Accelerating the convergence of a tokamak modeling code with Aitken's method

Abstract Up till now, the approach to solve the coupled equations arising in modeling wave heating in tokamaks modeling has been to sequentially solve one equation after the other until convergence is reached, a method known as Iterative Substructuring. In this paper we use an elementary model of the physics inside a tokamak, consisting of a simplified wave equation, a simplified Fokker–Planck equation and a diffusion equation. Our aim is to accelerate the solution of the coupled equations using Aitken’s δ 2 method. Results show that a substantial reduction in CPU time can be obtained with this approach. It is hoped that results obtained with the simplified model serve as a proof-of-principle and carry over to more complicated systems of coupled equations used to model tokamaks.

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