Energy equations and their fast solution

24 June 2013
10:00
Prof. Tongxiang Gu
Abstract

*****     PLEASE NOTE THIS SEMINAR WILL TAKE PLACE ON MONDAY 24TH JUNE 2013     *****

Energy equations describing magnetic and inertial confinement functions (ICF) are strongly coupled, time dependent non-linear PDEs. The huge disparity of the coefficients in the coupled non-linear equations brings tremendous numerical difficulties to get high resolution solutions. It results in highly ill-conditioned linear systems in each non-linear iteration. Solving the resulted non-linear systems is time-consuming which takes up to 90% in the total simulation time. Many customized numerical techniques have to be employed to get a robust and accurate solution.This talk will present an inexact Newton-Krylov-Schwarz framework to solve the problem, demonstrating how to integrate preconditioning, partial Jacobian matrix forming techniques, parallel computing techniques with the Newton-Krylov solvers to solve the challenging problem. The numerical results will be shown and other numerical problems will be mentioned.

*****     If anyone is planning to take the 11.36 train after the seminar to the NA conference in Glasgow a taxi from the Gibson building is being arranged. Please contact Jude, shengxin.zhu@maths.ox.ac.uk, to book a place in the taxi.     *****

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