Pereira, L. Felipe

Permanent URI for this collectionhttps://hdl.handle.net/10735.1/6672

Felipe Pereira is a Professor of Mathematical Sciences. His research has been in applied mathematics including:

  • Modeling the flow of oil in underground reservoirs
  • Injection strategies for permanently storing carbon dioxide in deep saline aquifers
  • Modeling fluid flow in heterogeneous formations, such as oil shale
  • Pore network construction algorithms
  • Numerical methods for partial differential equations
  • High performance, parallel, scientific computing

Browse

Recent Submissions

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    A Multiscale Direct Solver for the Approximation of Flows in High Contrast Porous Media
    (Elsevier B.V.) Akbari, H.; Engsig-Karup, A. P.; Ginting, V.; Pereira, L. Felipe; Pereira, L. Felipe
    We consider a non-overlapping domain decomposition approach to approximate the solution of elliptic boundary value problems with high contrast in their coefficients. We propose a method such that initially local solutions subject to Robin boundary conditions in each primal subdomain are constructed with (locally conservative) finite element or finite volume methods. Then, a novel approach is introduced to obtain a (discontinuous) global solution in terms of linear combination of the local subdomain solutions. In the proposed algorithm the computation of local solutions for unions of subdomains are localized at nearest-neighbor subdomain boundaries, thus avoiding the solution of global interface problems. We remove discontinuities in a smoothing step that is defined on a staggered grid or dual subdomains. The resulting algorithm is naturally parallelizable and can be employed as a parallel direct solver, offering great potential for the numerical solution of large problems. In fact, subdomains can be considered small enough to fit well in GPUs and the proposed procedure can handle adaptive (in space) simulations effectively. Numerical simulations are presented and discussed. We demonstrate the effectiveness of the proposed approach with two and three dimensional high contrast and channelized coefficients, that lead to challenging approximation problems. The new procedure, although designed for parallel processing, is also of value for serial calculations. ©2019 Elsevier B.V.
  • Thumbnail Image
    Item
    Convergence Analysis of MCMC Methods for Subsurface Flow Problems
    (Springer Verlag) Mamun, Abdullah-al; Pereira, Felipe; Rahunanthan, A.; Mamun, Abdullah-al; Pereira, Felipe
    In subsurface characterization using a history matching algorithm subsurface properties are reconstructed with a set of limited data. Here we focus on the characterization of the permeability field in an aquifer using Markov Chain Monte Carlo (MCMC) algorithms, which are reliable procedures for such reconstruction. The MCMC method is serial in nature due to its Markovian property. Moreover, the calculation of the likelihood information in the MCMC is computationally expensive for subsurface flow problems. Running a long MCMC chain for a very long period makes the method less attractive for the characterization of subsurface. In contrast, several shorter MCMC chains can substantially reduce computation time and can make the framework more suitable to subsurface flows. However, the convergence of such MCMC chains should be carefully studied. In this paper, we consider multi-MCMC chains for a single–phase flow problem and analyze the chains aiming at a reliable characterization.

Works in Treasures @ UT Dallas are made available exclusively for educational purposes such as research or instruction. Literary rights, including copyright for published works held by the creator(s) or their heirs, or other third parties may apply. All rights are reserved unless otherwise indicated by the copyright owner(s).