GPU-accelerated grid-free Monte Carlo methods for evaluating heat transport in stellarators*

We present the first results from a newly developed, scalable, high-performance numerical tool for accurate calculation of heat transport in complex geometry, with realistic features including rough surfaces, holes, and corners. Written in the Julia programming language, we use a grid-free Monte Carlo method, called the ‘walk on spheres’ algorithm to evaluate heat transport in complex two-dimensional domains. Our results demonstrate the viability of this approach for calculating heat transport in highly shaped stellarators, where complex magnetic field structures, such as chaotic magnetic fields and islands are present. We also discuss progress on implementing GPU-accelerated parallelization and extension to 3D geometry.

Walk on spheres is a Monte Carlo algorithm with robust convergence properties, that is demonstrated to be an effective method for solving elliptic partial different equations with spatially inhomogeneous coefficients in highly complex 3D geometry, as encountered in graphics rendering, for example.

R. Sawhney et al. “Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients.” ACM Trans. Graph. 41, 4, Article 53 (2022); https://doi.org/10.1145/3528223.3530134