Presentation
Harmonic Caching for Walk on Spheres
DescriptionWe present a variance reduction technique for Walk on Spheres (WoS) that solves elliptic partial differential equations (PDEs) by combining overlapping harmonic expansions of the solution, each estimated using unbiased Monte Carlo walks. Our method supports both the Laplace and screened-Poisson equations with Dirichlet, Neumann and Robin boundary conditions in 2D and 3D. By adaptively covering the domain with local expansion regions and extrapolating from each using a truncated Fourier basis, we achieve orders of magnitude lower error than traditional pointwise WoS, in equal time. While low-order truncations could achieve low bias, unbiased reconstruction is possible with stochastic truncation. Compared to other recently developed caching algorithms for WoS such as Boundary and Mean Value Caching, our approach generally generates results with lower error and fewer correlation artifacts.
Event Type
Technical Papers
TimeWednesday, 17 December 20251:31pm - 1:42pm HKT
LocationMeeting Room S426+S427, Level 4