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Article

About Revisiting Domain Decomposition Methods for Poroelasticity

Harold Vance Department of Petroleum Engineering, Texas A & M University, 3116 TAMU, College Station, TX 77843, USA
Mathematics 2018, 6(10), 187; https://doi.org/10.3390/math6100187
Received: 20 August 2018 / Revised: 23 September 2018 / Accepted: 27 September 2018 / Published: 2 October 2018
(This article belongs to the Special Issue Modern Finite Element Methods)
In this paper, we revisit well-established domain decomposition (DD) schemes to perform realistic simulations of coupled flow and poroelasticity problems on parallel computers. We define distinct solution schemes to take into account different transmission conditions among subdomain boundaries. Indeed, we examine two different approaches, i.e., Dirichlet-Neumann (DN) and the mortar finite element method (MFEM), and we recognize their advantages and disadvantages. The MFEM significantly lessens the computational cost of reservoir compaction and subsidence calculations by dodging the conforming Cartesian grids that arise from the pay-zone onto its vicinity. There is a manifest necessity of producing non-matching interfaces between the reservoir and its neighborhood. We thus employ MFEM over nonuniform rational B-splines (NURBS) surfaces to stick these non-conforming subdomain parts. We then decouple the mortar saddle-point problem (SPP) using the Dirichlet-Neumann domain decomposition (DNDD) scheme. We confirm that this procedure is proper for calculations at the field level. We also carry comprehensive comparisons between the conventional and non-matching solutions to prove the method’s accuracy. Examples encompass linking finite element codes for slightly compressible single-phase and poroelasticity. We have used this program to a category of problems ranking from near-borehole applications to whole field subsidence estimations. View Full-Text
Keywords: domain decomposition; Dirichlet-Neumann; mortar finite elements domain decomposition; Dirichlet-Neumann; mortar finite elements
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MDPI and ACS Style

Florez, H. About Revisiting Domain Decomposition Methods for Poroelasticity. Mathematics 2018, 6, 187. https://doi.org/10.3390/math6100187

AMA Style

Florez H. About Revisiting Domain Decomposition Methods for Poroelasticity. Mathematics. 2018; 6(10):187. https://doi.org/10.3390/math6100187

Chicago/Turabian Style

Florez, Horacio. 2018. "About Revisiting Domain Decomposition Methods for Poroelasticity" Mathematics 6, no. 10: 187. https://doi.org/10.3390/math6100187

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