An Interface Preserving Moving Mesh in Multiple Space Dimensions

TL;DR

This paper introduces an interface-preserving moving mesh algorithm for multiple dimensions that maintains a deforming interface within a conforming Delaunay mesh, with proven preservation and data projection methods.

Contribution

It presents a novel high-dimensional moving mesh algorithm that preserves interfaces during deformation and remeshing, with a rigorous proof of interface preservation.

Findings

Algorithm effectively preserves interfaces after deformation.

Mesh remains conforming and Delaunay during remeshing.

Open source implementation available for use.

Abstract

An interface preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving $(d-1)$-dimensional manifold directly within the $d$-dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-surfaces. The underlying mesh is a conforming simplicial partition that fulfills the Delaunay property. The local remeshing algorithms allow for strong interface deformations. We give a proof that the given algorithms preserve the interface after interface deformation and remeshing steps. Originating from various numerical methods, data is attached cell-wise to the mesh. After each remeshing operation the interface preserving moving mesh retains valid data by projecting the data to the new mesh cells.\newline An open source implementation of the moving mesh algorithm is available at [1].