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Porous media and conduit coupled systems are heavily used in a variety of areas such as groundwater system, petroleum extraction, and biochemical transport. A coupled dual porosity Stokes model has been proposed to simulate the fluid flow in a dual-porosity media and conduits coupled system. Data assimilation is the discipline that stud- ies the combination of mathematical models and observations. It can improve the accuracy of mathematical models by incorporating data, but also brings challenges by increasing complexity and computational cost. In this paper, we study the application of data assimilation methods to the coupled dual porosity Stokes model. We give a brief introduction to the coupled model and examine the performance of different data assimilation methods on a finite element implementation of the coupled dual porosity Stokes system. We also study how observations on different variables of the system affect the data assimilation process. 

Porous media and conduit coupled systems are heavily used in a vari- ety of areas. A coupled dual-porosity-Stokes model has been proposed to simu- late the fluid flow in a dual-porosity media and conduits coupled system. In this paper, we propose an implementation of this multi-physics model. We solve the system with the automated high performance differential equation solving envi- ronment FEniCS. Tests of the convergence rate of our implementation in both 2D and 3D are conducted in this paper. We also give tests on performance and scalability of our implementation. 

Nonlinear optimization problems arise in all industries. Accelerating optimization solvers is desirable. Efforts have been made to accelerate interior point methods for large scale problems. However, since the interior point algorithm used requires many function evaluations, the acceleration of the algorithm becomes less beneficial. We introduce a way to accelerate the sequential quadratic programming method, which is characterized by minimizing function evaluations, on graphical processing units.