Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid
Abstract
The discrete exterior calculus (DEC) defines a family of discretized differential operators which preserve certain desirable properties from the exterior calculus. We formulate and solve the porous convection equations in the DEC via the Decapodes.jl embedded domain-specific language (eDSL) for multiphysics problems discretized via CombinatorialSpaces.jl. CombinatorialSpaces.jl is an open-source Julia library which implements the DEC over simplicial complexes, and now offers a geometric multigrid solver over maps between subdivided simplicial complexes. We demonstrate numerical results of multigrid solvers for the Poisson problem and porous convection problem, both as a standalone solver and as a preconditioner for open-source Julia iterative methods libraries.
Keywords
Cite
@article{arxiv.2508.12501,
title = {Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid},
author = {Luke Morris and George Rauta and Kevin Carlson and James Fairbanks},
journal= {arXiv preprint arXiv:2508.12501},
year = {2025}
}