Paul Tranquilli"There are at least two ways to combat stiffness. One is to design a better computer, the other, to design a better algorithm." H. Lomax in Aiken 1985 

Affiliations VT CS@VT Computational Science Lab 
I am currently a postdoctoral associate in the
Process Systems Engineering Laboratory
in the department of Chemical Engineering at MIT.
My research is primarily focused on the development of new, efficient, highly scalable
methods for solving large, stiff systems of ordinary differential equations.
My work focuses on the development of numerical schemes to approximate
solutions of large, stiff systems of Ordinary Differential Equations.
I have developed a new class of matrixfree Rosenbrock type methods called RosenbrockKrylov methods. These methods are an extension of RosenbrockW methods which make use of a specific approximation of the Jacobian matrix to reduce the number of required order conditions. More interestingly they couple the time integrator and linear solver into one computational process, and account for errors in solutions to the linear systems in the order conditions. 2016P.Tranquilli, R. Glandon, A. Sarshar, and A. Sandu, 'Analytical Jacobianvector products for the matrixfree time integration of partial differential equations,' Journal of Computational and Applied Mathematics In Press, Accepted manuscript A. Moosavi, P. Tranquilli, and A. Sandu, 'Solving stochastic chemical kinetics by Metropolis Hastings sampling,' Journal of Applied Analysis and Computation 6:2, 322335 2015H. Zhang, A. Sandu, and P. Tranquilli, 'Application of approximate matrix factorization to high order linearly implicit RungeKutta methods,' Journal of Computational and Applied Mathematics 286, 196210 2014P. Tranquilli, A. Sandu, 'ExponentialKrylov methods for ordinary differential equations,' Journal of Computational Physics, 278, 3146 2013P. Tranquilli, R. Glandon, and A. Sandu, 'CUDA Acceleration of a Matrixfree RosenbrockK Method Applied to the Shallow Water Equations,' Proceedings of the Workshop on Latest Advances in Scalable Algorithms for LargeScale Systems, 5:15:6. P. Tranquilli and A. Sandu, 'RosenbrockKrylov Methods for Large Systems of Differential Equations,' SIAM Journal on Scientific Computing 36(3), A1313–A1338 2012M. Tokman, J. Loffeld, and P. Tranquilli, 'New Adaptive Exponential Propagation Iterative Methods of RungeKutta Type,' SIAM Journal on Scientific Computing 34(5), A2650–A2669 2007A.D. Kim and P. Tranquilli, 'Numerical Solution of a boundary value problem for the FokkerPlanck equation with variable coefficients,' Journal of Quantitative Spectroscopy and Radiative Transfer 109, 727740
