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

Year, pages: 2015, 425 - 457

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.

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. In Computing and Informatics, vol. 34, no.2, pp. 425-457. 1335-9150.

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. 1335-9150.