Lazy Cohomology Generators Enable the Use of Complementarity for Computing Halo Current Resistive Distribution in Fusion Reactors

This paper presents a methodology to efficiently calculate the resistive distribution of halo currents in 3-D conductive structures that surround the plasma in magnetic confinement fusion devices. The domain of the problem is so complicated that two complementary formulations are used to monitor the discretization error. It turns out that thousands of cohomology generators are needed by the electric vector potential electrokinetic formulation, which would require an enormous amount of memory and computing power to retrieve them even using state-of-the-art algorithms. To solve this challenging problem, we present a novel algorithm to generate the absolute second cohomology group generators exploiting the idea of lazy cohomology generators stored as sparse vectors. The proposed algorithm allows a saving of between four and five orders of magnitude computational time.