A parallel cut-cell algorithm for the free-boundary Grad-Shafranov problem

TL;DR

This paper introduces a parallel cut-cell algorithm for solving the free-boundary Grad-Shafranov problem, effectively handling complex geometries and optimizing coil currents with verified accuracy and scalability.

Contribution

It presents a novel parallel algorithm that reformulates the free-boundary problem, incorporating boundary detection, coil optimization, and embedded boundary methods.

Findings

Good parallel scaling observed.

Numerical results verify accuracy.

Efficient handling of complex geometries.

Abstract

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.