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Abstract In this paper, we propose and analyze a finite-element method of variational data assimilation for a second-order parabolic interface equation on a two-dimensional bounded domain. The Tikhonov regularization plays a key role in translating the data assimilation problem into an optimization problem. Then the existence, uniqueness and stability are analyzed for the solution of the optimization problem. We utilize the finite-element method for spatial discretization and backward Euler method for the temporal discretization. Then based on the Lagrange multiplier idea, we derive the optimality systems for both the continuous and the discrete data assimilation problems for the second-order parabolic interface equation. The convergence and the optimal error estimate are proved with the recovery of Galerkin orthogonality. Moreover, three iterative methods, which decouple the optimality system and significantly save computational cost, are developed to solve the discrete time evolution optimality system. Finally, numerical results are provided to validate the proposed method. 

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. 

Parallel computing using MPI has become ubiquitous on multi-node computing clusters. A common problem while developing parallel codes is determining whether or not a deadlock condition can exist. Ideally we do not want to have to run a large number of examples to find deadlock conditions through trial and error procedures. In this paper we describe a methodology using both static analysis and symbolic execution of a MPI program to make a determination when it is possible. We note that using static analysis by itself is insufficient for realistic cases. Symbolic execution has the possibility of creating a nearly infinite number of logic branches to investigate. We provide a mechanism to limit the number of branches to something computable. We also provide examples and pointers to software necessary to test MPI programs. 

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.