Software for simplified Lanczos and QMR algorithms
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
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
An overview of the Trilinos project
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)
On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices
Applied Numerical Mathematics
| Hi-index | 0.01 |
We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem$$A \mathbf{x} = \lambda M \mathbf{x}, \qquad C^T \mathbf{x} = \mathbf{0}. $$ The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic Maxwell equation in weak form by a combination of Nédélec (edge) and Lagrange (node) elements. We found the Jacobi–Davidson (JD) method to be a very effective solver provided that a good preconditioner is available for the correction equations that have to be solved in each step of the JD iteration. The preconditioner of our choice is a combination of a hierarchical basis preconditioner and a smoothed aggregation AMG preconditioner. It is close to optimal regarding iteration count and scales with regard to memory consumption. The parallel code makes extensive use of the Trilinos software framework.