University of Groningen

Abstract: The Kontsevich graph weights are period integrals whose
values make Kontsevich's star-product associative for any Poisson
structure. We illustrate, by using software, to what extent these
weights are determined by their properties: the associativity
constraint for the star-product (for all Poisson structures), the
multiplicativity (decomposition into prime graphs), the cyclic
relations, and some relations due to skew-symmetry. Up to the order 4
in ℏ we express all the weights in terms of 10 parameters (6
parameters modulo gauge-equivalence), and we verify pictorially that
the star-product expansion is associative modulo ō(ℏ⁴) for every value
of the 10 parameters. This is joint work with Arthemy Kiselev.
 

The climate is largely determined by the ocean flow, which in itself is driven by wind and by gradients in temperature and salinity. Nowadays numerical models exist that are able to describe the occurring phenomena not only qualitatively but also quantitatively. At the Institute for Marine and Atmospheric research Utrecht (IMAU) a so-called thermohaline circulation model is developed in which methods of dynamical systems theory are used to study the stability of ocean flows. Here bifurcation diagrams are constructed by varying the strength of the forcing, for instance the amount of fresh water coming in from the north due to melting. For every value of the strength we have to solve a nonlinear system, which is handled by a Newton-type method. This produces many linear systems to be solved. 

In the talk the following will be addressed: the form of the system of equations, a special purpose method which uses Trilinos and MRILU. The latter is a multilevel ILU preconditioner developed at Groningen University. Results of the approach obtained on the Dutch national supercomputer will be shown.