2016/09/12 by Charles M. Elliott, Elliott, Charles M., Hans Fritz +1
Computer Science · Engineering · Medicine · #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Winter Sports Injuries and Performance
paper · pdf · doi:10.48550/arxiv.1609.03373
openalex publication_date 2016/09/12 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper, we present a general approach to obtain numerical schemes with\ngood mesh properties for problems with moving boundaries, that is for evolving\nsubmanifolds with boundaries. This includes moving domains and surfaces with\nboundaries. Our approach is based on a variant of the so-called the DeTurck\ntrick. By reparametrizing the evolution of the submanifold via solutions to the\nharmonic map heat flow of manifolds with boundary, we obtain a new velocity\nfield for the motion of the submanifold. Moving the vertices of the\ncomputational mesh according to this velocity field automatically leads to\ncomputational meshes of high quality both for the submanifold and its boundary.\nUsing the ALE-method in [16], this idea can be easily built into algorithms for\nthe computation of physical problems with moving boundaries.\n