A comparison of solvers for large eigenvalue problems occuring in the design of resonant cavities

Arbenz, Peter; Geus, Roman

doi:10.1002/(sici)1099-1506(199901/02)6:1<3::aid-nla142>3.3.co;2-9

Cited by 6 publications

(11 citation statements)

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“…This algorithm is well-suited since it does not require the factorization of the matrices A or M . In [2,3,4] we found JDSYM to be the method of choice for this problem.…”

Section: The Eigensolvermentioning

confidence: 78%

“…Note that Y = M −1 C is a (very sparse) basis of the null space of A and that H = Y T C is the discretization of the Laplace operator in the nodal element space [3].…”

Section: The Symmetric Jacobi-davidson Algorithmmentioning

confidence: 99%

“…Since our finite element spaces consist of Nédélec and Lagrange finite elements of degree 2 and since we are using hierarchical bases, we employ the hierarchical basis preconditioner that we used successfully in [3]. Numbering the linear before the quadratic degrees of freedom, the matrices A and M in (1.2) get a 2-by-2 block structure,…”

Section: The Preconditionermentioning

confidence: 99%

“…In order to avoid spurious modes we approximate the electric field e by Nédélec (or edge) elements [20]. The Lagrange multiplier (a function) introduced to treat properly the divergence free condition is approximated by Lagrange (or nodal) finite elements [3].…”

Section: Introductionmentioning

confidence: 99%

“…In earlier studies [3] we found the Jacobi-Davidson algorithm [21,12] a very effective solver for this task. We have parallelized this solver in the framework of the Trilinos parallel solver environment [13].…”

Section: Introductionmentioning

confidence: 99%

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On a parallel multilevel preconditioned Maxwell eigensolver

et al. 2006

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We report on a parallel implementation of the Jacobi-Davidson algorithm to compute a few eigenvalues and corresponding eigenvectors of a large real symmetric generalized matrix eigenvalue problemThe 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 the ML smoothed aggregation AMG preconditioner. It is close to optimal regarding iteration count.The parallel code makes extensive use of the Trilinos software framework. In our examples from accelerator physics we observe satisfactory speedups and efficiencies.

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“…This algorithm is well-suited since it does not require the factorization of the matrices A or M . In [2,3,4] we found JDSYM to be the method of choice for this problem.…”

Section: The Eigensolvermentioning

confidence: 78%

“…Note that Y = M −1 C is a (very sparse) basis of the null space of A and that H = Y T C is the discretization of the Laplace operator in the nodal element space [3].…”

Section: The Symmetric Jacobi-davidson Algorithmmentioning

confidence: 99%

Section: The Preconditionermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%