Speaker
Description
Exponential operator splitting methods constitute a favourable class
of time integration methods for various kinds of linear and nonlinear evolution
equations. They rely on the presumption that the defining right-hand side comprises
two (or more) operators and that the numerical approximation of the associated
subproblems is significantly simpler compared to the numerical approximation of the
original problem. Under these premises, their excellent behaviour with respect to
stability, accuracy, and the preservation of conserved quantities has been confirmed
by a remarkable amount of contributions.
In my talk, I will review well-known achievements and recent advances on expo-
nential operator splitting methods. As fundamental test problems, I will study
Gross-Pitaevskii equations modelling Bose-Einstein condensates, their parabolic
counterparts arising in ground and excited state computations, complex Ginzburg-
Landau equations having a similar structure, and high-order semilinear parabolic
equations describing quasicrystalline patterns. I will contrast standard splitting
schemes involving real coefficients with two alternative approaches that are based
on the incorporation of complex coefficients or double commutators, respectively.