Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 10, 15:30 ~ 16:00

Magnus-type integrators combined with operator splitting methods and their areas of applications

Mechthild Thalhammer

Leopold--Franzens-Universität Innsbruck, Austria   -

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.

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