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

Hošek, Radim. "Face-to-face partition of 3D space with identical well-centered tetrahedra." Applications of Mathematics 60.6 (2015): 637-651. <http://eudml.org/doc/271805>.

@article{Hošek2015,
abstract = {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 \rightarrow \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. Numerical schemes for which quantities are defined on dual partitions usually require some additional quality. One of the used approaches is the concept of 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. For this value of the parameter, Sommerville tetrahedron is invariant with respect to reflection, i.e., 3D space is tiled by copies of a single tetrahedron.},
author = {Hošek, Radim},
journal = {Applications of Mathematics},
keywords = {rigid mesh; well-centered mesh; approximative domain; single element mesh; Sommerville tetrahedron; rigid mesh; well-centered mesh; approximative domain; single element mesh; Sommerville tetrahedron},
language = {eng},
number = {6},
pages = {637-651},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Face-to-face partition of 3D space with identical well-centered tetrahedra},
url = {http://eudml.org/doc/271805},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Hošek, Radim
TI - Face-to-face partition of 3D space with identical well-centered tetrahedra
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 6
SP - 637
EP - 651
AB - 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 \rightarrow \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. Numerical schemes for which quantities are defined on dual partitions usually require some additional quality. One of the used approaches is the concept of 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. For this value of the parameter, Sommerville tetrahedron is invariant with respect to reflection, i.e., 3D space is tiled by copies of a single tetrahedron.
LA - eng
KW - rigid mesh; well-centered mesh; approximative domain; single element mesh; Sommerville tetrahedron; rigid mesh; well-centered mesh; approximative domain; single element mesh; Sommerville tetrahedron
UR - http://eudml.org/doc/271805
ER -