlinear eigenproblems by automated multi-level substructuring
Advances in Engineering Software
State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems
Journal of Computational Physics
Optimal Scaling of Generalized and Polynomial Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Energy states of vertically aligned quantum dot array with nonparabolic effective mass
Computers & Mathematics with Applications
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Electronic states in three dimensional quantum dot/wetting layer structures
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
ACM Transactions on Mathematical Software (TOMS)
Hi-index | 31.45 |
We develop a parallel Jacobi-Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi-Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc's efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schrodinger's equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi-Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0GHz processors.