Browsing by Author "Guo, Wei"
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Item Boundary optimal control problems with inequality constraints(2019-08) Ratnavale, Saikanth; Bornia, Giorgio; Aulisa, Eugenio; Guo, WeiIn my work, I will introduce and analyze different approaches to overcome some issues in computing fractional Sobolev norms in the context of PDE-constrained boundary optimal control problems with Dirichlet control. Dirichlet boundary optimal control problems are perhaps the most interesting class of optimal control problems constrained by partial differential equations (PDEs). In fact, the possibility of controlling the behaviour of a physical system may often take place only by changing the values of certain quantities at the boundary of the domain, especially when the interior of the physical system is not accessible and when no physical mechanism can be triggered inside the domain from the outside. A first approach that is considered in this work keeps the control function on the boundary by replacing fractional norms with integer norms. This approach is a simple way to overcome the need of explicitly computing fractional norms. Then, two other approaches are proposed that make use of lifting functions of the boundary controls. These lifting functions become a new class of control functions in the statement of the optimal control problem. They can be chosen to be defi ned either inside the original domain of the state problem or outside of it. We compare these two lifting approaches with the first approach on the boundary. Another goal of this research is to add control inequality constraints to all the above approaches. In order to deal with these, the Primal-Dual Active Set method is used. The optimality systems arising from first-order necessary conditions are discretized using the finite element method. Numerical results are presented to compare the convergence rate, computational cost, and accuracy of each optimal control problem.Item Exact CutFEM polynomial integration(2022-08) Loftin, Jonathon; Aulisa, Eugenio; Bornia, Giorgio; Guo, WeiThe implementation of discontinuous functions occurs in many of today's state of the art partial differential equation solvers. In finite element methods this poses an inherent difficulty: there are no quadrature rules readily available when integrating functions whose discontinuity falls in the interior of the element. Many approaches to this issue have been developed in recent years, among them is the equivalent polynomial technique. This method replaces the discontinuous function with a polynomial, potentially allowing for the integration to occur over the entire domain, rather than integrating over complex subdomains. Although eliminating the issues involved with discontinuous function integration, the equivalent polynomial tactic introduces its own set of problems. In particular, either adaptivity is required to capture the discontinuity or error is introduced when regularization of the discontinuous function is implemented. In the current work, we eliminate both of these issues. The results of this work provide exact algebraic expressions for subdomain and interface polynomial integration, where the interface represents the boundary of the cut domain. We also provide algorithms for the implementation of these expressions for standard finite element shapes in one, two, and three dimensions, along with a hypercube of arbitrary dimension, for linear discontinuities. Discontinuities defined by more general curves are analyzed and closed-form algebraic expressions are given. Practical implementation considerations are provided with a considerable level of detail.Item Modeling and simulation of biomedical applications using finite element method(2021-08) Kara, Erdi; Aulisa, Eugenio; Bornia, Giorgio; Guo, WeiIn this dissertation, two novel applications of finite element method(FEM) are presented. In Chapter I, we propose a novel hybrid method that incorporates the Arbitrary Lagrangian-Eulerian (ALE) approach into material point method(MPM) for fluid-structure interaction(FSI) problems. In this formulation, fluid motion is described by Navier- Stokes equations formulated in ALE form. Variational formulation concerning the fluid is supported by the stabilizing residual- based variational multiscale(RBVM) method. Variational structural equations concerning the solid are assembled using MPM. We let fluid-solid interface cut the elements arbitrarily. To ensure well system conditioning and stability of the resulting system irrespective of how the interface intersects the cut elements, face-oriented ghost penalty stabilization is applied on the cut element faces. Continuity of velocities and normal stresses on the boundary is weakly enforced by the Nitsche’s method. The advantage of our hybrid approach is that it provides a framework which eliminates the mesh entanglement issues encountered in ALE based finite element methods for fluid structure interaction problems involving large structural deformation. In Chapter II, we derive a full 3-dimensional (3-D) model of inhomogeneous -- anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using Diffusion Tensor Magnetic Resonance Imaging (DTI) from a patient diagnosed with glioblastoma multiform (GBM). Then we numerically simulate the full model with FEM and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.Item Reliability analysis of elastic graphite packer in heat injection well during oil shale in-situ conversion(2023) Guo, Wei; Shui, Haoche; Liu, Zhao; Wang, Yuan; Tu, Jiawei (TTU)Heat injection is essential for oil shale in-situ conversion technology. The downhole of the heat injection well reaches temperatures above 400◦ C during the process of heat injection, and part of the high-temperature gas dissipates through the wellbore annulus. Consequently, in addition to causing energy loss, the dissipation causes thermal damage to the casing and wellhead. To avoid dissipation, components that are suitable for high-temperature environments should be sealed and used during heat injection while mining. Therefore, this study presents the design of a packer composed of elastic graphite rubber and a high-temperature-resistant material. The influence of numerous factors, such as downhole temperature, working load, and height of rubber, on the reliability of the packer was analyzed. Subsequently, the numerical simulation analysis of the packer reliability in in-situ conversion mining under high temperature and pressure environments was performed. The results indicate that when the operating temperature is stable, the operating load has the most obvious influence on the sealing reliability of the packer, whereas the change in the height of the rubber has the least significant effect on the maximum contact stress between the casing and rubber. The change in the operating temperature has the least significant effect on the overall sealing performance of the packer. Moreover, the rise of the temperature will increase the sealing reliability of the packer, and on the contrary, the drop in the temperature will decrease it.