+publisher:"University of Texas – Austin" +contributor:("Engquist, Bjorn")

University of Texas – Austin

1. Nguyen, Hieu Huu. Parallel-in-time methods for wave propagation in heterogeneous media.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2020, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/10151

► Wave propagation is ubiquitous in science and engineering applications, but solving the second-order wave equation in a parallel way is still computationally challenging. Specifically, as… (more)

Subjects/Keywords: Numerical method; Wave propagation

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APA (6^th Edition):

Nguyen, H. H. (2020). Parallel-in-time methods for wave propagation in heterogeneous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/10151

Chicago Manual of Style (16^th Edition):

Nguyen, Hieu Huu. “Parallel-in-time methods for wave propagation in heterogeneous media.” 2020. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://dx.doi.org/10.26153/tsw/10151.

MLA Handbook (7^th Edition):

Nguyen, Hieu Huu. “Parallel-in-time methods for wave propagation in heterogeneous media.” 2020. Web. 23 Apr 2021.

Vancouver:

Nguyen HH. Parallel-in-time methods for wave propagation in heterogeneous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2020. [cited 2021 Apr 23]. Available from: http://dx.doi.org/10.26153/tsw/10151.

Council of Science Editors:

Nguyen HH. Parallel-in-time methods for wave propagation in heterogeneous media. [Doctoral Dissertation]. University of Texas – Austin; 2020. Available from: http://dx.doi.org/10.26153/tsw/10151

University of Texas – Austin

2. Bello Rivas, Juan Manuel. Iterative milestoning.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/45791

► Computer simulation of matter using Molecular Dynamics (MD) is a staple in the field of Molecular Biophysics. MD yields results suitable for comparison with laboratory… (more)

▼ Computer simulation of matter using Molecular Dynamics (MD) is a staple in the field of Molecular Biophysics. MD yields results suitable for comparison with laboratory experiments and, in addition, it serves as a computational microscope by providing insight into a variety of molecular mechanisms. However, some of the most interesting problems pertaining to the investigation of biomolecules remain outside of the scope of MD due to the long time scales at which they occur. Milestoning is a method that addresses the long time simulation of biomolecular systems without giving up the fully-atomistic spatial resolution necessary to understand biological processes such as signalling and biochemical reactions. The method works by partitioning the phase space of the system into regions whose boundaries are called milestones. The dynamics of the system restricted to the milestones defines a stochastic process whose transition probabilities and exit times can be efficiently computed by numerical simulation. By calculating the transition probabilities and exit times of this process, we can obtain global thermodynamic and kinetic properties of the original system such as its stationary probability, free energy, and reaction rates. The calculation of these properties would be unfeasible for many systems of interest if we were to approach the problem by plain MD simulation. The success of milestoning computations relies on certain modeling assumptions. In this dissertation we introduce an iterative variant of the Milestoning method that relaxes the assumptions required by the original method and can be applied in the non-equilibrium setting. The new method works by iteratively approximating the transition probabilities and exit times until convergence is attained. In addition to a detailed description of the method, we give various pedagogical examples, showcase its practical applications to molecular systems, and provide an alternative formulation of the method in terms of boundary value problems. Advisors/Committee Members: Elber, Ron (advisor), Engquist, Bjorn (committee member), Makarov, Dmitrii E (committee member), Rodin, Gregory J (committee member), Zariphopoulou, Thaleia (committee member).

Subjects/Keywords: Molecular simulation; Dynamical systems

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APA (6^th Edition):

Bello Rivas, J. M. (2016). Iterative milestoning. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/45791

Chicago Manual of Style (16^th Edition):

Bello Rivas, Juan Manuel. “Iterative milestoning.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/45791.

MLA Handbook (7^th Edition):

Bello Rivas, Juan Manuel. “Iterative milestoning.” 2016. Web. 23 Apr 2021.

Vancouver:

Bello Rivas JM. Iterative milestoning. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/45791.

Council of Science Editors:

Bello Rivas JM. Iterative milestoning. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/45791

3. -1218-7450. Implicit boundary integral methods.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32830

► Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary… (more)

▼ Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary integrals in a level set framework, where the boundaries are described implicitly as the zero level set of a Lipschitz function. The advantage of IBIMs is that they can work on a fixed Cartesian grid without having to parametrize the boundaries. This dissertation extends the IBIM model and develops algorithms for problems in two application areas. The first part of this dissertation considers nonlinear interface dynamics driven by bulk diffusion, which involves solving Dirichlet Laplace Problems for multiply connected regions and propagating the interface according to the solutions of the PDE at each time instant. We develop an algorithm that inherits the advantages of both level set methods (LSMs) and BIMs to simulate the nonlocal front propagation problem with possible topological changes. Simulation results in both 2D and 3D are provided to demonstrate the effectiveness of the algorithm. The second part considers wave scattering problems in unbounded domains. To obtain solutions at eigenfrequencies, boundary integral formulations use a combination of double and single layer potentials to cover the null space of the single layer integral operator. However, the double layer potential leads to a hypersingular integral in Neumann problems. Traditional schemes involve an interpretation of the integral as its Hadamard's Finite Part or a complicated process of element kernel regularization. In this thesis, we introduce an extrapolatory implicit boundary integral method (EIBIM) that evaluates the natural definition of the BIM. It is able to solve the Helmholtz problems at eigenfrequencies and requires no extra complication in different dimensions. We illustrate numerical results in both 2D and 3D for various boundary shapes, which are implicitly described by level set functions. Advisors/Committee Members: Tsai, Yen-Hsi R. (advisor), Arbogast, Todd (committee member), Biros, George (committee member), Engquist, Bjorn (committee member), Ren, Kui (committee member).

Subjects/Keywords: Boundary integral methods; Level set methods; Mullins-Sekerka; Helmholtz equation; Laplace equation; Multiply connected domain; Exterior problem; Differential equation

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APA (6^th Edition):

-1218-7450. (2015). Implicit boundary integral methods. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Web. 23 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-1218-7450. Implicit boundary integral methods. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-1218-7450. Implicit boundary integral methods. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

4. Neupane, Prapti. Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds.

Degree: PhD, Computational and applied mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/41984

► Coastal areas are regions of high population density and urbanization. These areas are highly vulnerable to inundation and flooding not only because of hurricane storm… (more)

▼ Coastal areas are regions of high population density and urbanization. These areas are highly vulnerable to inundation and flooding not only because of hurricane storm surge, but also because of the torrential rainfall that often accompanies hurricanes. In order to accurately predict the extent of damage such an event might cause, any model that is used to simulate this process needs to couple rainfall with storm surge. The works that have tried to address this issue have mostly used a unidirectional coupling technique, where one of the following two approaches is taken. In the first approach, a hydrology model is used in the domain of interest and storm surge is incorporated in the domain as a boundary condition. In the second approach, a storm surge model is used in the domain of interest and rainfall is incorporated in the domain as a river inflow boundary condition. Neither of these approaches allows the rainwater and the surge water to interact bidirectionally. In order to improve on those efforts, in this dissertation, we develop a comprehensive framework for modeling flooding in coastal watersheds. We present an approach to decompose a watershed into multiple sub-domains depending on the dynamics of flow in the region. We use different simplifications of the shallow water equations on different sub-domains to gain computational efficiency without compromising on physical accuracy. The different sub-domains are coupled with each other through numerical fluxes in a discontinuous Galerkin framework. This technique allows for a tight coupling of storm surge with rainfall runoff, so that the flooding that occurs is truly influenced by the nonlinear interaction of these two processes. We present numerical tests to validate and verify the methods used for modeling flow in different sub-domains as well as the techniques used for coupling different sub-domains with each other. Advisors/Committee Members: Dawson, Clinton N. (advisor), Gamba, Irene M (committee member), Engquist, Bjorn (committee member), Bui-Thanh, Tan (committee member), Moser, Robert D (committee member).

Subjects/Keywords: Hurricane storm surge; Rainfall runoff; Flooding; Discontinuous Galerkin method; Computational hydrology; Multi-dimensional model; Shallow water equations

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APA (6^th Edition):

Neupane, P. (2016). Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/41984

Chicago Manual of Style (16^th Edition):

Neupane, Prapti. “Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/41984.

MLA Handbook (7^th Edition):

Neupane, Prapti. “Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds.” 2016. Web. 23 Apr 2021.

Vancouver:

Neupane P. Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/41984.

Council of Science Editors:

Neupane P. Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/41984

University of Texas – Austin

5. -5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/63471

► With the increase in compute power and the advent of the big data era, inverse problems have grown more complex, attempting to extract more information… (more)

▼ With the increase in compute power and the advent of the big data era, inverse problems have grown more complex, attempting to extract more information and to use more data. While this evolution manifests itself in multiple forms, we focus in this dissertation on three specific aspects: multi-source, multi-parameter, and multi-physics inverse problems. The computational cost of solving a multi-source inverse problem in- creases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear combinations of all experiments for solving the inverse problem. This approach applies to inverse problems where the PDE solution depends linearly on the right-hand side function that models the experiment. As this method is stochastic in essence, the quality of the obtained reconstructions can vary, in particular when only a small number of combinations are used. We propose to replace the random weights traditionally used in the linear combinations of the experiments, with deterministic weights (or, encoding weights). We approach the computation of these weights as an optimal experimental design problem, and develop a Bayesian formulation for the definition and computation of encoding weights that lead to a parameter reconstruction with the least uncertainty. We call these weights A-optimal encoding weights. Our framework applies to inverse problems where the governing PDE is nonlinear with respect to the inversion parameter field. We formulate the problem in infinite dimensions and follow the optimize-then-discretize approach, devoting special attention to the discretization and the choice of numerical methods in order to achieve a computational cost that is independent of the parameter discretization. We elaborate our method for a Helmholtz inverse problem, and derive the adjoint- based expressions for the gradient of the objective function of the optimization problem for finding the A-optimal encoding weights. The proposed method is potentially attractive for real-time monitoring applications, where one can invest the effort to compute optimal weights offline, to later solve an inverse problem repeatedly, over time, at a fraction of the initial cost. We define a multi-parameter inverse problem, also called joint inverse problem, as the simultaneous inference of multiple parameter fields. In this dissertation, we concentrate on two types of multi-parameter inverse problems. In the first case, we have at our disposal a single type of observations, generated by a single physical phenomenon which depends on multiple parameters. In the second case, we utilize multiple datasets generated from physical phenomena that depend on different parameters; when the data are generated from different physics, this is a multi-physics inverse problem. The regularization of a multi-parameter inverse problem plays a critical role. It not only acts as a regularizer to the inverse problem, but can also be used to impose coupling between the inversion parameters when they are known… Advisors/Committee Members: Ghattas, Omar N. (advisor), Engquist, Bjorn (committee member), Bui-Thanh, Tan (committee member), Fomel, Sergey (committee member), Ren, Kui (committee member), Stadler, Georg (committee member).

Subjects/Keywords: Multi-parameter; Multi-physics; Multi-source; Inverse problem; Joint inverse problem; Vectorial total variation; Primal-dual Newton method; Optimal experimental design; Bayesian inverse problem

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APA (6^th Edition):

-5094-3283. (2017). Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63471

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5094-3283. “Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/63471.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5094-3283. “Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.” 2017. Web. 23 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/63471.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/63471

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

6. Petrides, Socratis. Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/2153

► This dissertation focuses on the development of fast and efficient solution schemes for the simulation of challenging problems in wave propagation phenomena. In particular, emphasis… (more)

▼ This dissertation focuses on the development of fast and efficient solution schemes for the simulation of challenging problems in wave propagation phenomena. In particular, emphasis is given on high frequency acoustic and electromagnetic problems which are characterized by localized solutions. This kind of simulations are essential in various applications, such as ultrasonic testing, laser scanning and modeling of optical laser amplifiers. In wave simulations, the computational cost of any numerical method, is directly related to the frequency. In the high-frequency regime very fine meshes have to be used in order to satisfy the Nyquist criterion and overcome the pollution effect. This often leads to prohibitively expensive problems. Numerical methods based on standard Galerkin discretizations lack pre-asymptotic discrete stability and therefore adaptive mesh refinement strategies are usually inefficient. Additionally, the indefinite nature of the wave operator makes state of the art preconditioning techniques, such as multigrid, unreliable. In this work, a promising alternative approach is followed within the framework of the discontinuous Petrov–Galerkin (DPG) method. The DPG method offers numerous advantages for our problems of interest. First and foremost, it offers mesh and frequency independent discrete stability even in the pre-asymptotic region. This is made possible by computing, on the fly, an optimal test space as a function of the trial space. Secondly, it provides a built-in local error indicator that can be used to drive adaptive refinements. Combining these two properties together, reliable adaptive refinement strategies are possible which can be initiated from very coarse meshes. Lastly, the DPG method can be viewed as a minimum residual method, and therefore it always delivers symmetric (Hermitian) positive definite stiffness matrix. This is a desirable advantage when it comes to the design of iterative solution algorithms. Conjugate Gradient based solvers can be employed which can be accelerated by domain decomposition (one- or multi- level) preconditioners for symmetric positive definite systems. Driven by the aforementioned properties of the DPG method, an adaptive multigrid preconditioning technology is developed that is applicable for a wide range of boundary value problems. Unlike standard multigrid techniques, our preconditioner involves trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. Integration of the iterative solver within the DPG adaptive procedure turns out to be crucial in the simulation of high frequency wave problems. A collection of numerical experiments for the solution of linear acoustics and Maxwell equations demonstrate the efficiency of this technology, where under certain circumstances uniform convergence with respect to the mesh size, the polynomial order and the frequency can be achieved. The construction is complemented with theoretical estimates for the condition number in the one-level setting. Advisors/Committee Members: Demkowicz, Leszek (advisor), Biros, George (committee member), Bui-Thanh, Tan (committee member), Engquist, Bjorn (committee member), Gopalakrishnan, Jay (committee member), Simmons, Chris (committee member).

Subjects/Keywords: Multilevel iterative solvers; High frequency wave propagation; High order finite element methods; Domain decomposition preconditioners

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APA (6^th Edition):

Petrides, S. (2019). Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2153

Chicago Manual of Style (16^th Edition):

Petrides, Socratis. “Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://dx.doi.org/10.26153/tsw/2153.

MLA Handbook (7^th Edition):

Petrides, Socratis. “Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.” 2019. Web. 23 Apr 2021.

Vancouver:

Petrides S. Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 23]. Available from: http://dx.doi.org/10.26153/tsw/2153.

Council of Science Editors:

Petrides S. Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/2153

7. Ding, Tian, 1986-. Numerical algorithms for inverse problems in acoustics and optics.

Degree: PhD, Mathematics, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/31504

► The objective of this dissertation is to develop computational algorithms for solving inverse coefficient problems for partial differential equations that appear in two medical imaging… (more)

▼ The objective of this dissertation is to develop computational algorithms for solving inverse coefficient problems for partial differential equations that appear in two medical imaging modalities. The aim of these inverse problems is to reconstruct optical properties of scattering media, such as biological tissues, from measured data collected on the surface of the media. In the first part of the dissertation, we study an inverse boundary value problems for the radiative transport equation. This inverse problem plays important roles in optics-based medical imaging techniques such as diffuse optical tomography and fluorescence optical tomography. We propose a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknowns, both the unknown coefficient and the corresponding transport solutions (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analytically recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm. In the second part of the dissertation, we develop a three-dimensional reconstruction algorithm for photoacoustic tomography in isotropic elastic media. There have been extensive study of photoacoustic tomography in recent years. However, all existing numerical reconstructions are developed for acoustic media in which case the model for wave propagation is the acoustic wave equation. We develop here a two-step reconstruction algorithm to reconstruct quantitatively optical properties, mainly the absorption coefficient and the Grüneisen coefficient using measured elastic wave data. The algorithm consists of an inverse source step where we reconstruct the source function in the elastic wave equation from boundary data and an inverse coefficient step where we reconstruct the coefficients of the diffusion equation using the result of the previous step as interior data. We present some numerical reconstruction results with synthetic data to demonstrate the performance of our algorithm. This is, to the best of our knowledge, the first reconstruction algorithm developed for quantitative photoacoustic imaging in elastic media. Despite the fact that we separate the dissertation into these two different parts to make each part more focused, the algorithms we developed in the two parts are closely related. In fact, if we replace the diffusion model for light propagation in photoacoustic imaging by the radiative transport model, which is often done in the literature, the algorithm we developed in the first part can be integrated into the algorithm in the second part after some minor modifications. Advisors/Committee Members: Ren, Kui (advisor), Engquist, Bjorn (committee member), Gamba, Irene Martínez (committee member), Ghattas, Omar (committee member), Gonzalez, Oscar (committee member), Wheeler, Mary Fanett (committee member).

Subjects/Keywords: Inverse transport problems; Radiative transport equation; Subspace optimization method; Quantitative photoacoustic tomography (QPAT); Singular value decomposition; Optical imaging; Diffuse optical tomography; Fluorescence optical tomography; Inverse problems; Elastic wave equation; Convolutional perfectly matched layers (C-PML); Parallel computation; BFGS algorithm; Landweber iteration; Neumann series algorithm; Quantitative thermoacoustic tomography (QTAT)

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APA (6^th Edition):

Ding, Tian, 1. (2014). Numerical algorithms for inverse problems in acoustics and optics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31504

Chicago Manual of Style (16^th Edition):

Ding, Tian, 1986-. “Numerical algorithms for inverse problems in acoustics and optics.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/31504.

MLA Handbook (7^th Edition):

Ding, Tian, 1986-. “Numerical algorithms for inverse problems in acoustics and optics.” 2014. Web. 23 Apr 2021.

Vancouver:

Ding, Tian 1. Numerical algorithms for inverse problems in acoustics and optics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/31504.

Council of Science Editors:

Ding, Tian 1. Numerical algorithms for inverse problems in acoustics and optics. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/31504

8. -9567-1322. Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/63349

► This dissertation presents new numerical algorithms and related software for the numerical solution of elliptic boundary value problems with variable coefficients on certain classes of… (more)

▼ This dissertation presents new numerical algorithms and related software for the numerical solution of elliptic boundary value problems with variable coefficients on certain classes of geometries. The target applications are problems in electrostatics, fluid mechanics, low-frequency electromagnetic and acoustic scattering. We present discretizations based on integral equation formulations which are founded in potential theory and Green's functions. Advantages of our methods include high-order discretization, optimal algorithmic complexity, mesh-independent convergence rate, high-performance and parallel scalability. First, we present a parallel software framework based on kernel independent fast multipole method (FMM) for computing particle and volume potentials in 3D. Our software is applicable to a wide range of elliptic problems such as Poisson, Stokes and low-frequency Helmholtz. It includes new parallel algorithms and performance optimizations which make our volume FMM one of the fastest constant-coefficient elliptic PDE solver on cubic domains. We show that our method is orders of magnitude faster than other N-body codes and PDE solvers. We have scaled our method to half-trillion unknowns on 229K CPU cores. Second, we develop a high-order, adaptive and scalable solver for volume integral equation (VIE) formulations of variable coefficient elliptic PDEs on cubic domains. We use our volume FMM to compute integrals and use GMRES to solve the discretized linear system. We apply our method to compute incompressible Stokes flow in porous media geometries using a penalty function to enforce no-slip boundary conditions on the solid walls. In our largest run, we achieved 0.66 PFLOP/s on 2K compute nodes of the Stampede system (TACC). Third, we develop novel VIE formulations for problems on geometries that can be smoothly mapped to a cube. We convert problems on non-regular geometries to variable coefficient problems on cubic domains which are then solved efficiently using our volume FMM and GMRES. We show that our solver converges quickly even for highly irregular geometries and that the convergence rates are independent of mesh refinement. Fourth, we present a parallel boundary integral equation solver for simulating the flow of concentrated vesicle suspensions in 3D. Such simulations provide useful insights on the dynamics of blood flow and other complex fluids. We present new algorithmic improvements and performance optimizations which allow us to efficiently simulate highly concentrated vesicle suspensions in parallel. Advisors/Committee Members: Biros, George (advisor), Engquist, Bjorn (committee member), van de Geijn, Robert A (committee member), Hughes, Thomas J R (committee member), Kloeckner, Andreas (committee member).

Subjects/Keywords: Elliptic boundary value problems; Fast multipole method; Integral equations

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APA (6^th Edition):

-9567-1322. (2017). Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63349

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Chicago Manual of Style (16^th Edition):

-9567-1322. “Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/63349.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-9567-1322. “Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries.” 2017. Web. 23 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-9567-1322. Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/63349.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-9567-1322. Fast integral equation solver for variable coefficient elliptic PDEs in complex geometries. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/63349

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

9. Nagaraj, Sriram. DPG methods for nonlinear fiber optics.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/67704

► In recent years, the Discontinuous Petrov-Galerkin (DPG) method has been the subject of significant study. It comes with a collection of desirable properties, including uniform/mesh… (more)

▼ In recent years, the Discontinuous Petrov-Galerkin (DPG) method has been the subject of significant study. It comes with a collection of desirable properties, including uniform/mesh independent stability, localizable test norms via broken test spaces, and a canonical error indicator that is incorporated as part of the solution. In this work, the DPG method is applied to problems arising in fiber optics. Accurate modeling of wave propagation in nonlinear media is an important task in fiber optics applications. Nonlinear Maxwell equations in the context of optical fibers have been studied extensively in the past. Analysis of these intensity-dependent nonlinearities are based on several simplifying approximations which result in a nonlinear Schrodinger (NLS) type equation. The Schrodinger equation from a spacetime DPG perspective is discussed. In particular, a 2nd order L² stable ultraweak formulation of the Schrodinger equation is constructed by introducing the notion of an auxiliary boundary operator. This theoretical device requires an operator-specific conforming element to develop optimal convergence rates. Numerical studies show how, modulo (expected) roundoff issues, the theoretical convergence rates are delivered. Next, the use of the DPG method in modeling and simulating optical fiber laser amplifiers with nonlinear Raman gain is studied. In this application, the interaction of two time harmonic electromagnetic fields (the signal and pump fields) governed by two weakly coupled nonlinear Maxwell equations results in the amplification phenomenon. A novel Raman gain model for describing the phenomenon is proposed and an ultra weak DPG formulation is used for the discretization of the proposed model. The nonlinearity is handled by using simple iterations between the two systems. DPG implementation of a perfectly matched layer (PML) at the exit end of the fiber is essential in this model, as is the use of sum factorization for element computations. The presented results show that the signal field indeed gains power along the fiber, thereby justifying the use of the model. Auxiliary results presented in this dissertation include the construction of DPG Fortin operators for 2nd order problems. Advisors/Committee Members: Demkowicz, Leszek (advisor), Caffarelli , Luis A (committee member), Engquist, Bjorn (committee member), Bui-Thanh, Tan (committee member), Simmons, Christopher (committee member), Babuska, Ivo M (committee member).

Subjects/Keywords: Discontinuous Petrov-Galerkin method; Nonlinear fiber optics; Mathematical modeling; Finite element analysis

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APA (6^th Edition):

Nagaraj, S. (2018). DPG methods for nonlinear fiber optics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/67704

Chicago Manual of Style (16^th Edition):

Nagaraj, Sriram. “DPG methods for nonlinear fiber optics.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/67704.

MLA Handbook (7^th Edition):

Nagaraj, Sriram. “DPG methods for nonlinear fiber optics.” 2018. Web. 23 Apr 2021.

Vancouver:

Nagaraj S. DPG methods for nonlinear fiber optics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/67704.

Council of Science Editors:

Nagaraj S. DPG methods for nonlinear fiber optics. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/67704

10. Worthen, Jennifer Anne. Inverse problems in mantle convection : models, algorithms, and applications.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/19458

► Mantle convection is the principal control on the thermal and geological evolution of the earth, including the motion of the tectonic plates, which in turn… (more)

▼ Mantle convection is the principal control on the thermal and geological evolution of the earth, including the motion of the tectonic plates, which in turn influences earthquakes, tsunamis, and volcanic eruptions. This system is governed by the equations for balance of mass, momentum, and energy for a viscous incompressible non-Newtonian fluid. Taking present-day temperatures as given, the time dependence can be neglected, eliminating the energy equation. In this case, the physics of the mantle are modeled by the Stokes equation with nonlinear rheology (the so-called forward problem). This dissertation focuses on solving the mantle convection inverse problem governed by the nonlinear Stokes forward problem with full nonlinear rheology, with an infinite-dimensional adjoint-based inversion method. The need for inverse methods in the study of mantle convection stems from the fact that the constitutive parameters are subject to uncertainty. Inversion for nonlinear rheology parameters presents considerable difficulties, which are explored in this dissertation. A spectral analysis of the Hessian operator is performed to investigate the ill-posedness of the inverse problem. The general form of the numerical eigenvalues is found to agree with that of the theoretically-derived ones (based on a model 1D Stokes problem), both of which collapse rapidly to zero, suggesting a high degree of ill-posedness. This motivates the use in this thesis of regularizations that are of Tikhonov type (favoring smooth viscosity) and total variation type (favoring piecewise-smooth viscosity). In addition, the eigenfunctions of the Hessian indicate that increasingly smaller length scales of viscosity are increasingly less observable, and that resolution decays with depth. The wide range of spatial scales of interest (varying from 1 km scale associated with plate boundaries to 10⁴ km global scales) prompts the use of adaptive mesh refinement in a parallel framework. The results show that both higher levels of nonlinearity and larger orders of magnitude of variation in the viscosity cause the inverse problem to be more ill-conditioned, increasing the difficulty of solving the inverse problem. Despite the severe ill-posedness of the inverse problem, stemming from the small number of observations compared to large number of degrees of freedom of the viscosity parameters, with the correct regularization weight and the right type of regularization, it is possible to reasonably infer information about the viscosity of the mantle, particularly in shallow regions. A number of 2D and 3D inversions are shown to demonstrate these capabilities. Advisors/Committee Members: Ghattas, Omar N. (advisor), Gurnis, Michael (committee member), Dawson, Clint (committee member), Engquist, Bjorn (committee member), Lavier, Luc (committee member).

Subjects/Keywords: Inverse mantle convection

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APA (6^th Edition):

Worthen, J. A. (2012). Inverse problems in mantle convection : models, algorithms, and applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/19458

Chicago Manual of Style (16^th Edition):

Worthen, Jennifer Anne. “Inverse problems in mantle convection : models, algorithms, and applications.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/19458.

MLA Handbook (7^th Edition):

Worthen, Jennifer Anne. “Inverse problems in mantle convection : models, algorithms, and applications.” 2012. Web. 23 Apr 2021.

Vancouver:

Worthen JA. Inverse problems in mantle convection : models, algorithms, and applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/19458.

Council of Science Editors:

Worthen JA. Inverse problems in mantle convection : models, algorithms, and applications. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/19458

11. Tsuji, Paul Hikaru. Fast algorithms for frequency domain wave propagation.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/19533

► High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling… (more)

Subjects/Keywords: Fast algorithms; Boundary element methods; Boundary integral equations; Fast multipole methods; Nedelec elements; Spectral element methods; Finite element methods; Preconditioners; Perfectly matched layers; Radiation conditions; Time harmonic; Frequency domain; Wave propagation; Maxwell's equations; Helmholtz equation; Linear elasticity; Elastic wave equation; Computational electromagnetics; Computational acoustics; Electromagnetic cloaking; Seismic velocity models; Overthrust; Salt dome

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APA (6^th Edition):

Tsuji, P. H. (2012). Fast algorithms for frequency domain wave propagation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/19533

Chicago Manual of Style (16^th Edition):

Tsuji, Paul Hikaru. “Fast algorithms for frequency domain wave propagation.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/19533.

MLA Handbook (7^th Edition):

Tsuji, Paul Hikaru. “Fast algorithms for frequency domain wave propagation.” 2012. Web. 23 Apr 2021.

Vancouver:

Tsuji PH. Fast algorithms for frequency domain wave propagation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/19533.

Council of Science Editors:

Tsuji PH. Fast algorithms for frequency domain wave propagation. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/19533

12. Xue, Zhiguang. Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI.

Degree: PhD, Geological Sciences, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/63845

► Seismic imaging in geologically complicated areas is playing an extremely important role for hydrocarbon exploration. To improve the resolution and fidelity of subsurface image or… (more)

▼ Seismic imaging in geologically complicated areas is playing an extremely important role for hydrocarbon exploration. To improve the resolution and fidelity of subsurface image or velocity, an inverse problem is usually solved for obtaining an optimal solution, with which the synthetic data can match the observations. One popular inverse problem is least-squares reverse-time migration (LSRTM), which is linear and trys to obtain an image with a better amplitude fidelity. Another popular problem is full waveform inversion (FWI), which is non-linear and attempts to invert for a velocity model with a higher resolution. Both LSRTM and FWI can be solved in the framework of local optimization, and their solutions could be iteratively updated with a gradient at each iteration, until the data mismatch reaches a desired low level. Each gradient calculation requires to solve the full wave equations twice, and many iterations are usually performed for obtaining a desired solution. The need for iterations has made LSRTM and FWI prohibitively computationally expensive. Another challenge with the two inverse problems is the low robustness caused by the poor quality of the input seismic data and a possibly poor initial model. In this dissertation, I aim at developing regularization strategies for increasing efficiency and robustness of LSRTM and FWI. First, I utilize time-shift gathers to improve the efficiency of computing gradient/RTM. Time-shift gathers can be computed on a coarse grid, and then the information along the time-shift axis can be extracted to generate a final image on a much denser grid. Second, I propose to use attenuation-compensated gradient to accelerate the convergence rate, when the energy loss has been caused by viscous media. Fractional Laplacian wave equations having separate controls over phase distortion and amplitude loss effects are solved for viscoacoustic and viscoelastic modeling. Two methods are tried to solve the spatially varying-order fractional Laplacians: 1) local pseudo-spectral method and domain decomposition; 2) low-rank wave extrapolation. Attenuation-compensated FWI is formulated and implemented based on the low-rank wave extrapolation method. Third, I apply structure-oriented smoothing (SOS) operator as a model constraint to LSRTM and FWI for improving their robustness. In LSRTM, SOS has been formulated as a shaping operator and the inverse problem is solved in the framework of shaping regularization. In FWI, SOS is implemented by imposing sparsity promotion in the seislet domain, where a velocity model can be represented by basis functions aligned along locally planar structures. Finally, I add a smoothing kernel into the FWI misfit function to improve its robustness especially when the initial model is far from the true model. The smoothing is applied in both time and space directions, to emphasize low frequencies and low wavenumbers, which could mitigate the cycle-skipping problem. Numerous synthetic examples are used to test the practical application and accuracy of the proposed… Advisors/Committee Members: Fomel, Sergey B. (advisor), Engquist, Bjorn (committee member), Ghattas, Omar (committee member), Sen, Mrinal (committee member), Zhang, Houzhu (committee member).

Subjects/Keywords: Least-squares reverse-time migration; Full waveform inversion; Efficiency; Robustness; Regularization strategy

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APA (6^th Edition):

Xue, Z. (2018). Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63845

Chicago Manual of Style (16^th Edition):

Xue, Zhiguang. “Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/63845.

MLA Handbook (7^th Edition):

Xue, Zhiguang. “Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI.” 2018. Web. 23 Apr 2021.

Vancouver:

Xue Z. Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/63845.

Council of Science Editors:

Xue Z. Regularization strategies for increasing efficiency and robustness of least-squares RTM and FWI. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/63845

13. Chang, Henry, 1976-. Modeling turbulence using optimal large eddy simulation.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-05-4988

► Most flows in nature and engineering are turbulent, and many are wall-bounded. Further, in turbulent flows, the turbulence generally has a large impact on the… (more)

▼ Most flows in nature and engineering are turbulent, and many are wall-bounded. Further, in turbulent flows, the turbulence generally has a large impact on the behavior of the flow. It is therefore important to be able to predict the effects of turbulence in such flows. The Navier-Stokes equations are known to be an excellent model of the turbulence phenomenon. In simple geometries and low Reynolds numbers, very accurate numerical solutions of the Navier-Stokes equations (direct numerical simulation, or DNS) have been used to study the details of turbulent flows. However, DNS of high Reynolds number turbulent flows in complex geometries is impractical because of the escalation of computational cost with Reynolds number, due to the increasing range of spatial and temporal scales. In Large Eddy Simulation (LES), only the large-scale turbulence is simulated, while the effects of the small scales are modeled (subgrid models). LES therefore reduces computational expense, allowing flows of higher Reynolds number and more complexity to be simulated. However, this is at the cost of the subgrid modeling problem. The goal of the current research is then to develop new subgrid models consistent with the statistical properties of turbulence. The modeling approach pursued here is that of "Optimal LES". Optimal LES is a framework for constructing models with minimum error relative to an ideal LES model. The multi-point statistics used as input to the optimal LES procedure can be gathered from DNS of the same flow. However, for an optimal LES to be truly predictive, we must free ourselves from dependence on existing DNS data. We have done this by obtaining the required statistics from theoretical models which we have developed. We derived a theoretical model for the three-point third-order velocity correlation for homogeneous, isotropic turbulence in the inertial range. This model is shown be a good representation of DNS data, and it is used to construct optimal quadratic subgrid models for LES of forced isotropic turbulence with results which agree well with theory and DNS. The model can also be filtered to determine the filtered two-point third-order correlation, which describes energy transfer among filtered (large) scales in LES. LES of wall-bounded flows with unresolved wall layers commonly exhibit good prediction of mean velocities and significant over-prediction of streamwise component energies in the near-wall region. We developed improved models for the nonlinear term in the filtered Navier-Stokes equation which result in better predicted streamwise component energies. These models involve (1) Reynolds decomposition of the nonlinear term and (2) evaluation of the pressure term, which removes the divergent part of the nonlinear models. These considerations significantly improved the performance of our optimal models, and we expect them to apply to other subgrid models as well. Advisors/Committee Members: Moser, Robert deLancey (advisor), Engquist, Bjorn (committee member), Ghattas, Omar (committee member), Hughes, Thomas J. (committee member), Raman, Venkat (committee member).

Subjects/Keywords: Turbulence simulation; Large eddy simulation; Optimal large eddy simulation; Turbulence modeling; Subgrid models; Wall-bounded turbulence; Channel flow; Three-point third-order velocity correlation; Triple velocity correlation

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APA (6^th Edition):

Chang, Henry, 1. (2012). Modeling turbulence using optimal large eddy simulation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-05-4988

Chicago Manual of Style (16^th Edition):

Chang, Henry, 1976-. “Modeling turbulence using optimal large eddy simulation.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/ETD-UT-2012-05-4988.

MLA Handbook (7^th Edition):

Chang, Henry, 1976-. “Modeling turbulence using optimal large eddy simulation.” 2012. Web. 23 Apr 2021.

Vancouver:

Chang, Henry 1. Modeling turbulence using optimal large eddy simulation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-05-4988.

Council of Science Editors:

Chang, Henry 1. Modeling turbulence using optimal large eddy simulation. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-05-4988

14. Poulson, Jack Lesly. Fast parallel solution of heterogeneous 3D time-harmonic wave equations.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-12-6622

► Several advancements related to the solution of 3D time-harmonic wave equations are presented, especially in the context of a parallel moving-PML sweeping preconditioner for problems… (more)

Subjects/Keywords: Time-harmonic; Sweeping; Preconditioner; Wave equation; Parallel; Multifrontal; Kronecker product; Translation invariance

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APA (6^th Edition):

Poulson, J. L. (2012). Fast parallel solution of heterogeneous 3D time-harmonic wave equations. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-12-6622

Chicago Manual of Style (16^th Edition):

Poulson, Jack Lesly. “Fast parallel solution of heterogeneous 3D time-harmonic wave equations.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/ETD-UT-2012-12-6622.

MLA Handbook (7^th Edition):

Poulson, Jack Lesly. “Fast parallel solution of heterogeneous 3D time-harmonic wave equations.” 2012. Web. 23 Apr 2021.

Vancouver:

Poulson JL. Fast parallel solution of heterogeneous 3D time-harmonic wave equations. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-12-6622.

Council of Science Editors:

Poulson JL. Fast parallel solution of heterogeneous 3D time-harmonic wave equations. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-12-6622

University of Texas – Austin

15. Guillen, Nestor Daniel. Regularization in phase transitions with Gibbs-Thomson law.

Degree: PhD, Mathematics, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-12-2562

► We study the regularity of weak solutions for the Stefan and Hele- Shaw problems with Gibbs-Thomson law under special conditions. The main result says that… (more)

Subjects/Keywords: Nonlinear partial differential equations; Free boundary problems; Luckhaus theorem; Hele-shaw; Stefan problem; Lipschitz; Almost minimal surfaces

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APA (6^th Edition):

Guillen, N. D. (2010). Regularization in phase transitions with Gibbs-Thomson law. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-12-2562

Chicago Manual of Style (16^th Edition):

Guillen, Nestor Daniel. “Regularization in phase transitions with Gibbs-Thomson law.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed April 23, 2021. http://hdl.handle.net/2152/ETD-UT-2010-12-2562.

MLA Handbook (7^th Edition):

Guillen, Nestor Daniel. “Regularization in phase transitions with Gibbs-Thomson law.” 2010. Web. 23 Apr 2021.

Vancouver:

Guillen ND. Regularization in phase transitions with Gibbs-Thomson law. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2021 Apr 23]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-12-2562.

Council of Science Editors:

Guillen ND. Regularization in phase transitions with Gibbs-Thomson law. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-12-2562

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