Research Interests
My broad research interests are numerical analysis and scientific computing. Specifically, I am interested in high-order 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
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Y. Yang, A. Narayan, and D. Xiu
On decoupling coupled stochastic systems
In Preparation
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A. Narayan and D. Xiu
On the choice of interpolation nodes
In Preparation
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M. Feiszli and A. Narayan.
Numerical computation of Weil-Peterson geodesics on the Universal Teichmüller Space.
In Preparation.
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S. Kushnarev and A. Narayan.
Teichon solutions for geodesics on the Universal Teichmüller Space.
Arxiv preprint
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J. Jakeman, A. Narayan, and D. Xiu.
Minimal element stochastic collocation for uncertainty quantification of discontinuous functions.
Submitted.
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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
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A. Narayan, Y. Marzouk and D. Xiu.
Sequential assimilation of multiple models.
Journal of Computational Physics
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A. Narayan and D. Xiu.
Stochastic collocation methods on unstructured grids in high dimensions via interpolation.
SIAM Journal on Scientific Computing
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A. Narayan and J. S. Hesthaven.
Computation of connection coefficients and measure modifications for orthogonal polynomials.
BIT Numerical Mathematics, 2011.
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A. Narayan and D. Xiu.
Distributional Sensitivity for Uncertainty Quantification.
Communications in Computational Physics 10:140-160, 2011.
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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 80:1557-1583, 2010.
Theses and Technical Reports
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A. Narayan and A. Klöckner.
Deterministic Methods for the Boltzmann Equation.
Brown University Technical Report, 2009
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A. Narayan.
Generalized Wiener rational functions for spectral expansions on an infinite interval.
Ph.D. thesis, Brown University, 2009
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A. Narayan.
A study of spatial solitons.
Undergraduate thesis, Northwestern University, 2003.
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A. Narayan.
Modelling fiber-optic generated continuum.
Undergraduate thesis, Northwestern University, 2003.
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