Transformations of computational meshes

Computational meshes, as a way to partition space, form the basis of much of PDE simulation technology, for instance for the finite element and finite volume discretization methods. In complex simulations, we are often driven to modify an input mesh, for example, to refine, coarsen, extrude, change cell types, or filter it. Mesh manipulation code can be voluminous, error-prone, spread over many special cases, and hard to understand and maintain by subsequent developers. We present a simple, table-driven paradigm for mesh transformation which can execute a large variety of transformations in a performant, parallel manner, along with experiments in the open source library PETSc which can be run by the reader.