Merits and pitfalls of splitting methods

Relatore:  Alexander Ostermann - University of Innsbruck, Austria
  martedì 28 aprile 2015 alle ore 17.00 16:45 rinfresco, 17:00 inizio seminario
For the time integration of certain types of partial differential
equations splitting methods have been a popular choice since long. Important
examples comprise the incompressible Navier--Stokes equations and
semi-linear problems such as nonlinear Schr\"odinger equations. Meanwhile
the range of application of splitting methods has been extended to many more
equations and systems. In my talk I will highlight some merits of splitting
methods. First of all, when splitted in the right way, these methods have
superior geometric properties (such as preservation of positivity and long
term behaviour) as compared to standard time integration schemes. In certain
cases, it is also possible to overcome a CFL condition present in standard
discretizations. From a more practical point of view, one has to mention
that splitting methods can simply be implemented by resorting to existing
methods and codes for simpler problems, and they often admit parallelism in
a straight-forward way. On the other hand, the application of splitting
methods also requires some care. The presence of (non-trivial) boundary
conditions can lead to a strong order reduction and consequently to
computational inefficiency, and stability is always an issue with splitting
methods, in particular in non-Hilbert space norms and for non-linear
problems. In the numerical analysis of splitting methods the regularity of
the exact solution (or sometimes of the data) plays a prominent role, as
will be exemplified in my talk.

Ca' Vignal - Piramide, Piano 0, Sala Verde

Marco Caliari

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Data pubblicazione
8 aprile 2015

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