Walk on Decomposed Subdomains
AI Summary: Researchers have introduced a hybrid approach to solve elliptic partial differential equations (PDEs) on complex geometries. The method combines Monte Carlo estimation with deterministic global solves, decomposing the domain into subdomains and using Monte Carlo to estimate local solution operators. This approach yields stable and reusable solution operators, enabling accurate and efficient solves on coarse discretizations. The method is applied to microstructure simulation, flow-based path planning, and streamline visualization on complex two-dimensional domains.