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SUMMARY:Recent advancements in volume-preserving numerical methods for the
  numerical solution of divergence-free ODEs - Antonella Zanna (University 
 of Bergen)
DTSTART:20120426T140000Z
DTEND:20120426T150000Z
UID:TALK36661@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:In this talk we consider the task of designing volume preservi
 ng numerical methods for divergence-free ordinary differential equations.\
 nThis is a difficult task also due to the existence of no-go theorems in s
 paces of dimension three or higher: there exist no B-series method that is
  volume preserving for arbitrary divergence-free vector fields. Although a
  large class of numerical methods (like Runge-Kutta  or Taylor-series meth
 ods) are B-series methods\, this no-go theorem does not exclude that volum
 e can be preserved by other classes of methods\, for instance methods base
 d on splitting of the vector field.\nThe talk will be divided in two parts
 . In the first part\, I will introduce a new class of splitting methods ba
 sed on a monomial basis\, a Fourier basis and tensor product of these.\nIn
  the second part of the talk\, I will discuss some recent advancements bas
 ed on the theory of differential volume forms.
LOCATION:MR14\, CMS
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