Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method

Authors

  • 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

Keywords:

Petri nets, automatic hp adaptivity, finite element method, dead-end, borehole resistivity logging

Abstract

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.

Downloads

Download data is not yet available.

Author Biographies

Arkadiusz Szymczak, AGH University of Science and Technology, Krakow

PhD student at Department of Computer Science

Maciej Paszyński, AGH University of Science and Technology, Krakow, Poland

Vice-director of Department of Computer Science, Associate Professor

David Pardo, The University of The Basque Country, Bilbao

Research Professor, member of IKERBASQUE (Basque Foundation of Science)

Anna Paszyńska, Jagiellonian University

Assistant Professor at Department of Computer Graphics and Design

Downloads

Published

2015-10-19

How to Cite

Szymczak, A., Paszyński, M., Pardo, D., & Paszyńska, A. (2015). Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method. Computing and Informatics, 34(2), 425–457. Retrieved from http://147.213.75.17/ojs/index.php/cai/article/view/1839