Divakar Viswanath

Professor of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48103
email: divakar(at)umich(dot)edu

Education

BTech in Computer Science and Engineering, IIT Bombay, 1992
PhD in Computer Science, Cornell University, 1998

Research Interests

Much of my research is in numerical analysis and nonlinear dynamics. In 2016, I started working in mathematical genetics.

Book

Scientific Programming and Computer Architechture
MIT Press, 2017
ISBN 9780262036290
Book website and code repository
The book website includes the complete text of the book in html

Papers

• R. Navarrete and D. Viswanath, Delay embedding of periodic orbits using a fixed observation function. pdf. Physica D, Vol. 388, 2019, p. 1-9.
• A. Melfi and D. Viswanath, The Wright-Fisher site frequency spectrum as a perturbation of the coalescent’s. pdf. Theoretical Population Biology, Vol. 124, 2018, p. 81-92.
• A. Melfi and D. Viswanath, Single and simultaneous binary mergers in Wright-Fisher genealogies. pdf.Theoretical Population Biology, Vol. 121, 2018, p. 60-71.
• R. Navarrete and D. Viswanath, Prediction of dynamical time series using kernel based regression and smooth splines. pdf. Electronic Journal of Statistics, Vol. 12, 2018, p. 2217-2237.
• R. Navarrete and D. Viswanath, Accuracy and stability of inversion of power series. pdf. IMA J. of Numerical Analysis, Volume 36, Issue 1, 1 January 2016, p. 421–436.
• D. Viswanath, Spectral integration of linear boundary value problems. pdf. Journal of Computational and Applied Mathematics, Volume 36, 2015, p. 421–436.
• D. Viswanath and I. Tobasco, Navier–Stokes solver using Green’s functions I: Channel flow and plane Couette flow. pdf. Journal of Computational Physics, vol. 251 (2013), p. 414–431.
• B. Sadiq and D. Viswanath, Barycentric Hermite interpolation. pdf. SIAM Journal on Scientific Computing, vol. 35 (2013), p. A1254-A1270
• D. Viswanath, K. Serkh and X. Liang, Metric entropy and the optimal prediction of chaotic signals. pdf. SIAM Journal on Applied Dynamical Systems, vol. 12 (2013), p. 1085-1113.
• B. Sadiq and D. Viswanath, Finite difference weights, spectral differentiation, and superconvergence. pdf. Mathematics of Computation, vol. 83 (2014), p. 2403–2427.
• Y. Charles Li and D. Viswanath, Exact and asymptotic conditions on traveling wave solutions of the Navier-Stokes Equations. pdf. Physics of Fluids, vol. 21 (2009), 101703.
• D. Viswanath and S. Şahutoğlu, Complex singularities and the Lorenz attractor. pdf. SIAM Review, vol. 52 (2010), p. 294-314.
• D. Viswanath and P. Cvitanović, Stable manifolds and the transition to turbulence in pipe flow. pdf. J. Fluid Mech., vol. 627 (2009), p. 215-233. J. Fluid Mech., vol. 627 (2009), p. 215-233.
• J. Halcrow, J.F. Gibson, P. Cvitanović and D. Viswanath, Heteroclinic connections in plane Couette flow. pdf. J. Fluid Mech., vol. 611 (2009), p. 365-376.
• D. Viswanath, The critical layer in pipe flow at high Reynolds number. pdf. Phil. Trans. Roy. Soc., vol. 367 (2009).
• D. Viswanath, The dynamics of transition to turbulence in plane Couette flow. pdf. Mathematics and computation: a contemporary view. The Abel Symosium 2006. Springer-Verlag. Berlin. 2008.
• D. Viswanath, Recurrent motions within plane Couette turbulence. pdf. J. Fluid Mech., 580 (2007), 339-358.
• M. Conger and D. Viswanath, Shuffling cards for blackjack, bridge, and other card games. arxiv.
• D. Viswanath, Stable manifolds and homoclinic points near resonances in the restricted three-body problem. pdf. Celestial Mechanics and Dynamical Astronomy, 94 (2006), 213-235.
• M. Conger and D. Viswanath, Normal approximations for descents and inversions of permutations of multisets. pdf. J. Theor. Probab., 20 (2007), 309-325.
• D. Viswanath, Linear stability analysis of resonant periodic motions in the restricted three-body problem. pdf. Dynamics and Differential Equations, 17 (2005), 271-292.
• M. Conger and D. Viswanath, Riffle shuffles of decks with repeated cards. pdf. Annals of Probability, 34 (2006), 804-819.
• D. Viswanath, The fractal property of the Lorenz attractor. pdf. Physica D, 190 (2004), 115-128.
• D. Viswanath, Symbolic dynamics and periodic orbits of the Lorenz attractor. pdf. Nonlinearity, 16 (2003), 1035-1056.
• D. Viswanath, How many timesteps for a cycle? Analysis of the Wisdom-Holman algorithm? BIT, 42 (2002), 194-205.
• D. Viswanath, The Lindstedt-Poincaré technique as an algorithm for computing periodic orbits. pdf. SIAM Review, 43 (2001), 479-495.
• D. Viswanath, Global errors of numerical ODE solvers and Lyapunov’s theory of stability. pdf. IMA J. Numer. Anal., 21 (2001), 387-406.
• D. Viswanath, Random Fibonacci sequences and the number 1.13198824…pdf. Math. Comp., 69 (2000), 1131-1155.
• D. Viswanath and L.N. Trefethen, Condition numbers of random triangular matrices. pdf. SIAM J. Matrix. Anal. Appl., 19 (1998), 564-581.

Lorenz code and data