Berlin 2014 – scientific programme

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P: Fachverband Plasmaphysik

P 17: Poster Session - Helmholtz Graduate School for Plasma Physics

P 17.5: Poster

Wednesday, March 19, 2014, 16:30–18:30, SPA Foyer

Preconditioning for Eigenvalue Computations in Gene — •Juergen Braeckle and Thomas Huckle — TU Muenchen, Fakultaet fuer Informatik, Boltzmannstraße 3, D-85748 Garching

In the Plasma Turbulence Code Gene, turbulences are examined by finding the rightmost eigenvalues of the linear gyrokinetic operator. Finding these inner eigenvalues with the Jacobi- Davidson method requires an iterated solving of shifted linear systems (I−uu^*)(A− λ_k I)(I − uu^*)x_k = b_k (restriced to the subspace orthogonal to u) with a non-hermitian matrix A given as an implicit operator and changing eigenvalue approximations λ_k of A. With λ_k being a good approximation of an eigenvalue, (A − λ_k I) gets almost singular, and therefore this system has to be modified with a preconditioner (I − uu^* )M(I − uu^*). Besides a good preconditioning quality (M ≈ (A − λ_k I)⁻¹ ), we are interested in high scalability, a preconditioner applicable on implicit systems and with cheap updating capabilities for a sequence of different shifted matrices. With respect to these properties, we try to solve this problem using the SPAI method and polynomial preconditioners.