Structure-aware Krylov approximations to generalized Cayley transforms

Prof. Andreas Frommer - University of Wuppertal
Structure-aware Krylov approximations to generalized Cayley transforms

Abstract
Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods.