Courses
Previous Courses
Research
My research is in applied mathematics with a focus mainly on numerical
linear algebra. My main research interests are currently
in physics-based
preconditioning for incompressible fluid flow problems,
scalable preconditioners for implicit Runge-Kutta methods,
and machine learning algorithms.
Preconditioning for incompressible fluid flow problems:
Along with a number of collaborators, I have worked on developing and
analyzing scalable preconditioners for Navierâ€“Stokes simulations, including
problems that are extensions to standard incompressible flow models.
Many important scientific systems require solution of such extensions,
whether by incorporating additional nonlinear effects or by coupling to
other physical processes.
Scalable Preconditioners for Implicit Runge-Kutta Methods:
Another research area has been investigating scalable preconditioners
for implicit Runge-Kutta methods. Many important engineering and scientific
systems require the solution of time-dependent PDE systems.
Many of these sytems have specific stability needs in order to
compute realistic solutions. Certain
classes of implicit Runge-Kutta (IRK) methods provide this stability.
However, one price of using IRK methods is the need to solve large
linear systems at each time step, which can be quite expensive
computationally. Preconditioning is necessary for these
systems to be solved efficiently.
Publications
Software
Background & Other Info
Non-Math Life
Current Students
- Colton Mikes, Ph.D. student in Industrial, Manufacturing, and Systems Engineering
(co-chair with David H. Gutman, Texas A&M, and Ismael De Farias (decd.))
- Austin Nelson, Ph.D. student in mathematics
(co-chair with Wei Guo)
- Pavithra Venkatachalapathy, Ph.D. student in mathematics
Former Students & Postdocs
- Fahad Mostafa, Ph.D. August 2024
(co-chair with Dimitri Volchenkov and Linda Allen)
- Aman Rani, Ph.D. August 2024 (co-chair with Katharine Long)
- Michael Clines, Ph.D. May 2023 (co-chair with Katharine Long)
- Nicholas Moore, Ph.D. August 2021
- Md. Masud Rana, Ph.D. August 2021 (co-chair with Katharine Long and Angie Peace)
- Liang Chuan, M.S. in mathematics, May 2021
- Saba Nafees, M.S. in mathematics December 2020 (Ph.D. in biology, August 2020)
- Cadell Freund, undergraduate research student, 2020
- Ayush Dhumal, undergraduate research student, 2019
- Amin Nikakhtar, Ph.D in IE, May 2019 (co-chair with Ismael De Farias)
and M.S. in Mathematics, December 2018 (co-chair with Ashley Cherry, LCU)
- Guoyi Ke, postdoc completed May 2018
(with Eugenio Aulisa and Giorgio Bornia)
- Hum Nath Bhandari, Ph.D. August 2018,
Particle swarm optimization (PSO) algorithm: Analysis, improvements,
and applications
(co-chair with Phil Smith, Mathematics and HPCC, TTU)
- Ashley Meek, Ph.D. August 2016,
Block preconditioned implicit Runge-Kutta methods for the incompressible Navier-Stokes equations
- Ashley Cherry, Ph.D., August 2016,
Piecewise linear approximation for nonlinear programming problems
(co-chair with Ismael De Farias, Dept. of Industrial Engineering, TTU)
- Guoyi Ke, M.S., August 2016 (with Eugenio Aulisa and Giorio Bornia), Ph.D. University of Kansas
- Sarah Osborn, Ph.D. in Mathematics, August 2015,
Multilevel solution strategies for the Stochastic Galerkin Method;
M.S. in Mathematics, May 2012,
GPU vs. CPU performance for solutions of linear systems
arising from PDEs
- Jason Leyva, M.S. student,
(co-chair with Ismael De Farias, Dept. of Industrial Engineering, TTU)
- Geoffrey Dillon, Ph.D. in Mathematics, August 2014,
Block preconditioners for coupled physics problems
(Co-Chair, R. Kirby, Baylor Univ.)
- Kristin Yearkey, MS in Mathematics, August 2011,
A Stochastic Two-Patch Model for Disease Propagation
(co-chair, Linda Allen); currently a Ph.D. student in IE
- Ashlee Fuchs, MS in Mathematics, May 2011,
An Investigation of the Effectiveness of Block Preconditioners on
a Non-Newtonian Blood Flow Model
- Jonathan Adams, undergraduate research student, Fall 2010,
BS in Mathematics, May 2012
- Jerod Clopton, MS in Mathematics, August 2010,
An Investigation of Block Preconditioners for Solving the Steady
State Incompressible Navier-Stokes Equations
- Ellen Durant, undergraduate research student, BS in Mathematics,
May 2010
- Nicholas Murray, MS in Mathematics, August 2009,
Random Flow on Random Graphs: Amphibian Movement in the Playas
(co-chair, Clyde Martin)
Some useful Links
Last updated: August 2024
Copyright © 2008-2024,
Victoria Howle and
Department of Mathematics & Statistics, Texas Tech University
All rights reserved.
Comments:
victoria.howle@ttu.edu