$ show rohan-sawhney/zombie
This repository provides a header-only C++ library with Python bindings for solving partial differential equations (PDEs) using Monte Carlo methods, specifically Walk on Spheres (WoS) and Walk on Stars (WoS★) algorithms. It supports Laplace, Poisson, and screened Poisson equations with Dirichlet, Neumann, and Robin boundary conditions in 2D and 3D. The library includes variance reduction techniques (Boundary Value Caching, Reverse Walk on Stars) and handles exterior problems via the Kelvin transform. It is designed for grid-free PDE solving, relying on geometric queries (via FCPW BVH or SDF grids) rather than volume meshing. The codebase is research-oriented, with clear reference implementations and citations to foundational papers, but includes many TODO comments and incomplete optimizations. The architecture is modular with template-based dimension and value type abstraction, making it adaptable but also complex. Demo applications in C++ and Python illustrate usage on model problems with JSON configuration and image output.
The LLM identified 4 files worth highlighting for reuse:
Implements the Kelvin transform to convert exterior PDE problems to interior ones, enabling the use of standard solvers on unbounded domains. Reusable for any exterior Laplace/Poisson problem in 2D/3D.
Templated dense grid with bilinear/trilinear interpolation, supporting arbitrary channels and dimensions. Useful for storing and querying scalar or vector fields on a regular grid. Can be extracted for any grid-based computation.
Provides SphereSampler, CDFTable, AliasTable, and stratified sampling routines for Monte Carlo integration. Generic and reusable for any sampling-based algorithm.
Defines a pure virtual interface for geometric queries (distance, projection, intersection) that can be implemented by different backends (FCPW BVH, SDF grid). Enables decoupling of solver from geometry representation.