Jason S. Howell
Associate Teaching Professor, Director of Undergraduate Studies
6117 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
M.S. in Mathematical Sciences, Clemson University
Ph.D. in Mathematical Sciences, Clemson University
Prof. Howell's research in numerical analysis and computational mathematics is centered around several different aspects of numerical approximation of PDEs. Prof. Howell is interested in the theoretical underpinnings of the finite element method, in particular compatibility conditions for mixed methods. He is also interested in the development of finite element methods that directly approximate quantities of significant physical interest, such as fluid stresses, as well as those that relax regularity requirements. These methods are often employed for continuum models in fluid and structure dynamics. Finally, he is interested in fast and efficient linear solvers and decoupling approaches for time-dependent problems.
Prof. Howell is also interested in applications of math in the sciences, and has worked with chemists and physicists on projects ranging from solubility parameters to nanostructures.
Prof. Howell is very interested in undergraduate research in Mathematical Sciences, and mentors several students in research projects each summer. The projects range from fluid-structure interaction problems to numerical linear algebra to applications of differential equations.
Current Activities: Undergraduate Research in the Mathematical Sciences; Finite Element Methods for Fluids and Structures; Applications of Differential Equations in the Natural and Social Sciences; Direct Solution Methods for Large Sparse Linear Systems; Numerical and Computational Analysis of Arterial Blood Flow; Numerical Methods for Coupled Multiscale Problems in Fluid/Fluid and Fluid/Structure Interaction.
- General Interests: Numerical and Computational Analysis; Numerical Solution of Partial Differential Equations; Computational Fluid Dynamics; Finite Element Methods; Saddle Point Problems; Inf-Sup Conditions; Temporal Integration Methods for Systems of Ordinary Differential Equations; Operator-Splitting Methods; Defect Correction Methods; Continuation Methods; Newtonian and Non-Newtonian Fluid Flow; Reaction-Diffusion Equations; Flow in Porous Media; Iterative Linear and Nonlinear Solvers.
* indicates undergraduate co-author
- J. S. Howell, D. Toundykov, and J. T. Webster. A cantilevered extensible beam in axial flow: Semigroup well-posedness and post-flutter regimes. SIAM J. Math. Anal., 50(2), 2018,2048-2085. DOI
- J. S. Howell. Prestructuring sparse matrices with dense rows and columns via null space methods. Numer. Lin. Alg. Appl., 25(2), 2018, 1-30. DOI
- M. R. Roesing*, J. S. Howell, and D. S. Boucher. Solubility Characteristics of Poly(3-hexylthiophene). J. Polym. Sci. Part B: Polym. Phys., 55 (14), 2017, 1075-1087. DOI
- J. S. Howell, M. R. Roesing*, and D. S. Boucher. A functional approach to solubility parameter computations. J. Phys. Chem. B, 121 (16), 2017, 4191-4201. DOI
- C. A. Fletcher* and J. S. Howell. Dynamic modeling of nontargeted and targeted advertising strategies in an oligopoly. Journal of Dynamics and Games 4(2), 2017, 97-124. DOI
- D. S. Boucher and J. S. Howell. Solubility characteristics of PCBM and C60. J. Phys. Chem. B, 120 (44), 2016, 11556-11566. DOI
- N. Kuthirummal, G. Smith, L. Lopez*, R. Podila, J. S. Howell, C. Dun, and A. M. Rao. Synthesis and characterization of Ar-annealed zinc oxide nanostructures. AIP Advances, 6, 095225 (2016). DOI
- J. S. Howell, I. Lasiecka, and J. T. Webster. Quasi-stability and exponential attractors for a non-gradient system---applications to piston-theoretic plates with internal damping. Evolution Equations and Control Theory, 5(4), 2016, 567-603. DOI
- J. S. Howell, M. Neilan, and N. J. Walkington. A dual-mixed finite element method for the Brinkman problem. SMAI J. Comput. Math., 2, 2016, 1-17. DOI
- J. S. Howell and D. S. Boucher. Temperature dependence of the convex solubility parameters of organic semiconductors. J. Polym. Sci. Part B: Polym. Phys., 54(1), 2016, 81-88. DOI