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SUMMARY:Numerical solution of the radiative transfer equation with a poste
 riori error bounds - Olga Mula (CEREMADE\, Université Paris-Dauphine)
DTSTART:20180419T140000Z
DTEND:20180419T150000Z
UID:TALK96382@talks.cam.ac.uk
CONTACT:Clarice Poon
DESCRIPTION:We propose a new approach to the numerical solution of radiati
 ve transfer equations with certified\na posteriori error bounds. A key ing
 redient is the formulation of an iteration in a suitable (infinite dimensi
 onal) function\nspace that is guaranteed to converge with a fixed error re
 duction per step. The numerical scheme is based on approximately\nrealizin
 g this outer iteration within dynamically updated accuracy tolerances that
  still ensure convergence to the exact solution.\nOn the one hand\, since 
 in the course of this iteration the global scattering operator is only app
 lied\, this avoids solving linear systems with densely populated system ma
 trices while\nonly linear transport equations need to be solved. This\, in
  turn\, rests on a Discontinous Petrov--Galerkin scheme which\ncomes with 
 rigorous a posteriori error bounds. These bounds are crucial for guarantee
 ing the convergence of the outer\niteration. Moreover\, the application of
  the global (scattering) operator is accelerated through low-rank approxim
 ation and matrix\ncompression techniques. The theoretical findings are ill
 ustrated and complemented by numerical experiments with\na non-trivial sca
 ttering kernel.
LOCATION:MR14\, Centre for Mathematical Sciences
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