2021/12/22 by Maria Alkämper, Alkämper, Maria, Jim Magiera +3
Computer Science · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #cs.CG #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2112.11956
[1] Maria Alkämper and Jim Magiera. 2021. Interface Preserving Moving Mesh (Code). DOI: 10.18419/darus-1671
arxiv created 2021/12/22 · arxiv updated 2021/12/23
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].