Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for +publisher:"University of Texas – Austin" +contributor:("Shadid, John"). Showing records 1 – 2 of 2 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Texas – Austin

1. -6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics.

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

Discontinuous Galerkin (DG) methods combine the advantages of classical finite element and finite volume methods. Like finite volume methods, through the use of discontinuous spaces in the discrete functional setting, we automatically have local conservation, an essential property for a numerical method to behave well when applied to hyperbolic conservation laws. Like classical finite element methods, DG methods allow for higher order approximations with compact stencils. For time-dependent problems with implicit time stepping and for steady-state problems, DG methods give a larger globally coupled linear system than continuous Galerkin methods (especially for three dimensional problems and low polynomial orders). The primary motivation of the hybridized (or hybridizable) discontinuous Galerkin (HDG) methods is to reduce the number of globally coupled unknowns in DG methods when implicit time stepping or direct-to-steady-state solutions are desired. This is accomplished by the introduction of new “trace unknowns” defined on the mesh skeleton, the definition of one-sided numerical fluxes, and the enforcement of local conservation. This results in a globally coupled linear system where the local “volume unknowns” can be eliminated in a Schur complement procedure, resulting in a reduced globally coupled system in terms of only the trace unknowns. Magnetohydrodynamics (MHD) is the study of the flow of electrically conducting fluids under the influence of magnetic fields. The MHD equations are used to describe important physical phenomena including laboratory plasmas (plasma confinement in fusion energy devices), astrophysical plasmas (solar coronas, planetary magnetospheres) and liquid metal flows (metallurgy processes, the Earth’s molten core, cooling for nuclear reactors). Incompressible MHD, which is the main focus of this work, is relevant in low Lundquist number liquid metals, in high Lundquist number, large guide field fusion plasmas, and in low Mach number compressible flows. The equations of MHD are highly nonlinear, and are characterized by physical phenomena spanning wide ranges of length and time scales. For numerical methods, this presents challenges in both spatial and temporal discretization. In terms of temporal discretization, fully implicit numerical methods are attractive in their robustness; they allow for stable, high-order time integration over long time scales of interest. Advisors/Committee Members: Bui-Thanh, Tan (advisor), Arbogast, Todd (committee member), Demkowicz, Leszek (committee member), Ghattas, Omar (committee member), Shadid, John (committee member), Waelbroeck, François (committee member).

Subjects/Keywords: Finite element methods; Discontinuous Galerkin methods; Hybridized discontinuous Galerkin methods; Stokes equations; Oseen equations; Magnetohydrodynamics; Resistive magnetohydrodynamics

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th Edition):

-6327-2527. (2018). Hybridized discontinuous Galerkin methods for magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2865

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

Chicago Manual of Style (16th Edition):

-6327-2527. “Hybridized discontinuous Galerkin methods for magnetohydrodynamics.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/2865.

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

MLA Handbook (7th Edition):

-6327-2527. “Hybridized discontinuous Galerkin methods for magnetohydrodynamics.” 2018. Web. 28 Feb 2021.

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

Vancouver:

-6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/2865.

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

Council of Science Editors:

-6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://dx.doi.org/10.26153/tsw/2865

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


University of Texas – Austin

2. -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

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

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th 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

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

Chicago Manual of Style (16th 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.

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

MLA Handbook (7th 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.

Note: this citation may be lacking information needed for this citation format:
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

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

.