+publisher:"University of Texas – Austin" +contributor:("Demkowicz, Leszek F")

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University of Texas – Austin

1. Panneer Chelvam, Prem Kumar. Computational modeling of electromagnetic waves and their interactions with microplasmas.

Degree: PhD, Aerospace Engineering, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/63458

► Development of a computational model to study the interaction of high frequency electromagnetic (EM) waves with plasmas is presented. The plasma is described using a… (more)

▼ Development of a computational model to study the interaction of high frequency electromagnetic (EM) waves with plasmas is presented. The plasma is described using a fluid model which is a multi-species, multi-temperature continuum representation with nite rate chemistry. The governing equations in the plasma module comprise the conservation laws for species number densities, electron energy and heavy species energy. The EM waves are described using the classical Maxwell's equations. The plasma governing equations are discretized in space using the finite volume method and the backward Euler method is used for temporal discretization. Maxwell's equation are represented as a second order curl-curl equation for the electric fi eld which is discretized in space using the Nédélec finite elements of first type and discretized in time using the backward Euler method. Linear system of equations arising out of the discretization is solved using Krylov subspace methods, typically the GMRES algorithm. A preconditioner based on nodal auxiliary subspaces of H(curl) space and Multigrid algorithms is used for the curl-curl equation. This preconditioner accelerates the convergence of the Krylov method and provides a mesh and time-step independent convergence rate. Preconditioners for time-harmonic Maxwell's equations is also studied. A two-level preconditioner comprising the shifted Laplacian preconditioner and deflation preconditioner is developed and its performance for different problem sizes and frequencies is reported. The developed wave-plasma model is used to simulate the following physical problems. First is the simulation of gas breakdown and transient evolution of plasma in a direct current microdischarge. The study also simulates the effect of active external electron injection into the discharge from the electrode surfaces. The time scales of switching the plasma between the pre-injection and the post-injection steady state is found to be approximately 1 [mu]s. The second problem is the simulation of a microdischarge and its interaction with a high frequency EM wave propagating in a wave guide. This study is focused on understanding different regimes in wave-plasma interactions. The nature of wave propagation in an under-dense and over-dense plasma medium is reported. The over-dense plasma medium interacts strongly with the propagating wave and the epsilon-zero resonance is observed. The final problem considered is the simulation of plasma breakdown and evolution in a two cylindrical Dielectric Resonator (DR) structure. The spatial structure of the plasma at different instants of discharge evolution is examined. The evolving plasma medium acts as a lossy medium to the propagating wave and damps the resonance in the DR structure thereby providing a pathway for stable steady state operation. Advisors/Committee Members: Raja, Laxminarayan L. (advisor), Dawson, Clint N (committee member), Demkowicz, Leszek F (committee member), Varghese, Philip L (committee member), Hallock, Gary (committee member).

Subjects/Keywords: Electromagnetic waves; Plasmas; Computational modeling; Nédélec elements of first type; Nodal auxiliary space preconditioning; Preconditioning Helmholtz equation; Microdischarges; Dielectric resonators; Microplasmas

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APA (6^th Edition):

Panneer Chelvam, P. K. (2017). Computational modeling of electromagnetic waves and their interactions with microplasmas. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63458

Chicago Manual of Style (16^th Edition):

Panneer Chelvam, Prem Kumar. “Computational modeling of electromagnetic waves and their interactions with microplasmas.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/63458.

MLA Handbook (7^th Edition):

Panneer Chelvam, Prem Kumar. “Computational modeling of electromagnetic waves and their interactions with microplasmas.” 2017. Web. 28 Feb 2021.

Vancouver:

Panneer Chelvam PK. Computational modeling of electromagnetic waves and their interactions with microplasmas. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/63458.

Council of Science Editors:

Panneer Chelvam PK. Computational modeling of electromagnetic waves and their interactions with microplasmas. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/63458

University of Texas – Austin

2. Mood, Charles Gordon. Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures.

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

URL: http://dx.doi.org/10.26153/tsw/5858

► An efficient computational model is developed to simulate the growth of vertically oriented, height-contained hydraulic fractures. A symmetric Galerkin boundary element method, used to model… (more)

▼ An efficient computational model is developed to simulate the growth of vertically oriented, height-contained hydraulic fractures. A symmetric Galerkin boundary element method, used to model the behavior of the fracture, is specialized by exploiting knowledge of the fracture surface geometry and an assumption on the approximately elliptical, vertical cross section of the fracture. This geometric knowledge is used to reduce the governing weakly singular, weak-form traction integral equation from an integral over the fracture surface to an integral along the centerline of the fracture through an analytical integration with respect to the fracture height. The fluid flow within the fracture is treated using a Galerkin finite element method to model one-dimensional flow through an arbitrarily curved channel. Under the assumption that the fluid pressure is uniform over the fracture height (as in the case of a tunnel crack) and using the cross sectional form assumed by the fracture model, a specialized, weak-form, fluid flow equation is developed and integrated analytically with respect to the fracture height. The symmetric Galerkin boundary element method and Galerkin finite element method are coupled and the resulting system is solved using a Newton-Raphson method. The fracture propagation is governed by a mixed mode-I/II growth law based on linear elastic fracture mechanics, with stress intensity factors computed directly from the degrees of freedom associated with special crack tip elements designed to capture the square root behavior near the fracture tip. This new computational model is compared to an existing coupled SGBEM-FEM model designed for general, three-dimensional, non-planar fractures to illustrate the efficiency of the new model and the dramatic speedup it offers for modeling height-contained hydraulic fracturing scenarios. The model is extended to treat various conditions typical of hydraulic fracturing design including fracture growth near completed hydraulic fractures, staged fluid injection scenarios, fracture growth in multiple, vertically stacked pay zones, and the distribution of fluid injection to a set of fractures growing from a shared wellbore. Advisors/Committee Members: Mear, Mark E. (advisor), Demkowicz, Leszek F (committee member), Gonzalez, Oscar (committee member), Landis, Chad M (committee member), Rodin, Gregory J (committee member).

Subjects/Keywords: Hydraulic fracturing; SGBEM; Boundary elements

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APA (6^th Edition):

Mood, C. G. (2019). Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5858

Chicago Manual of Style (16^th Edition):

Mood, Charles Gordon. “Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/5858.

MLA Handbook (7^th Edition):

Mood, Charles Gordon. “Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures.” 2019. Web. 28 Feb 2021.

Vancouver:

Mood CG. Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/5858.

Council of Science Editors:

Mood CG. Coupled SGBEM-FEM for efficient simulation of height-contained hydraulic fractures. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5858

University of Texas – Austin

3. Toshniwal, Deepesh. Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion.

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

URL: http://dx.doi.org/10.26153/tsw/4799

► Isogeometric Analysis or IGA was introduced by Hughes et al. (2005) to facilitate efficient design-through-analysis cycles for engineered objects. The goal of this technology is… (more)

▼ Isogeometric Analysis or IGA was introduced by Hughes et al. (2005) to facilitate efficient design-through-analysis cycles for engineered objects. The goal of this technology is the unification of geometric modeling and engineering analysis, and this is realized by exploiting smooth spline spaces used for the former as finite element spaces required for the latter. As intended, this allows the use of geometrically exact representations for the purpose of analysis. Several new spline constructions have been devised on grid-like meshes since IGA’s inception. The excellent approximation and robustness offered by them has rejuvenated the study of high order methods, and IGA has been successfully applied to myriad problems. However, an unintended consequence of adopting a splinebased design-through-analysis paradigm has been the inheritance of open problems that lie at the intersection of the fields of modeling and approximation using splines. The first two parts of this dissertation focus on two such problems: splines of non-uniform degree and splines on unstructured meshes. The last part of the dissertation is focused on phase field modeling of corrosion using splines. The development of non-uniform degree splines is driven by the observation that relaxing the requirement for a spline’s polynomial pieces to have the same degree would be very powerful in the context of both geometric modeling and IGA. This dissertation provides a complete solution in the univariate setting. A mathematically sound foundation for an efficient algorithmic evaluation of univariate non-uniform degree splines is derived. It is shown that the algorithm outputs a nonuniform degree B-spline basis and that, furthermore, it can be applied to create C¹ piecewise-NURBS of non-uniform degree with B-spline-like properties. In the bivariate setting, a theoretical study of the dimension of non-uniform degree splines on planar T-meshes and triangulations is carried out. Combinatorial lower and upper bounds on the spline space dimension are presented. For T-meshes, sufficient conditions for the bounds to coincide are provided, while for triangulations it is shown that the spline space dimension is stable in sufficiently high degree. Modeling complex geometries using only quadrilaterals leads, in general, to unstructured meshes. In locally structured regions of the mesh, smooth splines can be built following standard procedures. However, there is no canonical way of constructing smooth splines on an unstructured arrangement of quadrilateral elements. This dissertation proposes new spline constructions for the two types of unstructuredness that can be encountered – polar points (i.e., mesh vertices that are collapsed edges) and extraordinary points (i.e., mesh vertices shared by µ ≠ 4 quadrilaterals). On meshes containing polar points, smooth spline basis functions that form a convex partition of unity are built. Numerical tests presented to benchmark the construction indicate optimal approximation behavior. On meshes containing extraordinary points, two… Advisors/Committee Members: Hughes, Thomas J. R. (advisor), Speleers, Hendrik (committee member), Landis, Chad M. (committee member), Demkowicz, Leszek F. (committee member), Ghattas, Omar (committee member).

Subjects/Keywords: Isogeometric Analysis; Finite elements; Smooth splines; Unstructured meshes; Non-uniform degree splines; Dimension formula; Corrosion modeling

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APA (6^th Edition):

Toshniwal, D. (2019). Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/4799

Chicago Manual of Style (16^th Edition):

Toshniwal, Deepesh. “Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/4799.

MLA Handbook (7^th Edition):

Toshniwal, Deepesh. “Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion.” 2019. Web. 28 Feb 2021.

Vancouver:

Toshniwal D. Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/4799.

Council of Science Editors:

Toshniwal D. Isogeometric Analysis : study of non-uniform degree and unstructured splines, and application to phase field modeling of corrosion. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/4799

University of Texas – Austin

4. -0826-8493. Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena.

Degree: PhD, Engineering Mechanics, 2020, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/7729

► Simulating the interplay between atmospheric, ocean, and overland physics is often too complicated for any single model to handle due to limitations on developmental and… (more)

▼ Simulating the interplay between atmospheric, ocean, and overland physics is often too complicated for any single model to handle due to limitations on developmental and computational costs. A variety of models that specialize in specific physics exist, such as 2D and 3D shallow water and transport models in ADvanced CIRCulation (ADCIRC) and Adaptive Hydraulics (AdH) for ocean and estuarine dynamics, Gridded Surface Subsurface Hydrologic Analysis (GSSHA) and Hydrologic Engineering Center's (HEC) River Analysis System (HEC-RAS) for 2D/1D overland flow, and Global Forecast System (GFS) and North American Mesoscale Forecast System (NAM) for atmospheric physics. This dissertation explores strong and weak coupling between different models to simulate complex phenomena that they cannot individually handle. One-way weak coupling from atmospheric models to ocean or overland flow models is already ubiquitous in the form of usage of meteorological forcing on the flow models. Coupling between 2D and 3D shallow water models including baroclinic transport, and between shallow water and overland flow models remain relatively unexplored. Strong coupling between 2D and 3D shallow water and baroclinic transport models is the major focus of this work. On studying multiple verification and validation cases, and applications testing the limits of 2D-3D coupling, it is concluded that strongly coupled 2D and 3D shallow water and transport models are conservative, stable, accurate, and convergent in line with theory, and are able to simulate physics that solely 2D or 3D models cannot in general. They also enable building computationally cheaper 3D models by enabling replacement of non-critical 3D regions with 2D subdomains. The second focus of this work is weak one/two-way coupling between 2D shallow water and 2D/1D overland flow models, which are in turn driven by one-way coupling from an atmospheric model. Two-way coupled models are shown to be conservative and capable of simulating compound flooding effects. An application of the coupled models to simulate flooding in Houston, Texas, due to Hurricane Harvey of August 2017 is presented, the results of which demonstrate the suitability of the models for use in high-fidelity forecasts of flooding during hurricanes, after some improvements. Advisors/Committee Members: Dawson, Clinton N. (advisor), Trahan, Corey J (committee member), Demkowicz, Leszek F (committee member), Heimbach, Patrick (committee member), Bui-Thanh, Tan (committee member).

Subjects/Keywords: 2D-3D coupling; Strong and weak coupling; Shallow water equations; Diffusive wave equations; Primitive equations; Wetting and drying; Baroclinic flow; Compound flooding

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APA (6^th Edition):

-0826-8493. (2020). Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/7729

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Chicago Manual of Style (16^th Edition):

-0826-8493. “Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena.” 2020. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/7729.

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

MLA Handbook (7^th Edition):

-0826-8493. “Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena.” 2020. Web. 28 Feb 2021.

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

Vancouver:

-0826-8493. Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2020. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/7729.

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

Council of Science Editors:

-0826-8493. Coupled atmospheric, hydrodynamic, and hydrologic models for simulation of complex phenomena. [Doctoral Dissertation]. University of Texas – Austin; 2020. Available from: http://dx.doi.org/10.26153/tsw/7729

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

University of Texas – Austin

5. -5667-4520. Topographic amplification of seismic motion.

Degree: PhD, Civil Engineering, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/47170

► Seismic hazard assessment relies increasingly on the numerical simulation of ground motion, since recent advances in numerical methods and computer architectures have made it ever… (more)

▼ Seismic hazard assessment relies increasingly on the numerical simulation of ground motion, since recent advances in numerical methods and computer architectures have made it ever more practical to obtain the surface response to idealized or realistic seismic events. The key motivation stems from the need to assess the performance of sensitive components of the civil infrastructure (nuclear power plants, bridges, lifelines, etc.), when subjected to realistic scenarios of seismic events. To date, most simulation tools rely on a flat-earth assumption, which ignores topography and its effects on seismic motion amplification. In an attempt to narrow the gap between modeling and physical reality, in this dissertation we study systematically the effects topographic features have on the surface motion when compared against motion obtained using a at-surface assumption. To this end, we discuss first an integrated approach that deploys best-practice tools for simulating seismic events in arbitrarily heterogeneous formations, while also accounting for topography. Specifically, we describe an explicit forward wave solver based on a hybrid formulation that couples a single-field formulation for the computational domain with an unsplit mixed-field formulation for Perfectly-Matched-Layers (PMLs or M-PMLs) used to limit the computational domain. We use spectral elements for spatial discretization, and an efficient Runge-Kutta explicit solver for time integration. Due to the material heterogeneity and the contrasting discretization needs it imposes, we also use an adaptive Runge-Kutta-Fehlberg time-marching scheme to optimally adjust the time step so that the local truncation error rests below a predefined tolerance. To account for the seismic load, we use the Domain- Reduction-Method to introduce the incoming seismic motion in the computational domain whenever the introduction of the actual seismic source would make the computational domain unnecessarily large. Lastly, we couple the DRM with the PMLs to complete the seismic motion simulation engine. Using the developed toolchain, we then report results of parametric studies involving idealized topographic features, which show motion amplification that depends, as expected, on the relation between the topographic features' characteristics and the dominant wavelength. More interestingly, we also report motion de-amplification patterns. Given the prevalence of lower dimensionality models for seismic risk assessment, we also report on the effects model dimensionality has in the presence of heterogeneity and topography. The results reported herein, support the thesis that, for purposes of seismic risk assessment, topography and heterogeneity are best treated when fully accounted for in three-dimensional models. Even this is only a first and necessary step towards higher fidelity modeling of seismic motion effects. Advisors/Committee Members: Kallivokas, Loukas F. (advisor), Assimaki, Dominic (committee member), Demkowicz, Leszek F. (committee member), Manuel, Lance (committee member), Stokoe II, Kenneth H. (committee member), Tassoulas, John L. (committee member).

Subjects/Keywords: Topographic amplification; Seismic motion; Earthquake engineering; Wave propagation; Site effects; Absorbing boundary conditions; Seismic simulations; Seismic response; Site response; Seismic effects; Topographic effects

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APA (6^th Edition):

-5667-4520. (2017). Topographic amplification of seismic motion. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/47170

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

Chicago Manual of Style (16^th Edition):

-5667-4520. “Topographic amplification of seismic motion.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/47170.

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

MLA Handbook (7^th Edition):

-5667-4520. “Topographic amplification of seismic motion.” 2017. Web. 28 Feb 2021.

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

Vancouver:

-5667-4520. Topographic amplification of seismic motion. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/47170.

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

Council of Science Editors:

-5667-4520. Topographic amplification of seismic motion. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/47170

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

University of Texas – Austin

6. Fathi, Arash. Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments.

Degree: PhD, Civil, Architectural, and Environmental Engineering, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/30515

► We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to… (more)

▼ We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations. Advisors/Committee Members: Kallivokas, Loukas F. (advisor), Dawson, Clinton N (committee member), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Manuel, Lance (committee member), Stokoe II, Kenneth H (committee member).

Subjects/Keywords: Full-waveform inversion; Seismic inversion; Inverse medium problem; PDE-constrained optimization; Elastic wave propagation; Perfectly-matched-layer (PML); Field data; Subsurface imaging

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APA (6^th Edition):

Fathi, A. (2015). Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/30515

Chicago Manual of Style (16^th Edition):

Fathi, Arash. “Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/30515.

MLA Handbook (7^th Edition):

Fathi, Arash. “Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments.” 2015. Web. 28 Feb 2021.

Vancouver:

Fathi A. Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/30515.

Council of Science Editors:

Fathi A. Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/30515

7. -8221-3645. Subsurface elastic wave energy focusing based on a time reversal concept.

Degree: PhD, Civil Engineering, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/61529

► In the context of wave propagation, time-reversal refers to the invariance of the wave equation when the direction of traversing the time line is reversed.… (more)

▼ In the context of wave propagation, time-reversal refers to the invariance of the wave equation when the direction of traversing the time line is reversed. To date, there have been several applications rooted in the time-reversal concept, primarily in acoustics and in electromagnetics, and in settings that typically involve closed, finite, domains. In recent times, the concept has been predominantly used for steering and focusing wave energy in medical therapeutics. The extension of the time-reversal concept to elastodynamics, particularly in unbounded domains, entails challenges: the presence of two velocities and two body wave types, the presence of surface waves, the unboundness of the host domain, and aperture constraints, all conspire to limit or weaken wave focusing. This dissertation concentrates on a computational study for assessing the feasibility of focusing elastic waves to one or multiple subsurface targets, based on the time-reversal concept. Of particular interest is the focusing of wave energy to subterranean geologic formations, embedded within heterogeneous hosts. The motivation stems from potential applications to wave-based enhanced oil recovery, though other applications also stand to benefit. We report on a study that systematically assesses each and every limitation that is present when a small number of surface motion records are time-reversed and broadcast back into a heterogenous halfspace, aimed at the illumination of subsurface targets. We report the results of numerical experiments in two and three dimensions, and the impact of the limitations on the focusing resolution. All in all, despite the difficulties imposed by the physical setting, we conclude that focusing of elastic wave energy is feasible and competitive when compared against inverse source methods with similar targeting or focusing goals. Advisors/Committee Members: Kallivokas, Loukas F (advisor), Fomel, Sergey B (committee member), Stokoe, Kenneth H (committee member), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Tassoulas, John L (committee member).

Subjects/Keywords: Wave focusing; Time-reversal; Wave propagation; PML; Absorbing boundary condition

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APA (6^th Edition):

-8221-3645. (2017). Subsurface elastic wave energy focusing based on a time reversal concept. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/61529

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

Chicago Manual of Style (16^th Edition):

-8221-3645. “Subsurface elastic wave energy focusing based on a time reversal concept.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/61529.

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

MLA Handbook (7^th Edition):

-8221-3645. “Subsurface elastic wave energy focusing based on a time reversal concept.” 2017. Web. 28 Feb 2021.

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

Vancouver:

-8221-3645. Subsurface elastic wave energy focusing based on a time reversal concept. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/61529.

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

Council of Science Editors:

-8221-3645. Subsurface elastic wave energy focusing based on a time reversal concept. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/61529

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

8. -4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows.

Degree: PhD, Engineering Mechanics, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5476

► As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD)… (more)

▼ As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD) tools in aerospace and research facilities are widely used to evaluate the aerodynamic performance of aircraft or wings. Weather forecasts are highly dependent on numerical weather prediction (NWP) model. However, it is still difficult to simulate the complex physical phenomena of a wide range of length and time scales with modern computational resources. In this study, we develop a robust, efficient and high-order accurate numerical methods and techniques to tackle the challenges. First, we use high-order spatial discretization using (hybridized) discontinuous Galerkin (DG) methods. The DG method combines the advantages of finite volume and finite element methods. As such, it is well-suited to problems with large gradients including shocks and with complex geometries, and large-scale simulations. However, DG typically has many degrees-of-freedoms. To mitigate the expense, we use hybridized DG (HDG) method that introduces new “trace unknowns” on the mesh skeleton (mortar interfaces) to eliminate the local “volume unknowns” with static condensation procedure and reduces globally coupled system when implicit time-stepping is required. Also, since the information between the elements is exchanged through the mesh skeleton, the mortar interfaces can be used as a glue to couple multi-phase regions, e.g., solid and fluid regions, or non-matching grids, e.g., a rotating mesh and a stationary mesh. That is the HDG method provides an efficient and flexible coupling environment compared to standard DG methods. Second, we develop an HDG-DG IMEX scheme for an efficient time integrating scheme. The idea is to divide the governing equations into stiff and nonstiff parts, implicitly treat the former with HDG methods, and explicitly treat the latter with DG methods. The HDG-DG IMEX scheme facilitates high-order temporal and spatial solutions, avoiding too small a time step. Numerical results show that the HDG-DG IMEX scheme is comparable to an explicit Runge-Kutta DG scheme in terms of accuracy while allowing for much larger timestep sizes. We also numerically observe that IMEX HDG-DG scheme can be used as a tool to suppress the high-frequency modes such as acoustic waves or fast gravity waves in atmospheric or ocean models. In short, IMEX HDG-DG methods are attractive for applications in which a fast and stable solution is important while permitting inaccurate processing of the fast modes. Third, we also develop an EXPONENTIAL DG scheme for an efficient time integrators. Similar to the IMEX method, the governing equations are separated into linear and nonlinear parts, then the two parts are spatially discretized with DG methods. Next, we analytically integrate the linear term and approximate the nonlinear term with respect to time. This method accurately handles the fast wave modes in the linear operator. To efficiently evaluate a matrix exponential, we employ… Advisors/Committee Members: Bui-Thanh, Tan (advisor), Bisetti, Fabrizio (committee member), Willcox, Karen E (committee member), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Arbogast, Todd (committee member).

Subjects/Keywords: Discontinuous Galerkin; DG; HDG; Hybridized DG; IMEX; Implicit-explicit; Exponential time integrator; ALE; Arbitrary Lagrangian-Eulerian; Sliding mesh; Nonconforming mesh; Degenerate elliptic equation; Mortar; Scalability

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APA (6^th Edition):

-4649-9727. (2019). High-order (hybridized) discontinuous Galerkin method for geophysical flows. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5476

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Chicago Manual of Style (16^th Edition):

-4649-9727. “High-order (hybridized) discontinuous Galerkin method for geophysical flows.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/5476.

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MLA Handbook (7^th Edition):

-4649-9727. “High-order (hybridized) discontinuous Galerkin method for geophysical flows.” 2019. Web. 28 Feb 2021.

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Vancouver:

-4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/5476.

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Author name may be incomplete

Council of Science Editors:

-4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5476

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

University of Texas – Austin

9. -6430-5266. A hybridized discontinuous Galerkin method for nonlinear dispersive water waves.

Degree: PhD, Engineering Mechanics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/47354

► Simulation of water waves near the coast is an important problem in different branches of engineering and mathematics. For mathematical models to be valid in… (more)

▼ Simulation of water waves near the coast is an important problem in different branches of engineering and mathematics. For mathematical models to be valid in this region, they should include nonlinear and dispersive properties of the corresponding waves. Here, we study the numerical solution to three equations for modeling coastal water waves using the hybridized discontinuous Galerkin method (HDG). HDG is known to be a more efficient and in certain cases a more accurate alternative to some other discontinuous Galerkin methods, such as local DG. The first equation that we solve here is the Korteweg-de Vries equation. Similar to common HDG implementations, we first express the approximate variables and numerical fluxes in each element in terms of the approximate traces of the scalar variable, and its first derivative. These traces are assumed to be single-valued on each face. We next impose the conservation of the numerical fluxes via two sets of equations on the element boundaries. We solve this equation by Newton-Raphson method. We prove the stability of the proposed method for a proper choice of stabilization parameters. Through numerical examples, we observe that for a mesh with kth order elements, the computed variable and its first and second derivatives show optimal convergence at order k + 1 in both linear and nonlinear cases, which improves upon previously employed techniques. Next, we consider solving the fully nonlinear irrotational Green-Naghdi equation. This equation is often used to simulate water waves close to the shore, where there are significant dispersive and nonlinear effects involved. To solve this equation, we use an operator splitting method to decompose the problem into a dispersive part and a hyperbolic part. The dispersive part involves an implicit step, which has regularizing effects on the solution of the problem. On the other hand, for the hyperbolic sub-problem, we use an explicit hybridized DG method. Unlike the more common implicit version of the HDG, here we start by solving the flux conservation condition for the numerical traces. Afterwards, we use these traces in the original PDEs to obtain the internal unknowns. This process involves Newton iterations at each time step for computing the numerical traces. Next, we couple this solver with the dispersive solver to obtain the solution to the Green-Naghdi equation. We then solve a set of numerical examples to verify and validate the employed technique. In the first example we show the convergence properties of the numerical method. Next, we compare our results with a set of experimental data for nonlinear water waves in different situations. We observe close to optimal convergence rates and a good agreement between our numerical results and the experimental data. Advisors/Committee Members: Dawson, Clinton N. (advisor), Demkowicz, Leszek F (committee member), Gamba, Irene M (committee member), Hodges, Ben R (committee member), Landis, Chad M (committee member), Raja, Laxminarayan L (committee member).

Subjects/Keywords: Discontinuous Galerkin; DG; Hybridized; HDG; Nonlinear shallow water; Green-Naghdi; NSWE; GN; Galerkin method; Water waves; Nonlinear water waves; Dispersive water waves; Water wave simulation; Coastal water waves modeling; Korteweg-de Vries equation

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APA (6^th Edition):

-6430-5266. (2017). A hybridized discontinuous Galerkin method for nonlinear dispersive water waves. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/47354

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Chicago Manual of Style (16^th Edition):

-6430-5266. “A hybridized discontinuous Galerkin method for nonlinear dispersive water waves.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/47354.

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

MLA Handbook (7^th Edition):

-6430-5266. “A hybridized discontinuous Galerkin method for nonlinear dispersive water waves.” 2017. Web. 28 Feb 2021.

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

Vancouver:

-6430-5266. A hybridized discontinuous Galerkin method for nonlinear dispersive water waves. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/47354.

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

Council of Science Editors:

-6430-5266. A hybridized discontinuous Galerkin method for nonlinear dispersive water waves. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/47354

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

10. -5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications.

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

URL: http://hdl.handle.net/2152/46503

► The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability,… (more)

▼ The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability, sand production, waste deposition, hydraulic fracturing, CO₂ sequestration, and hydrocarbon recovery. From a pure computational point of view, such a coupling can be quite a challenging and complicated task. This stems from the fact that the constitutive equations governing geomechanical deformations are different in nature from those governing porous media flow. The geomechanical effects account for the influence of deformations in the porous media caused due to the pore pressure and can be very important especially in the case of stress-sensitive and fractured reservoirs. Considering that fractures are very much prevalent in the porous media and they have strong influence on the flow profiles, it is important to study coupled geomechanics and flow problems in fractured reservoirs. In this work, we pursue three main objectives: first, to rigorously design and analyze iterative and explicit coupling algorithms for coupling flow and geomechanics in both poro-elasitc and fractured poro-elastic reservoirs. The analysis of iterative coupling schemes relies on studying the equations satisfied by the difference of iterates and using a Banach contraction argument to derive geometric convergence (Banach fixed-point contraction) results. The analysis of explicit coupling schemes result in analogous stability estimates. In this work, conformal Galerkin is used for mechanics, and a mixed formulation, including the Multipoint Flux Mixed Finite Element method as a special case, is used for the flow model. For fractured poro-elastic media, our iteratively coupled schemes are adaptations, due to the presence of fractures, of the classical fixed stress-splitting scheme, in which fractures are treated as possibly non-planar interfaces. The second main objective in this work is to exploit the different time scales of the mechanics and flow problems. Due to its physical nature, the geomechanics problem can cope with a coarser time step compared to the flow problem. This makes the multirate coupling scheme, the one in which the flow problem takes several (finer) time steps within the same coarse mechanics time step, a natural candidate in this setting. Inspired by that, we rigorously formulate and analyze convergence properties of both multirate iterative and explicit coupling schemes in both poro-elastic and fractured poro-elastic reservoirs. In addition, our theoretically derived Banach contraction estimates are validated against numerical simulations. The third objective in this work is to optimize the solution strategy of the nonlinear flow model in coupled flow and mechanics schemes. The global inexact Newton method, combined with the line search backtracking algorithm along with heuristic forcing functions, can be efficiently employed to reduce the number of flow linear iterations, and hence, the overall CPU run time. We first validate… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Demkowicz, Leszek F. (committee member), Delshad, Mojdeh (committee member), Dhillon, Inderjit (committee member), Kumar, Kundan (committee member).

Subjects/Keywords: Poroelasticity; Biot system; Fixed-stress split iterative coupling; Undrained split iterative coupling; Explicit coupling; Single rate scheme; Multirate scheme; Banach fixed-point contraction; Fractured poroelastic media; A priori error estiamtes; Global inexact Newton methods

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APA (6^th Edition):

-5603-2533. (2016). Efficient algorithms for flow models coupled with geomechanics for porous media applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46503

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Chicago Manual of Style (16^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/46503.

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Author name may be incomplete

MLA Handbook (7^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Web. 28 Feb 2021.

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Author name may be incomplete

Vancouver:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/46503.

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

Council of Science Editors:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/46503

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

University of Texas – Austin

11. -5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.

Degree: PhD, Aerospace Engineering, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5474

► The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking,… (more)

▼ The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp – scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner Advisors/Committee Members: Bui-Thanh, Tan (advisor), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Raja, Laxminarayan L (committee member), Shadid, John N (committee member), Waelbroeck, Francois L (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hybridized discontinuous Galerkin; Fast solvers; Multigrid; Multilevel; MHD; Domain decomposition

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APA (6^th Edition):

-5494-1880. (2019). Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5474

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Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/5474.

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Author name may be incomplete

MLA Handbook (7^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Web. 28 Feb 2021.

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

Vancouver:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/5474.

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Author name may be incomplete

Council of Science Editors:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5474

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Author name may be incomplete

University of Texas – Austin

12. Taus, Matthias Franz. Isogeometric Analysis for boundary integral equations.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32824

► Since its emergence, Isogeometric Analysis (IgA) has initiated a revolution within the field of Finite Element Methods (FEMs) for two reasons: (i) geometry descriptions originating… (more)

▼ Since its emergence, Isogeometric Analysis (IgA) has initiated a revolution within the field of Finite Element Methods (FEMs) for two reasons: (i) geometry descriptions originating from Computer Aided Design (CAD) can be used directly for analysis purposes, and (ii) the availability of smooth exact geometry descriptions and smooth basis functions can be used to develop new, highly accurate and highly efficient numerical methods. Whereas in FEMs the first issue is still open, it has already been shown that Isogeometric BEMs (IBEMs) provide a complete design-through-analysis framework. However, in contrast to FEMs, the effect of smoothness provided by IgA has not yet been explored in IBEMs. In this dissertation, we address this aspect of IgA. We show that the smoothness and exactness properties provided by the IgA framework can be used to design highly accurate and highly efficient BEMs which are not accessible with conventional BEMs. We develop Collocation IBEMs on piecewise smooth geometries. This allows us to show that IBEMs converge in the expected rates and result in system matrices with mesh-independent condition numbers. The latter property is particularly beneficial for large-scale problems that require iterative linear solvers. However, using conventional Collocation BEMs, this approach is not accessible because hyper-singular integrals have to be evaluated. In contrast, using Collocation IBEMs, the smoothness properties of the IgA framework can be used to regularize the hyper-singular integrals and reduce them to weakly singular integrals which can be evaluated using well-known techniques. We perform several numerical examples on canonical shapes to show these results. In addition, we use well-known mathematical results to develop a sound theoretical foundation to some of our methods, a result that is very rare for Collocation discretizations. Finally, using the exactness of IgA geometry descriptions, we design Patch Tests that allow one to rigorously test IBEM implementations. We subject our implementation to these Patch Tests which not only shows the reliability of our method but also shows that IBEMs can be as accurate as machine precision. We apply our IBEMs to Laplace's equation and the equations of linear elasticity. In addition, input files for our implementation can be automatically obtained from commercial CAD packages. These practical aspects allow us to apply IBEMs to analyze a propeller under a wind load. Advisors/Committee Members: Rodin, G. J. (Gregory J.) (advisor), Hughes, Thomas J. R. (advisor), Demkowicz, Leszek F. (committee member), Biros, George (committee member), Sayas, Francisco Javier (committee member).

Subjects/Keywords: Boundary integral equations; Isogeometric Analysis; Boundary element methods; Isogeometric boundary element methods; Collocation

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APA (6^th Edition):

Taus, M. F. (2015). Isogeometric Analysis for boundary integral equations. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32824

Chicago Manual of Style (16^th Edition):

Taus, Matthias Franz. “Isogeometric Analysis for boundary integral equations.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/32824.

MLA Handbook (7^th Edition):

Taus, Matthias Franz. “Isogeometric Analysis for boundary integral equations.” 2015. Web. 28 Feb 2021.

Vancouver:

Taus MF. Isogeometric Analysis for boundary integral equations. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/32824.

Council of Science Editors:

Taus MF. Isogeometric Analysis for boundary integral equations. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32824

University of Texas – Austin

13. -5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry.

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

URL: http://hdl.handle.net/2152/68171

► Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work,… (more)

▼ Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Wheeler, Mary F (committee member), Ghattas, Omar (committee member), Demkowicz, Leszek F (committee member), Hesse, Marc A (committee member).

Subjects/Keywords: Multiphase flow; Porous media; Mixed finite element; H(div)-approximation; Arbogast-Tao element; Arbogast-Correa element; Direct serendipity element; Serendipity element; Enriched Galerkin method; Entropy viscosity stabilization; Capillary flux reconstruction; Heterogeneous capillary pressure; Two-phase flow

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APA (6^th Edition):

-5063-5889. (2017). Numerical analysis of multiphase flows in porous media on non-rectangular geometry. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68171

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Chicago Manual of Style (16^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/68171.

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MLA Handbook (7^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Web. 28 Feb 2021.

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

Vancouver:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/68171.

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

Council of Science Editors:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/68171

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

14. Mirabito, Christopher Michael. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.

Degree: PhD, Computational and Applied Mathematics, 2011, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2011-08-4130

► Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes,… (more)

▼ Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events. Advisors/Committee Members: Dawson, Clinton N. (advisor), Demkowicz, Leszek F. (committee member), Gamba, Irene M. (committee member), Ghattas, Omar (committee member), Kim, Wonsuck (committee member).

Subjects/Keywords: Shallow water equations; Sediment transport; Local discontinuous Galerkin; A priori estimates; Finite elements; Bed morphology

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APA (6^th Edition):

Mirabito, C. M. (2011). Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-08-4130

Chicago Manual of Style (16^th Edition):

Mirabito, Christopher Michael. “Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.” 2011. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2011-08-4130.

MLA Handbook (7^th Edition):

Mirabito, Christopher Michael. “Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.” 2011. Web. 28 Feb 2021.

Vancouver:

Mirabito CM. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2011. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4130.

Council of Science Editors:

Mirabito CM. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. [Doctoral Dissertation]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4130

University of Texas – Austin

15. Li, Jun, 1977-. A computational model for the diffusion coefficients of DNA with applications.

Degree: PhD, Computational and Applied Mathematics, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-05-1098

► The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties… (more)

▼ The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties at the base-pair level. One promising way to predict these properties as a function of sequence is to model DNA with a set of base-pair parameters that describe the local stacking of the different possible base-pair step combinations. In this dissertation research, we develop and study a computational model for predicting the diffusion coefficients of short, relatively rigid DNA fragments from the sequence and the base-pair parameters. We focus on diffusion coefficients because various experimental methods have been developed to measure them. Moreover, these coefficients can also be computed numerically from the Stokes equations based on the three-dimensional shape of the macromolecule. By comparing the predicted diffusion coefficients with experimental measurements, we can potentially obtain refined estimates of various base-pair parameters for DNA. Our proposed model consists of three sub-models. First, we consider the geometric model of DNA, which is sequence-dependent and controlled by a set of base-pair parameters. We introduce a set of new base-pair parameters, which are convenient for computation and lead to a precise geometric interpretation. Initial estimates for these parameters are adapted from crystallographic data. With these parameters, we can translate a DNA sequence into a curved tube of uniform radius with hemispherical end caps, which approximates the effective hydrated surface of the molecule. Second, we consider the solvent model, which captures the hydrodynamic properties of DNA based on its geometric shape. We show that the Stokes equations are the leading-order, time-averaged equations in the particle body frame assuming that the Reynolds number is small. We propose an efficient boundary element method with a priori error estimates for the solution of the exterior Stokes equations. Lastly, we consider the diffusion model, which relates our computed results from the solvent model to relevant measurements from various experimental methods. We study the diffusive dynamics of rigid particles of arbitrary shape which often involves arbitrary cross- and self-coupling between translational and rotational degrees of freedom. We use scaling and perturbation analysis to characterize the dynamics at time scales relevant to different classic experimental methods and identify the corresponding diffusion coefficients. In the end, we give rigorous proofs for the convergence of our numerical scheme and show numerical evidence to support the validity of our proposed models by making comparisons with experimental data. Advisors/Committee Members: Gonzalez, Oscar, 1968- (advisor), Demkowicz, Leszek F. (committee member), Makarov, Dmitrii E. (committee member), Rodin, Gregory J. (committee member), van de Geijn, Robert A. (committee member).

Subjects/Keywords: Computational; Diffusion coefficient; Diffusion tensor; Stokes law; Stokes-Einstein relation; DNA; Base-pair parameters; Stokes equations; Convection-diffusion equation; Boundary integral formulation; Surface potential; Nyström approximation; Singularity subtraction; Integral equations of the second kind; Single-layer potential; Double-layer potential; Parallel surface

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Li, Jun, 1. (2010). A computational model for the diffusion coefficients of DNA with applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-05-1098

Chicago Manual of Style (16^th Edition):

Li, Jun, 1977-. “A computational model for the diffusion coefficients of DNA with applications.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2010-05-1098.

MLA Handbook (7^th Edition):

Li, Jun, 1977-. “A computational model for the diffusion coefficients of DNA with applications.” 2010. Web. 28 Feb 2021.

Vancouver:

Li, Jun 1. A computational model for the diffusion coefficients of DNA with applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-1098.

Council of Science Editors:

Li, Jun 1. A computational model for the diffusion coefficients of DNA with applications. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-1098

University of Texas – Austin

16. Kucukcoban, Sezgin. The inverse medium problem in PML-truncated elastic media.

Degree: PhD, Civil Engineering, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-12-2183

► We introduce a mathematical framework for the inverse medium problem arising commonly in geotechnical site characterization and geophysical probing applications, when stress waves are used… (more)

▼ We introduce a mathematical framework for the inverse medium problem arising commonly in geotechnical site characterization and geophysical probing applications, when stress waves are used to probe the material composition of the interrogated medium. Specifically, we attempt to recover the spatial distribution of Lame's parameters ( and μ) of an elastic semi-infinite arbitrarily heterogeneous medium, using surface measurements of the medium's response to prescribed dynamic excitations. The focus is on characterizing near-surface deposits, and to this end, we develop a method that is implemented directly in the time-domain, is driven by the full waveform response collected at receivers on the surface, while the domain of interest is truncated using Perfectly-Matched-Layers (PMLs) to limit the originally semi-infinite extent of the physical domain. There are two key issues associated with the problem at hand: (a) the forward problem, namely the numerical simulation of the wave motion in the domain of interest; and (b) the framework and strategies for tackling the inverse problem. To address the forward problem, it is necessary that the domain of interest be truncated, and the resulting finite domain be forced to mimic the physics of the original problem: to this end, we introduce unsplit-field PMLs, and develop and implement two new formulations, one fully-mixed and one hybrid (mixed coupled with a non-mixed approach) that model wave motion within the, now PML-truncated, domain. To address the inverse problem, we adopt a partial-differential-equation-constrained optimization framework that results in the usual triplet of an initial-and-boundary-value forward problem, a final-and-boundary-value adjoint problem, and a time-independent boundary-value control problem. This triplet of boundary-value-problems is used to guide the optimizer to the target profile of the spatially distributed Lame parameters. Given the multiplicity of solutions, we assist the optimizer, by deploying regularization schemes, continuation schemes (regularization factor and source-frequency content), as well as a physics-driven simple procedure to bias the search directions. We report numerical examples attesting to the quality, stability, and efficiency of the forward wave modeling. We also report moderate success with numerical experiments targeting inversion of both smooth and sharp profiles in two dimensions. Advisors/Committee Members: Kallivokas, Loukas F. (advisor), Demkowicz, Leszek F. (committee member), Ghattas, Omar (committee member), Kinnas, Sypros A. (committee member), Rodin, Gregory J. (committee member), Torres-Verdin, Carlos (committee member).

Subjects/Keywords: Wave propagation; PML; Mixed FEM; Time-domain elastodynamics; Full-waveform-based inversion; Elastic media; Perfectly matched layers

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kucukcoban, S. (2010). The inverse medium problem in PML-truncated elastic media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-12-2183

Chicago Manual of Style (16^th Edition):

Kucukcoban, Sezgin. “The inverse medium problem in PML-truncated elastic media.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2010-12-2183.

MLA Handbook (7^th Edition):

Kucukcoban, Sezgin. “The inverse medium problem in PML-truncated elastic media.” 2010. Web. 28 Feb 2021.

Vancouver:

Kucukcoban S. The inverse medium problem in PML-truncated elastic media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-12-2183.

Council of Science Editors:

Kucukcoban S. The inverse medium problem in PML-truncated elastic media. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-12-2183

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