2 research outputs found
A rational SHIRA method for the Hamiltonian eigenvalue problem
The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency
Primal and Dual Interface Concentrated Iterative Substructuring Methods
This paper is devoted to the fast solution of interface concentrated finite element
equations. The interface concentrated finite element schemes are constructed
on the basis of a non-overlapping domain decomposition where a conforming
boundary concentrated finite element approximation is used in every subdomain.
Similar to data-sparse boundary element domain decomposition methods
the total number of unknowns per subdomain behaves like ,
where H, h, and d denote the usual scaling parameter of the subdomains, the
average discretization parameter of the subdomain boundaries, and the spatial
dimension, respectively. We propose and analyze primal and dual substructuring
iterative methods which asymptotically exhibit the same or at least almost
the same complexity as the number of unknowns. In particular, the so-called
All-Floating Finite Element Tearing and Interconnecting solvers are
highly parallel and very robust with respect to large coefficient jumps