Journal of Computational Science 31 (2019) 126–136 Contents lists available at ScienceDirect Journal of Computational Science j ourna l h om epage: www.elsevier.com/locate/jocs Speeding up multi-objective optimization of liquid fossil fuel reserve exploitation with parallel hybrid memory integration Barbara Barabasz b , Stephen Barrett b , Leszek Siwik a , Marcin Lo´ s a , Krzysztof Podsiadło a , Maciej Wo´ zniak a,∗ a AGH University of Science and Technology, Krakow, Poland b School of Computer Science and Statistics, Trinity College, Dublin, Ireland a r t i c l e i n f o Article history: Received 29 July 2018 Received in revised form 14 November 2018 Accepted 1 January 2019 Available online 3 January 2019 Keywords: Isogeometric analysis Hybrid parallelization Inverse problems a b s t r a c t In this paper, we show a hybrid parallelization method for reducing the computational cost of a solver using hybrid-memory parallel machines. We show how the hybrid parallelization can be utilized to speed up challenging computational applications. Namely, we focus on the liquid fossil fuel reservoir exploitation problem (LFFEP), the optimization inverse problem where we try to find the optimal locations of pumps and sinks during the oil exploitation technique with hydraulic fracturing to maximize the amount of oil and minimize groundwater contamination. In our simulations, we combine a hierarchical genetic search (HGS) with an isogeometric finite element method solver. © 2019 Elsevier B.V. All rights reserved. 1. Introduction The isogeometric analysis (IGA) combined with the finite ele- ment method (FEM) introduced in [8] and called IGA-FEM is a modern technique for integrating geometrical modeling within CAD systems, with the engineering computations performed in CAE systems. The IGA method utilizes B-splines or their rationalized version NURBS [9] for both descriptions of the problem geometry as well as the engineering simulations’. The isogeometric analy- sis has multiple applications in shear deformable shell theory [5], phase field modeling [10,11], phase-separation simulations [13,14], wind turbine aerodynamics [16], incompressible hyper-elasticity [12], turbulent flow simulations [7], or biomechanics [15,3,2,1,6]. In this paper, we present a parallelization of the algorithm for generating the explicit dynamics simulations with isogeometric L 2 projections (see Appendix A). We have parallelized the integration routines of the three-dimensional IGA code. We utilize the IGA-FEM solver as the computational kernel for solving the liquid fossil fuel reservoir exploitation problem (LFFEP) [20]. The LFFEP is an optimization problem related to hydraulic fracturing (fracking), the oil/gas extraction technique consisting ∗ Corresponding author. E-mail addresses: barabaszb@gmail.com (B. Barabasz), stephen.barrett@tcd.ie (S. Barrett), siwik@agh.edu.pl (L. Siwik), los@agh.edu.pl (M. Lo´ s), podsiadl@agh.edu.pl (K. Podsiadło), macwozni@agh.edu.pl (M. Wo´ zniak). of high-pressure fluid chemicals injection into the deposit. The method is highly efficient, although it can lead to contamination of the ground water. Thus, we have two conflicting objectives in our LFFEP: the first is to maximize the resource extraction, and the second is to minimize the groundwater contamination. The fracking problem is modeled as a non-linear flow in the heterogeneous media. ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ ∂u ∂t - ∇ · ((x, u) ∇u) = h(x, t ) in  × [0, T ] ∇u · ˆ n = 0 on ∂  × [0, T ] u(x, 0) = u 0 in  , where the unknown u is the pressure.  is the given permeability. (x, u) = K q (x)b(u) , where K q (x) is the static permeability, the property of the terrain obtained from the formation map presented in Figure 1, and b is the dynamic permeability depending on the local pressure: b(u) = e u , and  = 10 is a model constant. Below the formation, we assume the presence of groundwater. https://doi.org/10.1016/j.jocs.2019.01.001 1877-7503/© 2019 Elsevier B.V. All rights reserved.