Dune-MMesh: The Dune Grid Module for Moving Interfaces

Dune-MMesh is an implementation of the well-developed Dune (Bastian et al., 2021) grid interface tailored for numerical applications with moving physical interfaces and is well-suited for the numerical discretization of partial differential equations. The package wraps two and three dimensional CGAL triangulations (The CGAL Project, 2020) in high-level objects like intersections of grid entities, index and id sets and geometry transformations and exports a predefined set of facets as a separate interface grid. In two dimensions, the arbitrary movement of vertices is enhanced with a re-meshing algorithm that implements non-hierarchical adaptation procedures. Besides the adaptation of the triangulation, Dune-MMesh provides the necessary data structures to adapt discrete functions defined on the bulk grid or the interface. This adaptation approach complements existing grid implementations within the Dune framework that strictly rely on hierarchical adaptation. Various examples in Python have been implemented based on the discretization module dune-fem (Dedner et al., 2020) that demonstrate the versatile applicability of Dune-MMesh. Due to the ability to handle custom PDEs in their weak from written in Unified Form Language (UFL) and the mesh adaptation capabilities, we believe Dune-MMesh provides a useful tool for solving mixed-dimensional PDEs on moving interfaces that arise from various fields of modelling. This upload contains the source code of release 1.3.2 `dune-mmesh-source.zip` and the corresponding pip package `dune-mmesh-1.3.2.tar.gz`