Coupled isogeometric Finite Element Method and Hierarchical Genetic Strategy with balanced accuracy for solving optimization inverse problem

Abstract

The liquid fossil fuel reservoir exploitation problem (LFFEP) has not only economical signification but also strong natural environment impact. When the hydraulic fracturing technique is considered from the mathematical point of view it can be formulated as an optimization inverse problem, where we try to find optimal locations of pumps and sinks to maximize the amount of the oil extracted and to minimize the contamination of the groundwater. In the paper, we present combined solver consisting of the Hierarchical Genetic Strategy (HGS) with variable accuracy for solving optimization problem and isogeometric finite element method (IGA-FEM) with different mesh size for modeling a non-stationary flow of the non-linear fluid in heterogeneous media. The algorithm was tested and compared with the strategy using Simple Genetic Algorithm (SGA) as optimization algorithm and the same IGA-FEM solver for solving a direct problem. Additionally, a parallel algorithm for non-stationary simulations with isogeometric L2 projections is discussed and preliminarily assessed for reducing the computational cost of the solvers consisting of genetic algorithm and IGA-FEM algorithm. The theoretical asymptotic analysis which shows the correctness of algorithm and allows to estimate computational costs of the strategy is also presented.