Currently the method only works for elliptic, linear PDEs like the heat equation. Keenan and his students are trying to extend the method to more general PDEs (they recently had a paper showing how to do elliptic PDEs with non-constant coefficients) but currently the Navier-Stokes equation from fluid dynamics is out of scope.
That's my view of the method in a nutshell: using walk-on-spheres as a practical method to solve PDEs arising in simulations is a departure from what most people have tried in recent years. Whether it's a total game-changer or a curious novelty will depend on whether it generalizes beyond diffusion-like PDEs.
That's my view of the method in a nutshell: using walk-on-spheres as a practical method to solve PDEs arising in simulations is a departure from what most people have tried in recent years. Whether it's a total game-changer or a curious novelty will depend on whether it generalizes beyond diffusion-like PDEs.