A PARALLEL CUT-CELL ALGORITHM FOR THE FREE-BOUNDARY GRAD-SHAFRANOV PROBLEM\ast

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. The algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

Automated summary

This study introduces a parallel cut-cell algorithm to solve the free-boundary problem of the Grad--Shafranov equation, which reformulates the problem in an irregular bounded domain and utilizes various methods to optimize the solution process, resulting in good parallel scaling.