Education

Funding History

  1. Air Force Office of Scientific Research: Radial Basis Functions for Numerical Simulation, Co-PI (with Benjamin F. Akers), $110,491 ($55,245 responsibility), 2018{2020. Generate new numerical algorithms which are both highly flexible and accurate. Two primary application areas will be considered: atmospheric effects of high energy lasers (HEL) and coherent structures in interfacial fluid dynamics.

  2. Office of Naval Research: Atmospheric Propagation Sciences and High Energy Lasers, Co-PI (with Steven Fiorino, Benjamin F. Akers, Sivaguru S. Sritharan), $878,183 ($219,545.75 responsibility), 2016-2019. Investigate the evolution of high energy lasers through the atmosphere and the effect that laser propagation has on the atmosphere.

Refereed Journal Articles

  1. J. A. Reeger and B. Fornberg. "Numerical quadrature over smooth surfaces with boundaries." J. Comput. Phys, 355:176-190, 2018.

  2. N. Smith, C. Arendt, R. Cobb, and J. A. Reeger. "Implementing Conditional Inequality Constraints for Optimal Collision Avoidance." J Aeronaut Aerospace Eng., 6 (195). doi: 10.4172/2168-9792.1000195

  3. B. F. Akers and J. A. Reeger. "Three-dimensional interfacial traveling waves." Wave Motion, 68: 210-217, 2017.

  4. J. A. Reeger, B. Fornberg, and M. L. Watts. "Numerical quadrature over smooth, closed surfaces." P. Roy. Soc. Lon. A Mat., 472. doi: 10.1098/rspa.2016.0401.

  5. C. J. Humphreys, R. G. Cobb, D. Jacques, and J. A. Reeger. "A Hybrid Technique to Rapidly Solve the Intermediate-Target Optimal Control Problem." Global J. Tech. Optim., 7(2): 1-8, 2016. doi: 10.4172/2229-8711.1000200.

  6. J. A. Reeger and B. Fornberg. "Numerical quadrature over the surface of a sphere." Stud. Appl. Math. 137 (2): 174-188, 2016.

  7. M. Ghrist, B. Fornberg, and J. A. Reeger. "Stability ordinates of Adams predictor-corrector methods." BIT Numerical Mathematics, 55(3): 733-750, 2015.

  8. J. A. Reeger and B. Fornberg. "Painleve IV: A numerical study of the fundamental domain and beyond." Physica D, 280-281: 1-13, 2014.

  9. J. A. Reeger and B. Fornberg. "Painleve IV with both parameters zero: A numerical study." Stud. Appl. Math., 130(2):108-133, 2013.

Refereed Conference Papers

  1. C. J. Humphreys, R. G. Cobb, D. R. Jacques, and J. A. Reeger. "Dynamic Re-Plan of the Loyal Wingman Optimal Control Problem." AIAA Guidance, Navigation, and Control Conference, AIAA Science and Technology Forum and Exposition 2017. GNC-28, Aerospace Robotics Guidance and Navigation. Grapevine, Texas. January 12, 2017. (Accepted based on review of extended abstract/draft manuscript.)

  2. C. J. Humphreys, R. G. Cobb, D. R. Jacques, and J. A. Reeger. "Dynamic Re-Plan of the Loyal Wingman Optimal Control Problem in a Changing Mission Environment." The AIAA SciTech Forum and Exhibition 2016. San Diego, CA. 4-8 January 2016. (Accepted based on review of extended abstract/draft manuscript.)

  3. C. J. Humphreys, R. G. Cobb, K. Kauffman, and J. A. Reeger. "Optimal Mission Path for the Uninhabited Loyal Wingman." The 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Aviation Forum 2015. Dallas, TX. 22-26 June 2015. (Accepted based on review of extended abstract/draft manuscript.)

Submitted Publications

  1. C. J. Humphreys, R. G. Cobb, D. Jaques, and J. A. Reeger. "Dynamic re-plan of the loyal wingman optimal control problem." under review with J. Guid. Control Dynam.

  2. B. F. Akers, J. Gustafsson, J. A. Reeger and S. S. Sritharan. "Atmoshpheric Propagation of High Energy Lasers." under review with Comput. Math. Appl.

Publications in Preparation

  1. B. F. Akers and J. A. Reeger. "Thermal blooming with laser-induced convection."

  2. J. A. Reeger. "High Accuracy Mesh Generation for Surfaces."

  3. J. A. Reeger. "Numerical Quadrature for Polytopes in 3D."

  4. B. Fornberg and J. A. Reeger. "An Improved Gregory-Like Method for 1-D Quadrature."

  5. B. F. Akers, J. A. Reeger, and M. Siegel. "Three-Dimensional Travelling Waves in Vortex Sheets."

  6. J. Ng and J. A. Reeger. "A Radial Basis Function Generated Finite-Difference Integrating Factors Method for the Nonlinear Schrodinger Equation."

Invited Presentations

  1. J. A. Reeger and B. Fornberg. "Numerical Quadrature Over Bounded Smooth Surfaces." Colloquium. Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan, United States. 15 December 2017.

  2. J. A. Reeger and B. Fornberg. "Numerical Quadrature Over Bounded Smooth Surfaces." Colloquium. Department of Mathematics, Western Washington University, Bellingham, Washington, United States. 6 November 2017.

  3. J. A. Reeger, B. Fornberg, and M. L. Watts. "Numerical quadrature over smooth, closed surfaces." Localized kernel-based meshless methods for partial differential equations. The Institute for Computational and Experimental Research in Mathematics. Brown University. Providence, Rhode Island, United States. 7-11 August 2017.

  4. J. A. Reeger and B. F. Akers. "Three-dimensional traveling waves in vortex sheets." 2nd IMA Conference on Nonlinear Waves and Coherent Structures. Norwich, Norfolk, United Kingdom. 22 June 2017.

  5. J. A. Reeger and B. F. Akers. "Three-dimensional traveling waves in vortex sheets." SIAM Conference on Nonlinear Waves and Coherent Structures. Philadelphia, Pennsylvania, United States. 9 August 2016.

  6. J. A. Reeger and B. F. Akers. "Three-dimensional overturned traveling water waves." The Burgers Program 2016 Summer Research School on Fluid Dynamics: Topics in Nonlinear Water Waves. University of Maryland, College Park, Maryland, United States. 6 June 2016.

  7. J. A. Reeger and B. Fornberg. "Numerical quadrature over the surface of a sphere." Colloquium, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, United States. 23 September 2015.

  8. J. A. Reeger and B. Fornberg. "Numerical quadrature over the surface of a sphere." Seminar, Department of Mathematics and Statistics. Air Force Institute of Technology. Wright-Patterson Air Force Base, Ohio, United States. 17 September 2015.

  9. J. A. Reeger. "Toward the use of Gaussian radial basis functions in numerical quadrature." Seminar, Department of Mathematics and Statistics. Air Force Institute of Technology. Air Force Base, Ohio, United States. 23 July 2015.

  10. J. A. Reeger and B. Fornberg. "Explorations of the solution space of the fourth Painleve equation." The 13th International Symposium on Orthogonal Polynomials, Special Functions, and Applications. The National Institute for Standards and Technology. Gaithersburg, Maryland, United States. 1-5 June 2015.

  11. J. A. Reeger and B. Fornberg. "Explorations of the solution space of the fourth Painleve equation." The 9th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory. University of Georgia. Athens, Georgia, United States. 1-4 April 2015.

  12. J. A. Reeger and B. Fornberg. "On solving initial value problems in the presence of poles: Solutions of the fourth Painleve equation with no closed form." Colloquium, Department of Mathematics and Statistics. Air Force Institute of Technology. Wright-Patterson Air Force Base, Ohio, United States. 12 February 2015.

  13. J. A. Reeger. "A comparison of transcription techniques for the optimal control of the International Space Station." Colloquium, Department of Mathematics and Statistics. Air Force Institute of Technology. Wright-Patterson Air Force Base, Ohio, United States. 31 October 2013.

Students Advised

  1. Justin Ng. Master of Science in Applied Mathematics. Air Force Institute of Technology. Wright-Patterson Air Force Base, Ohio. In Progress.

  2. Maloupu L. Watts. Master of Science in Applied Mathematics. Air Force Institute of Technology. Wright-Patterson Air Force Base, Ohio. March 2015. Thesis: Radial Basis Function Based Quadrature over Smooth Surfaces.

Honors and Awards

  • 2017-2018 Faculty Excellence Award presented by the Southwestern Ohio Council for Higher Education

  • Instructor of the Quarter. Air Force Institute of Technology, Department of Mathematics and Statistics. Winter Quarter 2017.

  • Instructor of the Quarter, Air Force Institute of Technology Department of Mathematics and Statistics, Spring 2016

  • Fellowship, Charles Stark Draper Laboratories, Houston, Texas, 2007, 2008, 2009.

  • Outstanding Cadet in Mathematics, Sponsored by National Defense Industrial Association, United States Air Force Academy, 2007

Courses Taught

  1. MATH 508 (Air Force Institute of Technology) - Applied Numerical Methods (Winter 2014, 2015, 2016, 2017, 2018 and Spring 2015, 2016, 2017)

  2. MATH 509 (Air Force Institute of Technology) - Mathematical Methods in the Physical Sciences (Summer 2014)

  3. MATH 511 (Air Force Institute of Technology) - Methods of Applied Mathematics I (Summer 2013)

  4. MATH 523 (Air Force Institute of Technology)- Numerical Analysis and Linear Algebra (Fall 2013, 2014, 2015, 2016, 2017)

  5. MATH 699 - Topics in Radial Basis Functions (Spring 2015)

Employment and Service History

  • August 2018 to Present - Assistant Professor of Mathematics, Mathematics Department, United States Naval Academy, Annapolis, Maryland

  • June 2013 to June 2018 - Assistant Professor of Mathematics, Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio

  • August 2010 to June 2013 - Student, Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado

  • May 2009 to August 2010 - Project Officer, Third Generation Infrared Surveillance, Space and Missile Systems Center, Los Angeles Air Force Base, California

  • August 2007 to May 2009 - Student, Department of Computational and Applied Mathematics, Rice University, Houston, Texas

  • August 2007 to May 2009 - Draper Laboratory Fellow, Spacecraft Guidance, Navigation, and Control Systems, The Charles Stark Draper Laboratory, Houston, Texas