Curriculum Vitae

Thomas R. Benson
Curriculum Vitae
[email protected]
www.tomrbenson.com
US Citizen
Tufts University
Department of Mathematics
503 Boston Avenue
Medford, MA 02155
Research Interests
My research interests are in the areas of computational applied mathematics and scientific computation. Specifically, I am interested in numerical linear algebra and the numerical solution
of partial differential equations. My current research focuses on extending methods that were
developed for incompressible fluid dynamics to complex fluid systems. Part of my current project
investigates the use of monolithic multigrid methods as preconditioners for an incompressible twodimensional visco-resistive formulation of magnetohydrodynamics (MHD). I am also studying the
applicability of several preconditioners for physics-conforming finite-element discretizations of the
Stokes equations.
Education
Tufts University, Department of Mathematics, Medford, MA
Ph.D. Candidate: September 2010 – Present
Advisors: James Adler (Tufts) and Scott MacLachlan (Now at MUN)
Expected Graduation: May 2015
Current GPA: 3.74
Tufts University, School of Arts and Sciences, Medford, MA
B.A. in Mathematics: May 2010
Honors Thesis: Collective Relaxation Techniques for Finite-Element Discretizations of
Systems of PDEs
Advisor: Scott MacLachlan
Professional Experience
Tufts University, Department of Mathematics, Medford, MA
Research Assistant: January 2012 – Present
Advisors: Scott MacLachlan and James Adler
This NSF-funded project investigates monolithic multigrid preconditioners for magnetohydrodynamics. We have extended the well-known schemes of Vanka and Braess-Sarazin
for incompressible fluid flow for the MHD problem, and I have implemented these methods in the Ifpack2 and Teko packages of the Trilinos library (C++), respectively. We
are studying the applicability of such preconditioners for a variety of finite-element discretizations. We are also studying effective preconditioners for various finite-element
discretizations of the Stokes equations. This includes implementing Local Fourier Analysis (LFA) techniques in MATLAB and Python.
Teaching Assistant (Instructor): January 2014 – May 2014
I was the instructor for a section of Calculus II (Math 34), which consisted of teaching
three 50-minute classes and holding three office hours each week. I also assisted with
the proctoring and grading of exams.
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Teaching Assistant (Grader): September 2010 – December 2011
Undergraduate courses:
- Linear and Nonlinear Partial Differential Equations (Math 151/152 at Tufts)
- Real Analysis I (Math 135)
Graduate courses:
- Linear Partial Differential Equations (previously Math 250)
- Numerical Methods for PDEs (also previously Math 250).
Undergraduate Research Assistant: June 2009 – August 2009
Advisor: Scott MacLachlan
As the ground work for my undergraduate honors thesis, I studied monolithic multigrid
methods for a mixed finite-element discretization of the Stokes equations. I implemented
the discretization as well as a geometric multigrid solver with Vanka relaxation for these
problems using MATLAB.
Journal of Modern Dynamics, The Pennsylvania State University, State College, PA
Technical Editor: November 2011 – Present
Managing Editor: Boris Hasselblatt
I reformat accepted papers (20-25 papers per year) into the style and format of the
Journal and perform light copy-editing. The papers are typeset using LATEX.
Memorial University of Newfoundland, St. John’s, NL, Canada
Visiting Graduate Student: August 2014 – October 2014
Supervisor: Scott MacLachlan
While continuing my thesis research (see above), I also began a collaborative effort with
Professor Andrew Wathen of Oxford University analyzing indefinite splitting methods
for saddle-point systems. We show sufficient conditions for the convergence of Vanka
relaxation as a stand-alone method.
Sandia National Laboratories, Livermore, CA
CSRI Summer Intern: June 2012 – August 2012, May 2013 – October 2013
Mentor: Ray Tuminaro
In 2012, we investigated the application of a new physics-based relaxation scheme to
a one-fluid, visco-resistive formulation of MHD in two dimensions. For the proof-ofconcept stage of this project, I implemented the relaxation scheme as well as components of geometric multigrid using the MueMat toolbox in MATLAB. In 2013, I began
implementing these methods in the Trilinos library (C++). This involved implementing support for a new class of blocked matrices in Tpetra, as well as developing and
incorporating support for geometric multigrid in the MueLu package.
Schlumberger-Doll Research, Cambridge, MA
Summer Research Associate: May 2010 – August 2010
I assisted in developing a multigrid preconditioner for a finite-difference discretization of
Maxwell’s equations for applications in Controlled-Source Electromagnetics (CSEM). I
implemented and tested the geometric multigrid preconditioner and the Krylov method
(BICGStab) in FORTRAN90.
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Publications
J. H. Adler, T. R. Benson, E. C. Cyr, S. P. MacLachlan, R. S. Tuminaro. Monolithic Multigrid
Methods for 2D Resistive Magnetohydrodynamics. SIAM J. Sci. Comput. (SISC), submitted
2015.
J. H. Adler, T. J. Atherton, T. R. Benson, D. B. Emerson, and S. P. MacLachlan. Energy
Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects. SIAM J.
Sci. Comput. (SISC), submitted 2014.
Patents
T. M. Kroeger, T. R. Benson. Serial Interpolation for Secure Membership Testing and Matching
in a Secret-Split Archive. Patent preliminary filing.
Presentations
Seventeenth Copper Mountain Conference on Multigrid Methods
March 22-27, 2015: Copper Mountain, CO, USA
Preconditioning For Divergence-Conforming Discretizations of the Stokes Equations,
Submitted
SIAM Conference on Computational Science and Engineering 2015
March 14-18, 2015: Salt Lake City, UT, USA
Robust Multigrid Methods for Magnetohydrodynamics, Accepted
Tufts Chapter of SIAM
December 3, 2014: Tufts University, Medford, MA, USA
Monolithic Multigrid for 2D Magnetohydrodynamics
Memorial University of Newfoundland CAG Group Meeting
October 15, 2014: Memorial University of Newfoundland, St. John’s, NL, Canada
Monolithic Multigrid for 2D Magnetohydrodynamics
Thirteenth Copper Mountain Conference on Iterative Methods
April 6-11, 2014: Copper Mountain, CO, USA
Robust Multigrid Methods for Magnetohydrodynamics
Ninth International Conference on Large-Scale Scientific Computing
June 3-7, 2013: Sozopol, Bulgaria
Multigrid Smoothers for Magnetohydrodynamics
Sixteenth Copper Mountain Conference on Multigrid Methods
March 17-22, 2013: Copper Mountain, CO, USA
Multigrid Smoothers for Magnetohydrodynamics
SIAM Conference on Computational Science and Engineering 2013
February 25 – March 1, 2013: Boston, MA, USA
Multigrid for Divergence-Conforming Discretizations of the Stokes Equations
Twelfth Copper Mountain Conference on Iterative Methods
March 25-30, 2012: Copper Mountain, CO, USA
Monolithic Multigrid for the Stokes Equations
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Other Conferences Attended
2014 AARMS-CRM Workshop on Adaptive Methods for PDEs
August 17-22, 2014: Memorial University of Newfoundland, St. John’s, NL, Canada
11th World Congress on Computational Mechanics (WCCM XI)
July 20-25, 2014: Barcelona, Spain
Software Institute for Methodologies and Abstractions for Codes (SIMAC3)
November 4-5, 2013: Boston University, Boston, MA, USA
Skills
Computer Languages, Libraries: C; C++; FORTRAN90; Python; MPI; OpenMP; MATLAB; Mathematica; LATEX; zsh; bash; SQL; VBA
Numerical Libraries: Trilinos; Deal.II; PETSc; FEniCS
Operating Systems: Linux, BSD, OSX
Professional Service and Activities
Tufts University
Treasurer, Tufts University Chapter of SIAM: September 2010 – September 2011
- Managed the chapter funds
- Purchased food for chapter meetings
Secretary, Tufts University Chapter of SIAM: September 2009 – September 2010
- Kept chapter notes and records of meetings
- Assisted other officers in their duties as needed
Honors and Awards
Graduate Student Travel Award for the Twelfth Copper Mountain Conference on Iterative
Methods, Graduate School of Arts and Sciences, Tufts University, January 2012
High Senior Thesis Honors, Tufts University, May 2010
Memberships
Society for Industrial and Applied Mathematics (SIAM)
American Mathematical Society (AMS)
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