We consider two graph grammar based Petri nets models for anisotropic refinements of three dimensional hexahedral grids. The first one detects possible dead-end problems during the graph grammar based anisotropic refinements of the mesh. The second one employs an enhanced graph grammar model that is actually dead-end free. We apply the resulting algorithm to the simulation of resistivity logging measurements for estimating the location of underground oil and/or gas formations. The graph grammar based Petri net models allow to fix the self-adaptive mesh refinement algorithm and finish the adaptive computations with the required accuracy needed by the numerical solution.
Publié le : 2015-10-19
Classification:
Petri nets, automatic hp adaptivity, finite element method, dead-end, borehole resistivity logging,
68Q05, 68Q42, 68Q60, 68Q85
@article{cai1839,
author = {Arkadiusz Szymczak; AGH University of Science and Technology, Krakow and Maciej Paszy\'nski; AGH University of Science and Technology, Krakow, Poland and David Pardo; The University of The Basque Country, Bilbao and Anna Paszy\'nska; Jagiellonian University},
title = {Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method},
journal = {Computing and Informatics},
volume = {33},
number = {3},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/cai1839}
}
Arkadiusz Szymczak; AGH University of Science and Technology, Krakow; Maciej Paszyński; AGH University of Science and Technology, Krakow, Poland; David Pardo; The University of The Basque Country, Bilbao; Anna Paszyńska; Jagiellonian University. Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method. Computing and Informatics, Tome 33 (2015) no. 3, . http://gdmltest.u-ga.fr/item/cai1839/