Research

How to define efficient models to describe multiphysics systems?

Sequential schemes and modular programming are extremely important to provide an answer to this question. On one hand, a sequential scheme is used to provide reliable approximations of a multiphysics system described by coupled PDE's, such a sequential scheme employs appropriated linear/non-linear solver to render an approximated solution of each subproblem. On the other hand, modular programming allows the implementation of the required linear/non-linear solvers.

I am interested in such approximations and how they can be implemented and employed in an efficient way to provide neat solver examples.

Google scholar link:
https://scholar.google.com/citations?user=HyjxEasAAAAJ&hl=en

Scientific Articles:

Conformal FE approximation spaces:

• P. R. B. Devloo, O. Duran, S. M. Gomes, and M. Ainsworth. High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions. Working paper. 2019. 
• P. R. B. Devloo, O. Duran, and S. M. Gomes. H(div)-conforming spaces based on general meshes,  with interface constraints:  accuracy enhancement, multiscale, and hp-adaptivity. In press - International Conference on Boundary and Interior Layers, BAIL 2018. 2019.
• D. A. Castro, P. R. Devloo, A. M. Farias, S. M. Gomes, and O. Y. Duran.Hierarchical high order finite element bases for spaces based on curved meshes for two-dimensional regions or manifolds. In: Journal of Computational and Applied Mathematics301 (2016), pp. 241–258.
• D. A. Castro, P. R. Devloo, A. M. Farias, S. M. Gomes, D. de Siqueira, and O. Duran. Three dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy. In: Computer Methods in Applied Mechanics and Engineering 306 (July 2016), pp. 479–502. 
• P. R. B. Devloo, O. Duran, S. M. Gomes, and N. Shauer. Mixed finite element approximations based on 3D hp-adaptive curved meshes with two types of H(div)-conforming spaces. In: International Journal for Numerical Methods in Engineering(2017). nme.5698, n/a–n/a.
• P. R. B. Devloo, O. Duran, A. M. Farias, and S. M. Gomes. Effects of mesh deformation on the accuracy of mixed finite element approximations for 3D Darcy’s flows. working paper or preprint. Sept. 2018.

Multiscale FE approximations:

• O.  Duran,  P.  R.  B.  Devloo,  S.  M.  Gomes,  and  F.  Valentin.  A  multi-scale hybrid method for Darcy’s problems using mixed finite element local solvers. In press - CMAME. 2019.[10]    O. Dur ́an, M. Sanei, and P. R. B. Devloo. “ An enhanced sequential fully implicit scheme for poroelastic-plasticity ”. 2019.

Sequential scheme approximations:

• O Duran, P. Devloo, S. Gomes, J. Villegas. A multiscale mixed method for a two-phase reservoir simulator. (2020) (Submitted to Computer Methods in Applied Mechanics and Engineering)
• O. Duran, M. Sanei,  P. Devloo, E. Santos. An enhanced sequential fully implicit scheme for reservoir geomechanics. (2020) (Submitted to Computational Geosciences)

Constitutive modeling:

• M. Sanei, O. Duran,  P. Devloo, E. Santos. An innovative procedure to improve the integration algorithm for the modified Cam-Clay plasticity model. (2020) (Submitted to Computer and geotechnics)

Alrotighm and implementations:

• Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Inga Berre, Wietse M. Boon, Bernd Flemisch, Alessio Fumagalli, Dennis Glaser, Eirik Keilegavlen, Anna Scotti, Ivar Stefansson, Alexandru Tatomire, Konstantin Brenner, Samuel Burbulla, Philippe Devloo, Omar Duran, Marco Favino, Julian Hennicker, I-Hsien Lee, Konstantin Lipnikov, Roland Masson, Klaus Mosthaf, Maria Giuseppina Chiara Nestolap Chuen-Fa Nil, Kirill Nikitin, Philipp Schadler, Daniil Svyatskiyn, Ruslan Yanbarisovq Patrick Zulian. (2020, to appear).
• N.  V.  Boas,  P.  R.  B.  Devloo,  and  O.  Duran.  A CUDA  accelerated numerical integration of elastoplastic finite elements. (2020, to appear).

Applications:

• N. Batalha, Omar Duran, P. Devloo, L. Vieira. Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through a heterogeneous field. Oil & Gas Science and Technology – Rev. IFP Energies Nouvelles (2020).
• G. Dollé, O. Duran, N. Feyeux, E. Frénod, M. Giacomini, and C. Prud’homme. Mathematical modeling and numerical simulation of a bioreactor land-fill using Feel++. In:ESAIM: Proceedings and Surveys55 (Dec. 2016). Ed.  by  E.  Frénod,  E.  Maitre,  A.  Rousseau,  S.  Salmon,  and  M.  Szopos, pp. 83–110. 

Scientific Events:

• Participant at summer school and long research session of  CEMRACS-2015 Coupling Multi-Physics Models involving Fluids.  The CEMRACS is a scientific event of the SMAI (the French Society of Applied and Industrial Mathematics).  July 20 - August 28, 2015, CIRM, Marseille.

We may meet...

• E. Burman, O. Duran, A. Ern.  Explicit and implicit hybrid high-order methods for the acoustic wave equation. World  Congress on  Computational  Mechanics  (WCCM).  Advances in computational methods for Subsurface Modeling: In Honor of Professor Mary F. Wheeler.July - 2020, Paris, France. (to attend).

• O. Duran, P. Devloo, S. Gomes. A Multiscale Hybrid Method for Darcy’sProblems Using Mixed Finite Element Local Solvers. US National Congress on  Computational  Mechanics  (USNCCM).  Advances in computational methods for Subsurface Modeling: In Honor of Professor Mary F. Wheeler.July - 2019, Austin, USA.
• O.  Duran,  P.  Devloo,  S.  Gomes.  A  multi-scale hybrid method using mixed finite elements for two-phase flow considering gravity effects.  SixthChilean  Workshop on  Numerical  Analysis of  Partial  Differential  Equations.  January - 2019, Concepcion, Chile.
• O. Duran, P. Devloo, S. M. Gomes.  A Multi-scale Method for a Three-Phase Reservoir Simulator Considering Gravity Effects World  Congress on  Computational  Mechanics  (WCCM  XIII)  2ndPan American Congress on Computational Mechanics (PANACM II) July- 2018, New York, NY, USA.
• O.  Duran,  J.  Villegas,  S.  Gomes,  P.  Devloo. Conservative high order coupled mixed finite element-finite volume method for two-phase flows in heterogeneous media.  Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations.  January - 2016, Concepcion, Chile.