Accelerating the solution of a physics model inside a tokamak using the (Inverse) Column Updating Method

Many physics problems can only be studied by coupling various numerical codes, each modeling a subaspect of the physics problem that is addressed. In most cases, the “brute force” technique of running the codes one after the other in a loop until convergence is reached requires excessive CPU time. The present paper illustrates that re-writing the coupling as a root-finding problem, to which a quasi-Newton method–here the (Inverse) Column Updating Method–can be applied, is useful to push down the computation time, at the expense of a very modest amount of supplementary programming. A simplified version of the set of codes commonly used to describe plasma heating by radio frequency waves in a tokamak plasma is adopted for illustrating the potential of the speed-up method. It consists of a wave equation as well as a Fokker–Planck velocity space diffusion and a radial energy diffusion model. It is shown that with this approach a substantial reduction in CPU time needed for convergence can be obtained.