论文信息 - Towards a Parallel Multilevel Preconditioned Maxwell Eigensolver

Towards a Parallel Multilevel Preconditioned Maxwell Eigensolver

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 Ax = λMx, C T x = 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 Nedelec (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.

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