+publisher:"University of Texas – Austin" +contributor:("Waelbroeck, Francois L")

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University of Texas – Austin

1. -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, 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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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 April 11, 2021. http://dx.doi.org/10.26153/tsw/5474.

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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. 11 Apr 2021.

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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 Apr 11]. Available from: http://dx.doi.org/10.26153/tsw/5474.

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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

2. Liu, Xing, (Ph. D. in physics). Gyrokinetic simulation of pedestal turbulence using GENE.

Degree: PhD, Physics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/69104

We present here a study based on gyrokinetic simulations (using GENE) to model turbulence in the pedestals on several well-diagnosed shots: two H-modes on DIII-D and one I-mode on Alcator C-Mod. We match frequencies, power balance, and other transport characteristics in multiple channels with the observations. The observed quasi-coherent fluctuations on the DIII-D shots are identified as Micro Tearing Modes (MTM). The MTMs match frequency and power balance (together with heat loss from Electron Temperature Gradient (ETG) driven turbulence), and cause low transport in the particle, ion heat and impurity particle transport channels – consistent with observed inter-ELM evolution of ion and electron temperature, electron and impurity density or transport analysis of those channels. We find the Weakly Coherent Mode on C-Mod I-mode to be an electrostatic Ion Temperature Gradient/Impurity density gradient (ITG/Impurity) driven mode. The ITG/Impurity mode match frequency and the impurity confinement time observed on the I-mode. Electron scale turbulence, ETG, provides energy transport to match power balance. A novel concept called the transport fingerprints is used throughout this work, which greatly assists in identifying the instabilities. This work shows that the concept should be very valuable in many future investigations of pedestal turbulence. Advisors/Committee Members: Mahajan, Swadesh M. (advisor), Hazeltine, R. D. (Richard D.) (advisor), Waelbroeck, Francois L (committee member), Hallock, Gary A (committee member).

Subjects/Keywords: Gyrokinetic; Simulation; Transport; Tokamak; Fusion; Plasma

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APA (6^th Edition):

Liu, Xing, (. D. i. p. (2018). Gyrokinetic simulation of pedestal turbulence using GENE. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/69104

Chicago Manual of Style (16^th Edition):

Liu, Xing, (Ph D in physics). “Gyrokinetic simulation of pedestal turbulence using GENE.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 11, 2021. http://hdl.handle.net/2152/69104.

MLA Handbook (7^th Edition):

Liu, Xing, (Ph D in physics). “Gyrokinetic simulation of pedestal turbulence using GENE.” 2018. Web. 11 Apr 2021.

Vancouver:

Liu, Xing (Dip. Gyrokinetic simulation of pedestal turbulence using GENE. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2152/69104.

Council of Science Editors:

Liu, Xing (Dip. Gyrokinetic simulation of pedestal turbulence using GENE. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/69104

3. -1430-6073. Explosive evolution of near-threshold kinetic instabilities.

Degree: PhD, Physics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/62258

In the past, studies of waves close to marginal stability have revealed a rich variety of behavior in different physical contexts. One of the possible outcomes is an explosive growth of the mode amplitude, which forms the core of this thesis. This outcome has been predicted in both the fluid mechanics and the plasma literature. While we make some comments regarding the fluids context, in this work we focus on the near-threshold waves that are excited in kinetic systems (such as plasmas). With a few exceptions, the explosive behavior is found to asymptote to an attractor that depends on a system parameter that we shall discuss. When the mode amplitude is sufficiently large, the explosive growth loses physical meaning, and here we explore the transition between the weakly-nonlinear regime where the explosive description holds, and the strongly-nonlinear phase where the mode amplitude saturates. By investigating the phase space dynamics associated with the kinetic response, we find a link between a local flattening, or folding, of the particle distribution function and the breakdown of the explosive description. Since the explosive growth sets the stage for long-term frequency chirping modes, it is hoped that the present work can be of relevance for the prediction of the variety of chirping modes that have been observed in many experimental situations. These modes are expected to have a very significant effect on the confinement properties of fusion plasmas. Advisors/Committee Members: Berk, H. L. (advisor), Breizman, Boris N. (advisor), Morrison, Philip J (committee member), Waelbroeck, Francois L (committee member), Gamba, Irene M (committee member).

Subjects/Keywords: Physics; Plasma physics; Nuclear fusion; Nonlinear physics; Wave instabilities; Nonlinear waves

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

APA (6^th Edition):

-1430-6073. (2017). Explosive evolution of near-threshold kinetic instabilities. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/62258

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

Chicago Manual of Style (16^th Edition):

-1430-6073. “Explosive evolution of near-threshold kinetic instabilities.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 11, 2021. http://hdl.handle.net/2152/62258.

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

MLA Handbook (7^th Edition):

-1430-6073. “Explosive evolution of near-threshold kinetic instabilities.” 2017. Web. 11 Apr 2021.

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

Vancouver:

-1430-6073. Explosive evolution of near-threshold kinetic instabilities. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2152/62258.

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

Council of Science Editors:

-1430-6073. Explosive evolution of near-threshold kinetic instabilities. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/62258

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

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