GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific Computing
Robust preconditioning of large, sparse, symmetric eigenvalue problems
Journal of Computational and Applied Mathematics
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
International Journal of Computational Science and Engineering
Computing several eigenpairs of Hermitian problems by conjugate gradient iterations
Journal of Computational Physics
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
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The paper presents two ways of improving the Jacobi-Davidson method for calculating the eigenvalues and eigenvectors described by eight-band k.p model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband k.p model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band k.p Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the k.p model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band k.p Hamiltonian and the eigensolver are provided.