Experiments on a Parallel Nonlinear Jacobi–Davidson Algorithm | Zendy

Yoichi Matsuo | Zendy; Hua Guo | Zendy; Peter Arbenz | Zendy

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Experiments on a Parallel Nonlinear Jacobi–Davidson Algorithm

Author(s) -

Yoichi Matsuo,

Hua Guo,

Peter Arbenz

Publication year - 2014

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2014.05.051

Subject(s) - preconditioner , eigenvalues and eigenvectors , computer science , computation , nonlinear system , mathematics , convergence (economics) , quadratic equation , jacobi method , algorithm , iterative method , physics , geometry , quantum mechanics , economics , economic growth

The Jacobi–Davidson (JD) algorithm is very well suited for the computation of a few eigen-pairs of large sparse complex symmetric nonlinear eigenvalue problems. The performance of JD crucially depends on the treatment of the so-called correction equation, in particular the preconditioner, and the initial vector. Depending on the choice of the spectral shift and the accuracy of the solution, the convergence of JD can vary from linear to cubic. We investigate parallel preconditioners for the Krylov space method used to solve the correction equation.We apply our nonlinear Jacobi–Davidson (NLJD) method to quadratic eigenvalue problems that originate from the time-harmonic Maxwell equation for the modeling and simulation of resonating electromagnetic structures

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