Date Added: May 2010
The authors present a highly efficient numerical solver for the Poisson equation on irregular voxelized domains supporting an arbitrary mix of Neumann and Dirichlet boundary conditions. The approach employs a multigrid cycle as a preconditioner for the conjugate gradient method, which enables the use of a lightweight, purely geometric multigrid scheme while drastically improving convergence and robustness on irregular domains. The method is designed for parallel execution on shared-memory platforms and poses modest requirements in terms of bandwidth and memory footprint. The solver will accommodate as many as 7682 x 1152 voxels with a memory footprint less than 16GB, while a full smoke simulation at this resolution fits in 32GB of RAM.