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SUMMARY:Mesh generation for Tokamaks and Automated Isogeometric Analysis
DTSTART:20200303T161500
DTEND:20200303T171500
DTSTAMP:20260531T063742Z
UID:c72f39419f0f146f9f833a3204d17806e77036c6a336e5b40726773c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ahmed Ratnani (Mohammed VI Polytechnic University\, Marocco 
 — previously responsible for Software development at Max Planck IPP) \
 nComputational Mathematics Seminar\nAbstract : Due to the very large aniso
 tropic character of strongly magnetized plasma\, the use of flux aligned g
 rid is generally believed to be highly useful (or even mandatory) to obtai
 n accurate and reliable simulations for fusion applications. For real geo
 metries\, the magnetic topology can only be computed by the use of special
 ized equilibrium solvers solving the non-linear Grad-Shafranov equation. 
  The output of these solvers then have to be used as input to construct f
 lux aligned meshes that respect the magnetic topology. This process usuall
 y requires some manual input and expertise from the final users to identif
 y the relevant features of the magnetic topology (X points\, magnetic axis
 ).\nIn the first part of this talk\, we will describe an original method f
 or the automated construction of flux aligned grids. This method assumes t
 hat the magnetic flux is a Morse function and consequently that the result
 s of Morse theory can be applied. Then we will describe a new method for c
 onstructing Adaptive and Anistotropic mappings by solving an Optimal Trans
 port problem. This method leads to equidistributed meshes and ensures the 
 one-to-one constraint.\nIn the second part of the talk\, we will describe 
 a new framework\, à la FENICS/FreeFem++\, for IsoGeometric Analysis.  Co
 mpared to existing solutions\, our formal language captures the semantic o
 f mathematical expressions and therefor can be presented as a static compi
 ler. The framework is based on ideas from Type Theory and Category Theory\
 , which allow us to do some verifications before discretization and keep t
 rack of different algebraic structures from the formal/continuous level to
  the discrete one.\nMoreover\, it also exposes DeRham complexes\, which tu
 rns out to add additional levels of type checking.  Different examples wi
 ll be shown both on the formal language\, associated discretizations and p
 arallel computing.\n 
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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