Research Interests
My broad research interests are numerical analysis and scientific computing. Specifically, I am interested in highorder numerical methods for differential equations, applications in the field of uncertainty quantification, spectral methods, and orthogonal polynomials.
My current and past projects include:
 spectral expansions on infinite intervals
 theory and computational methods for univariate orthogonal polynomials
 uncertainty quantification (UQ) for stochastic systems
 generalized polynomial chaos methods
 sensitivity of stochastic systems with respect to probability distribution
 assimilation of multiple models and sources of data
 polynomial interpolation in high dimensions on unstructured grids with applications to UQ
Publications

Y. Yang, A. Narayan, and D. Xiu
On decoupling coupled stochastic systems
In Preparation

A. Narayan and D. Xiu
On the choice of interpolation nodes
In Preparation

M. Feiszli and A. Narayan.
Numerical computation of WeilPeterson geodesics on the Universal Teichmüller Space.
In Preparation.

S. Kushnarev and A. Narayan.
Teichon solutions for geodesics on the Universal Teichmüller Space.
Arxiv preprint

J. Jakeman, A. Narayan, and D. Xiu.
Minimal element stochastic collocation for uncertainty quantification of discontinuous functions.
Submitted.

A. Narayan and J. S. Hesthaven.
A Generalization of the Wiener Rational Basis Functions on Infinite Intervals: Part II  Numerical Examples.
To appear: Journal of Computational and Applied Mathematics

A. Narayan, Y. Marzouk and D. Xiu.
Sequential assimilation of multiple models.
Journal of Computational Physics

A. Narayan and D. Xiu.
Stochastic collocation methods on unstructured grids in high dimensions via interpolation.
SIAM Journal on Scientific Computing

A. Narayan and J. S. Hesthaven.
Computation of connection coefficients and measure modifications for orthogonal polynomials.
BIT Numerical Mathematics, 2011.

A. Narayan and D. Xiu.
Distributional Sensitivity for Uncertainty Quantification.
Communications in Computational Physics 10:140160, 2011.

A. Narayan and J. S. Hesthaven
A Generalization of the Wiener Rational Basis Functions on Infinite Intervals: Part I  Derivation and Theory.
Mathematics of Computation 80:15571583, 2010.
Theses and Technical Reports

A. Narayan and A. Klöckner.
Deterministic Methods for the Boltzmann Equation.
Brown University Technical Report, 2009

A. Narayan.
Generalized Wiener rational functions for spectral expansions on an infinite interval.
Ph.D. thesis, Brown University, 2009

A. Narayan.
A study of spatial solitons.
Undergraduate thesis, Northwestern University, 2003.

A. Narayan.
Modelling fiberoptic generated continuum.
Undergraduate thesis, Northwestern University, 2003.
