Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 12, 17:00 ~ 17:30 - Room 111

Commutator-free Magnus based methods

Karolina Kropielnicka

Polish Academy of Sciences, Poland   -

In this talk, I shall introduce the class of commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations and identify different areas of application.

Commutator-free quasi-Magnus exponential integrators are (formally) given by a composition of several exponentials that comprise certain linear combinations of the values of the defining operator at specified nodes. Avoiding the evaluation of commutators, they provide a favourable alternative to standard Magnus integrators.

Non-autonomous linear evolution equations also arise as a part of more complex problems, for instance in connection with nonlinear evolution equations of the form u'(t) = A(t) u(t) + B(u(t)). A natural approach is thus to apply commutator-free quasi-Magnus exponential integrators combined with operator splitting methods. Relevant applications include Schrödinger equations with space-time-dependent potential describing Bose-Einstein condensation or diffusion-reaction systems modelling pattern formation

Joint work with Philipp Bader (La Trobe University, Australia), Iserles Arieh (University of Cambridge, UK), Pranav Singh (University of Oxford, UK).

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