State of the Art in Grid-Free Monte Carlo Methods for Partial Differential Equations

Figure 1: Grid-free Monte Carlo methods can significantly speedup the engineering design cycle by eliminating the major bottleneck of discretization in conventional solvers for partial differential equations (left).Lifting the dependence on discretization and global solves improves robustness, and like Monte Carlo ray tracing allows for computational effort to be focused entirely on local regions of interest (right).