Natasha Flyer

Position Scientist Institute for Mathematics Applied to Geosciences Computational Mathematics Group Office Phone +1 (303) 497-1292 Fax +1 (303) 497-1286 Email flyer@ucar.edu Mailing Address NCAR 1850 Table Mesa Dr. Boulder, CO 80305 USA

Research Interests

• Computational Mathematics - Numerical Analysis

Development of hybrid numerical/aymptotic methodologies for PDEs

Radial basis functions (especially with regard to geophysical flows)

Spectral & high-order methods

Initial-boundary value problems

• Mathematical-Numerical Modeling

Nonlinear flows in the atmosphere, ocean, and solid earth

Modeling of solar magnetic topology

• Special Functions

Publications

• Kenneth Miller, Bengt Fornberg, Natasha Flyer, and B.C. Low, Magnetic Relaxation of the Solar Corona , ApJ. , 690, 2009, 720-733.
• Bengt Fornberg, Natasha Flyer, and Jennifer Russell, Comparisons between pseudospectral and radial basis function derivative approximations , IMA J. Num. Anal. , in press, 2009.
• Natasha Flyer and Grady Wright, A radial basis function method for the shallow water equations on a sphere, Proc. R. Soc. A , 465(2106), 2009, 1949-1976.
• Anders Malmberg, Avelino Arellano, David P Edwards, Natasha Flyer, Doug Nychka, and Christopher K Wikle, Interpolating Fields of Carbon Monoxide Data using a Hybrid Statistical-Physical Model , Ann. Appl. Stat. , 2(4), 2008, 1231-1248.
• Mei Zhang and Natasha Flyer, The dependence of the helicity bound of force-free magnetic fields on boundary conditions , ApJ., 683(2), 2008, 1160-1167.
• Natasha Flyer and A.S. Fokas, A hybrid analytical-numerical method for solving evolution partial differential equations. I. The half-line, Proc. Roy. Soc. A , 464(2095), 2008, 1823-1849.
• Bengt Fornberg, Natasha Flyer, Susan Hovde, Cecile Piret, Locality properties of radial basis function expansion coefficients for equispaced interpolation, IMA J. Num. Anal., 28(1), 2008, 121-142.
• B.C. Low and Natasha Flyer, The topological nature of boundary value problems for force-free magnetic fields, ApJ., 668(1), 2007, 557-570.
• Natasha Flyer and Grady Wright, Transport schemes on a sphere using radial basis functions, J. Comp. Phys., 226, 2007, 1059-1084.
• Natasha Flyer, Exact polynomial reproduction for oscillaory radial basis functions on infinite lattices, Comp. Math. Appl. Vol. 51(8), 2006, 1199-1208.
• Bengt Fornberg and Natasha Flyer The Gibbs Phenomenon for Radial Basis Functions, submitted as book chapter in The Gibbs Phenomenon in Various Representations and Applications , ed. A. Jerri, Sampling Publishing, Potsdam, NY.
• Mei Zhang, Natasha Flyer, B.C. Low, Magnetic field confinement in the corona: The role of magnetic helicity Accumulation, ApJ., 644 (1), 2006, 575-586.
• Natasha Flyer, Bengt Fornberg, Steve Thomas and B.C. Low, Magnetic field confinement in the solar corona. II. The weight of plasmas, ApJ ., 631(1) , 2005.
• Natasha Flyer, Bengt Fornberg, Steve Thomas and B.C. Low, Magnetic field confinement in the solar corona. I. Force-free fields, ApJ. ,606, 10 May 2004, p.1210-1222.
• Bengt Fornberg and Natasha Flyer , Accuracy of radial basis function interpolation and derivative approximations in 1-D., Adv. Comp. Math. , Volume 23, Issue 1-2, Jul 2005, Page 5.
• Natasha Flyer and Bengt Fornberg, On the nature of initial-boundary value solutions for dispersive equations, SIAM J. Applied Math., Vol. 64 (2), 2004, pp. 546-564.
• Natasha Flyer and Bengt Fornberg, Accurate numerical solution of initial transients in convective-diffusive equations, J. Comp. Phys, vol 184(2), 2003, pp 526 -539.
• Natasha Flyer and N. Swarztrauber, Convergence of spectral and finite difference methods for initial-boundary value problems, SIAM J. Scientific Computing, 2002, Vol. 23 (5), pp. 1731-1751.
• John P. Boyd and Natasha Flyer, Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods, Comp. Meth. Appl. Mech. Eng., 175(1999), 281-309.
• Konstantin Kabin and Natasha Flyer (translation), Reminiscences about difference schemes by Sergei Konstantinovich Godunov, J. Comp. Phys., July 1999, pp. 6-25.
• Natasha Flyer, Asymptotic upper bounds for the coefficients in the Chebyshev series expansion for a general order integral of a function, Math. Comp., 67 (1998), 1601-1616.
• Natasha Flyer, The effect of upper level features in the atmosphere on linear theory and linearized Benjamin-Davis-Ono (BDO) theory for internal gravity waves, Ph.D. Thesis , 1999, University of Michigan, Ann Arbor.

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