Ross Glandon

   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





Computational Science Lab

Computational Science Lab

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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 matrix-free Rosenbrock type methods called Rosenbrock-Krylov methods. These methods are an extension of Rosenbrock-W 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.


P.Tranquilli, R. Glandon, A. Sarshar, and A. Sandu, 'Analytical Jacobian-vector products for the matrix-free 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, 322-335


H. Zhang, A. Sandu, and P. Tranquilli, 'Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods,' Journal of Computational and Applied Mathematics 286, 196-210


P. Tranquilli, A. Sandu, 'Exponential-Krylov methods for ordinary differential equations,' Journal of Computational Physics, 278, 31-46


P. Tranquilli, R. Glandon, and A. Sandu, 'CUDA Acceleration of a Matrix-free Rosenbrock-K Method Applied to the Shallow Water Equations,' Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, 5:1-5:6.

P. Tranquilli and A. Sandu, 'Rosenbrock-Krylov Methods for Large Systems of Differential Equations,' SIAM Journal on Scientific Computing 36(3), A1313–A1338


M. Tokman, J. Loffeld, and P. Tranquilli, 'New Adaptive Exponential Propagation Iterative Methods of Runge--Kutta Type,' SIAM Journal on Scientific Computing 34(5), A2650–A2669


A.D. Kim and P. Tranquilli, 'Numerical Solution of a boundary value problem for the Fokker-Planck equation with variable coefficients,' Journal of Quantitative Spectroscopy and Radiative Transfer 109, 727-740