An algorithm for transferring 2d arbitrary hp-refined finite element axially symmetric meshes to three dimensions

Maciej Paszyński¹, David Pardo², Leszek Demkowicz³, Carlos Torres-Verdin²

¹Department of Computer Science, AGH University of Science and Technology.
²Department of Petroleum Engineering, The University of Texas in Austin.
³Institute for Computational Engineering and Sciences, ICES, The University of Texas in Austin.

DOI:

https://doi.org/10.7494/cmms.2007.2.0154

Abstract:

The 2D and 3D fully automatic hp adaptive Finite Element Method (FEM) codes generate a sequence of optimal hp refined meshes delivering exponential convergence rate of the numerical error with respect to the number of degrees of freedom (and CPU time). The optimal meshes are generated by performing a sequence of h or p refinements on the initial mesh. However, generation of optimal meshes in three dimensions is computationally expensive. We propose an algorithm for transferring of generated 2D optimal meshes into 3D meshes. The algorithm allows us to replace expensive 3D generation of optimal hp mesh by relatively inexpensive 2D generation of optimal meshes. The algorithm generates full revolution of the recorded optimal 2D mesh. The algorithm supports generation of either 3D axially symmetric meshes or non-axially symmetric tilted meshes. We apply that algorithm to perform a sequence of 3D DC borehole resistivity measurements simulations.

Cite as:

Paszyński, M., Pardo, D., Demkowicz, L., & Torres-Verdin, C. (2007). An algorithm for transferring 2d arbitrary hp-refined finite element axially symmetric meshes to three dimensions. Computer Methods in Materials Science, 7(2), 269 – 275. https://doi.org/10.7494/cmms.2007.2.0154

Article (PDF):

Keywords:

Finite Element Method, DC resistivity borehole measurements, Hp adaptivity

References:

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Pardo, D., Paszyński, M., Torres-Verdin, C., Demkowicz, L., 2006, Numerical Simulations of 3D DC Borehole Resistivity Measurements using an hp-Adaptive Goal-Oriented Finite Element Formulation, Sixth Annual Report of Joint Industry Research Consortium on Formation Evaluation, The University of Texas at Austin, August 16-18.