Face-to-face partition of 3D space with identical well-centered tetrahedra

0452193 - MÚ 2017 RIV CZ eng J - Journal Article
Hošek, Radim
Face-to-face partition of 3D space with identical well-centered tetrahedra.
Applications of Mathematics. Roč. 60, č. 6 (2015), s. 637-651. ISSN 0862-7940. E-ISSN 1572-9109
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : rigid mesh * well-centered mesh * approximative domain
Subject RIV: BA - General Mathematics
Impact factor: 0.507, year: 2015
http://hdl.handle.net/10338.dmlcz/144451

The motivation for this paper comes from physical problems defined on bounded smooth domains $Omega $ in 3D. Numerical schemes for these problems are usually defined on some polyhedral domains $Omega _h$ and if there is some additional compactness result available, then the method may converge even if $Omega _h to Omega $ only in the sense of compacts. Hence, we use the idea of meshing the whole space and defining the approximative domains as a subset of this partition. endgraf Numerical schemes for which quantities are defined on dual partitions usually require some additional quality. One of the used approaches is the concept of emph {well-centeredness}, in which the center of the circumsphere of any element lies inside that element. We show that the one-parameter family of Sommerville tetrahedral elements, whose copies and mirror images tile 3D, build a well-centered face-to-face mesh. Then, a shape-optimal value of the parameter is computed.
Permanent Link: http://hdl.handle.net/11104/0253222