RESEARCH

JONATHAN S. GRAF

PhD Candidate - Applied Mathematics - UMBC


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My current research interests center on the numerical solution of time-dependent partial differential equations. In this work I also study parallel and high performance computing including the use of modern highly parallel architectures like the NVIDIA GPU and Intel Phi. My recent work focus on a Calcium Induced Calcium Release model of calcium ion dynamics in a heart cell and uses the second-generation Intel Xeon Phi, Knights Landing (KNL). Below you will find more information on research positions I have held and some of the related projects.

General Research Work

Research Group under Dr. Matthias Gobbert

Publications:

Jonathan Graf, Philipp Birken and Matthias Gobbert. SDIRK Time Stepping within Finite Volume Method or Parabolic Advection-Diusion-Reaction Equations with Point Sources. In preparation.

Jonathan Graf and Matthias Gobbert. Effective Strategies for use of the Configuration Modes for the Intel Xeon Phi Knights Landing. In preparation.

Ishmail A. Jabbie, George Owen, Benjamin Whiteley, Jonathan S. Graf, Matthias K. Gobbert, and Samuel Khuvis. Performance Comparison of Intel Xeon Phi Knights Landing. Submitted 2017.

Kallista Angeloff, Carlos Barajas, Alexander D. Middleton, Uchenna Osia, Jonathan S. Graf, Matthias K. Gobbert, and Zana Coulibaly. Examining the Effect of Introducing a Link from Electrical Excitation to Calcium Dynamics in a Cardiomyocyte. Spora: A Journal of Biomathematics, vol. 2, article 6, 2016.

Matthew W. Brewster, Jonathan S. Graf, Xuan Huang, Zana Coulibaly, Matthias K. Gobbert and Bradford E. Peercy. Calcium Induced Calcium Release with Stochastic Uniform Flux Density in a Heart Cell. In Proceedings of the 47th Summer Computer Simulation Conference (SCSC), Chicago, IL, 2015.

Talks:

Performance Analysis and Numerical Method Tuning for a System of Non-Linear Time-Dependent Advection-Diffusion-Reaction Equations. Poster presentation in the Minsymposterium: Parallel Computing for Models using Partial Differential Equations. SIAM CSE, February 28, 2017 (upcoming).

Efficient Time-Stepping Methods for the Numerical Solution of Large Stiff Systems Within Parabolic Partial Differential Equations. Session Chair, CP15: Numerical PDEs I. SIAM Annual Meeting 2016, July 13, 2016.

Implementation of the SDIRK method for the solution of the ODE system within a method of lines discretization for parabolic PDE. UMBC Mathematics & Statistics Graduate Student Seminar, November 11, 2015.

Singly Diagonally Implicit Runge-Kutta schemes within the Numerical Solution of Partial Differential Equations. Fall 2015 MAA Sectional meeting (MD-DC-VA), November 7, 2015.

Calcium Induced Calcium Release with Stochastic Uniform Flux Density in a Heart Cell. Modeling & Simulation in Medicine Track in the Summer Computer Simulation Conference. SCS SummerSIM, July 27, 2015.

The Interplay Between Numerical Methods Within the Numerical Solution of a Three-Dimensional Model of Calcium Waves in a Heart Cell. Student Colloquium. SCS SummerSIM, July 26, 2015.

Numerical Solution of Partial Differential Equations through High Performance Com- puting on Modern Architectures. 2015 UMBC Graduate Research Conference, March 25, 2015.

Overview and Contrast of Modern Computer Architectures Including the Intel Phi. Minisymposium: Parallel Computing for Partial Differential Equations on CPUs, GPUs, and Intel Phi. SIAM Computational Science and Engineering Conference, March 17, 2015.

The Interplay Between Methods Within the Numerical Solution of Nonlinear Time-Dependent Partial Differential Equations. DE Seminar Department of Mathematics and Statistics, UMBC, April 28, 2014.

Research Assistant

High Performance Computing Facility (HPCF) at UMBC

Publications:

Kourosh M. Kalayeh, Jonathan S. Graf and Matthias K. Gobbert. FEM Convergence for PDEs with Point Sources in 2-D and 3-D. In Proceedings of the COMSOL Conference 2015, Boston, MA, 2015.

Kourosh M. Kalayeh, Jonathan S. Graf and Matthias K. Gobbert. FEM convergence studies for 2-D and 3-D elliptic PDEs with smooth and non-smooth source terms in COMSOL 5.1. Technical Report HPCF-2015-19. UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2015.

Jonathan S. Graf and Matthias K. Gobbert. Parallel performance studies for a parabolic test problem on the cluster maya. Technical Report HPCF-2015-7. UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2015.

Jonathan S. Graf and Matthias K. Gobbert. Parallel performance studies for a parabolic test problem on maya 2013. Technical Report HPCF-2014-7. UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2014.

Talk:

FEM Convergence for PDEs with Point Sources in 2-D and 3-D. Oral Presentation and Poster. COMSOL Conference, October, 2015.

Graduate Assistant

REU: Interdisciplinary Program in High Performance Computing at UMBC

Publications:

Sergio Garcia Tapia, Rebecca Hsu, Alyssa Hu, Darren Stevens II, Jonathan S. Graf, Matthias K. Gobbert, and Tyler Simon. Applications of Tensor Decomposition. Technical Report HPCF-2016-17, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2016.

Ishmail A. Jabbie, George Owen, Benjamin Whiteley, Jonathan S. Graf, Matthias K. Gobbert, and Samuel Khuvis. Performance Comparison of Intel Xeon Phi Knights Landing. Technical Report HPCF-2016-16, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2016.

Kallista Angeloff, Carlos Barajas, Alexander D. Middleton, Uchenna Osia, Jonathan S. Graf, Matthias K. Gobbert, and Zana Coulibaly. Coupling the Electrical and Calcium Dynamics in a Heart Cell. Technical Report HPCF-2016-15, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2016.

Wesley Collins, Daniel T. Martinez, Michael Monaghan, Alexey A. Munishkin, Ari Rapkin Blenkhorn, Jonathan S. Graf, Samuel Khuvis, Matthias K. Gobbert, and John C. Linford. Comparison of performance analysis tools for parallel programs applied to CombBLAS. Technical Report HPCF-2015-28, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2015.

Fernando X. Avila-Soto, Alec N. Beri, Eric Valenzuela, Abenezer Wudenhe, Ari Rap- kin Blenkhorn, Jonathan S. Graf, Samuel Khuvis, Matthias K. Gobbert, and Jerimy Polf. Parallelization for fast image reconstruction using the stochastic origin ensem- ble method for proton beam therapy. Technical Report HPCF-2015-27, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2015.

Changling Huang, Christopher C. Lowman, Brandon E. Osborne, Gabrielle M. Salib, Ari Rapkin Blenkhorn, Jonathan S. Graf, Samuel Khuvis, Matthias K. Gobbert, Tylor Simon, and David J. Mountain. Performance studies of the Blossom V algorithm. Technical Report HPCF-2015-26, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2015.

Oluwapelumi Adenikinju, Julian Gilyard, Joshua Massey, Thomas Stitt, Jonathan S. Graf, Xuan Huang, Samuel Khuvis, Matthias K. Gobbert, Marc Olano, Yu Wang Real Time Global Illumination Solutions to the radiosity algorithm using hybrid CPU/GPU nodes. Technical Report number HPCF-2014-15. University of Maryland, Baltimore County, August 2014.

Adam Cunningham, Gerald Payton, Jack Slettebak, Jordi Wolfson-Pou, Jonathan S. Graf, Xuan Huang, Samuel Khuvis, Matthias K. Gobbert, Thomas Salter, and David J. Mountain. Pushing the Limits of the Maya Cluster. Technical Report number HPCF-2014-14. UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2014.

Talk:

Graduate Student Mentorship for Diverse Teams of Undergraduate Researchers in an REU Site. SIAM Conference on Applied Mathematics Education, upcoming: September 30, 2016.

Undergraduate Researcher

Applied Mathematics Laboratory (AML) at Towson University

Talk:

Study of Deer Population in Baltimore County. Baltimore County Department of Environmental Protection and Resource Management (DEPRM). May 2009.

REU: James Madison University

Publication

Jonathan Graf and Olga Stulov. What Moves You: Using Legs for Vehicular Transportation. SIAM Undergraduate Research Online SIURO, vol. 5 (2012), pp. 35-55.

Talks:

What Moves You: Using Legs for Vehicular Transportation. Towson University Mathematics Colloquium. Towson, MD, April 22nd, 2010.

What Moves You: Using Legs for Vehicular Transportation. 2010 Joint Mathematics Meetings (AMS & MAA), San Francisco. January 16th, 2010.

What Moves You: Using Legs for Vehicular Transportation. Fall 2009 MAA MD-DC-VA Sectional meeting, Goucher College. November 14th, 2009.


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