A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
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Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Zoltan Data Management Service for Parallel Dynamic Applications
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An Improved Algebraic Multigrid Method for Solving Maxwell's Equations
SIAM Journal on Scientific Computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
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Future Generation Computer Systems
Towards a parallel multilevel preconditioned maxwell eigensolver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Journal of Computational Physics
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A parallel implementation of the Jacobi-Davidson eigensolver for unsymmetric matrices
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
ACM Transactions on Mathematical Software (TOMS)
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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 problemAx=@lMx,C^Tx=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 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.