%0 Journal Article %1 10.1145/3630000 %A Alkämper, Maria %A Magiera, Jim %A Rohde, Christian %C New York, NY, USA %D 2024 %I Association for Computing Machinery %J ACM Trans. Math. Softw. %K PN1 PN1-9 EXC2075 updated %N 1 %R 10.1145/3630000 %T An Interface-Preserving Moving Mesh in Multiple Space Dimensions %U https://doi.org/10.1145/3630000 %V 50 %X 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.An open source implementation of the moving mesh algorithm is available at Reference 1.

@article{10.1145/3630000, 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.An open source implementation of the moving mesh algorithm is available at Reference [1].}, added-at = {2024-04-05T10:28:06.000+0200}, address = {New York, NY, USA}, articleno = {5}, author = {Alk\"{a}mper, Maria and Magiera, Jim and Rohde, Christian}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2ec8e8dbd36c60ef6a9f4ff5629790509/simtech}, doi = {10.1145/3630000}, interhash = {8cea97ae0a9bd0d8e817ed98ccf87d7d}, intrahash = {ec8e8dbd36c60ef6a9f4ff5629790509}, issn = {0098-3500}, issue_date = {March 2024}, journal = {ACM Trans. Math. Softw.}, keywords = {PN1 PN1-9 EXC2075 updated}, month = mar, number = 1, numpages = {28}, publisher = {Association for Computing Machinery}, timestamp = {2024-04-05T10:28:06.000+0200}, title = {An Interface-Preserving Moving Mesh in Multiple Space Dimensions}, url = {https://doi.org/10.1145/3630000}, volume = 50, year = 2024 }