A Differential Monte Carlo Solver For the Poisson Equation

The Poisson equation is an important partial differential equation (PDE) with numerous applications in physics, engineering, and computer graphics. Conventional solutions to the Poisson equation require discretizing the domain or its boundary, which can be very expensive for domains with detailed geometries. To overcome this challenge, a family of grid-free Monte Carlo solutions has recently been developed. By utilizing walk-on-sphere (WoS) processes, these techniques are capable of efficiently solving the Poisson equation over complex domains.