"After spending years doing mathematics and computer science research, I decided I'd like to focus on education. I chose Coker College due to the exceptional faculty, and the way in which Coker can transform students into young adults prepared for the real world. Coker allows me to educate while continuing research in the form of student collaboration."
My primary research interests are in computational mathematics. I am currently working on the following projects:
- Arbitrary Precision Calculation and CUDA:We are attempting to accelerate the computation of the inverse Laplace Transform using arbitrary precision calculation on an NVIDIA graphics processing unit (GPU). Numerically, the inverse Laplace Transform is incredibly hard to compute, since it requires the integral of a product of two terms over an infinite domain. One of these terms decays exponentially, while the other often grows exponentially. In order to compute the product of these two terms, we generally need very high precision calculations.
- Subsurfa ce Characterization : Using computational and probabilistic techniques, we attempt to characterize the permeability of the ground, given some limited information, such as data from a pressure sensor on the surface of a f ield. Many interesting techniques, such as Markov chain Monte Carlo (MCMC) methods can be used for this application.
- Very High Dimensional Interpolation : Through modifications of the MCMC algorithm in the application of subsurface characterization, we developed an algorithm which uses very high dimensional interpolation to speed up the MCMC algorithm. This technique uses the Smolyak algorithm for choosing interpolation nodes. This is not a widely used technique, and we have been writing a software package which we hope will encourage usage of the Smolyak algorithm, and high dimensional interpolation in general.
- General Parallel Computing : I am very interested in massively parallel computers, and modifying algorithms to take advantage of multiple processors and multicore processor. I strongly believe this is technique that all computational scientists must master if they would like to be successful.
I am very interested in using technology in the classroom, when appropriate. I have incorporated Matlab into various classes, and believe technology can be used to help students see relevant applications of the mathematics they are learning. Additionally, I have been using a Tablet PC to record and post video lectures online for students in Math 210 (Trigonometry). Eventually, I would like to attempt teaching a class that is either totally, or partially, taught online.
- P. Kano, M. Brio, P. Dostert, and J. Cain, Dempster-Shafer Evidential Theory for the Automated Selection of Parameters for Talbot’s Method Contours and Application to Matrix Exponentiation, Computers and Mathematics with Applications, Volume 63, Issues 11, 1519-1535 (2012).
- P. Dostert, Y. Efendiev and B.Mohanty, Efficient uncertainty quantification techniques for Richards' equation, Advances in Water Resources 32, 329-339 (2009).
- C. Douglas, P. Dostert, Y. Efendiev, R. Ewing, D. Li, and R. Lodder, DDDAS Predictions for Water Spills, Proceedings of the 8th international conference on Computational Science, Part III (ICCS '08), 54-63 (2008).
- P. Dostert, Y. Efendiev and T.Y. Hou, Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification, Computer Methods in Applied Mechanics and Engineering, Volume 197, Issues 43-44, 3445-3455 (2008).
- C. Douglas, P. Dostert, Y. Efendiev, R.E. Ewing, and D. Li, Improving Predictions for Water Spills Using DDDAS, Proceedings of NSF Workshop session at IPDPS (2008).
- C. Douglass, M. Cole, P. Dostert, Y. Efendiev, R. Ewing, G. Hassee. J. Hatcher, M. Iskandarani, C. Johnson, and R. Lodder, Dynamically identifying and tracking contaminants in water bodies, ICCS 2007. LNCS, vol. 4487, pp. 1002–1009. Springer, Heidelberg (2007).
- P. Dostert, Uncertainty Quantification Using Multiscale Methods for Porous Media Flows, PhD thesis, Texas A&M University, College Station, TX (2007)
- C. Douglass, M. Cole, P. Dostert, Y. Efendiev, R. Ewing, G. Hassee. J. Hatcher, M. Iskandarani, C. Johnson, and R. Lodder, Dynamic Contaminant Identiﬁcation in Water, ICCS 2006. LNCS, vol. 3993, pp. 393–400. Springer, Heidelberg (2006).
- P. Dostert, Y. Efendiev, T.Y. Hou, and W. Luo, Coarse-Gradient Langevin Algorithms for Dynamic Data Integration and Uncertainty Quantification, Journal of Computational Physics, 217(1), 123-142 (2006).
- J. Liu, J. Sochacki, and P. Dostert, Singular perturbations and approximations for integrodifferential equations, Proceedings of the International Conference on Control and Differential Equations, Lecture Notes in Pure and Applied Mathematics, Differential Equations and Control Theory, Vol. 225 (2002).