ÐÓ°ÉÂÛ̳

Research Interests

I'm interested in computational and applied mathematics. Much of my work involves developing numerical methods and models for atmospheric phenomena, such as an adaptive multigrid model for hurricanes. I also use mathematics in studying problems from atmospheric dynamics. More information, selected publications, and links to the classes I teach can be found on my homepage.

Current Projects:

• High-order balanced models of atmospheric dynamics
• Multigrid solution of nonlinear balance equations of the Monge-Ampere type
• Higher-order semi-implicit time differencing
• Vertical normal mode transforms with a continuous spectrum
• Adaptive multigrid methods for partial differential equations

Publications

• Chen, Y., and S. R. Fulton, 2010: An Adaptive Continuation-Multigrid Method for the Balanced Vortex Model. , 229, 2236-2248. Available online: or
• Hendricks, E. A., W. H. Schubert, S. R. Fulton, and B. D. McNoldy, 2010: Spontaneous-adjustment emission of inertia-gravity waves by unsteady vortical motion in the hurricane core. 136, 537-548. Available online:
• Zhou, G., and S. R. Fulton, 2009: Fourier Analysis of Multigrid Methods on Hexagonal Grids. SIAM J. Sci. Comp., 31, 1518-1538. Available online: or as
• Sifalakis, A. G., S. R. Fulton, E. P. Papadopoulou, and Y. G. Saridakis, 2009: Direct and iterative solution of the generalized Dirichlet-Neumann Map for elliptic PDEs on square domains. , 227, 171-184. Available online: or
• Sifalakis, A. G., A. S. Fokas, S. R. Fulton, and Y. G. Saridakis, 2008: The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation. , 219, 9-34. Available online: or
• Xenophontos, C. A., Kurtz, J., and S. R. Fulton, 2006: A p-version MITC finite element method for Reissner-Mindlin plates with curved boundaries. , 192, 374-395. Available online:
• Fulton, S. R., A. S. Fokas, and C. A. Xenophontos, 2004: An analytical method for linear elliptic PDEs and its numerical implementation. , 167, 465-483. Available online:
• Prieto, R., B. D. McNoldy, S. R. Fulton, and W. H. Schubert, 2003: A classification of tropical cyclone binary interactions. Mon. Wea. Rev., 131, 2656-2666. Available online: and *
• Fulton, S. R., 2003: Calculus ABCs: A gateway for freshman calculus. , 13, 361-372. Available online:
• Vigh, J., S. R. Fulton, M. DeMaria, and W. Schubert, 2003: Evaluation of a multigrid barotropic tropical cyclone track model. Mon. Wea. Rev., 131, 1629-1636. Available online: and*
• Xenophontos, C., and S. R. Fulton, 2003: Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh., 19, 89-111. Available online:
• Fulton, S. R., 2003: On the accuracy of multigrid truncation error estimates. , 15, 29-37. Available online: and
• Fulton, S. R., 2001: An adaptive multigrid barotropic tropical cyclone track model. Mon. Wea. Rev., 129, 128-151. Available online: and *
• Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonal eyewalls, asymmetric eye contraction and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 1197-1223. Available online: and *
• Fulton, S. R., 1997: A comparison of multilevel adaptive methods for hurricane track prediction. ., 6, 120-132. Available online: and
• Fulton, S., R., W. H. Schubert, and S. A. Hausman, 1995: Dynamical adjustment of mesoscale convective anvils. Mon. Wea. Rev., 123, 3215-3226. Available online: and *
• Fulton, S. R., 1994: Can Maple help in teaching calculus with limited time and staff? In Maple V: Mathematics and Its Application, R. J. Lopez, ed., Birkhäuser, 63-70.
• Fulton, S. R., 1993: A semi-implicit spectral method for the anelastic equations. , 106, 299-305. Available online:
• Fulton, S. R., 1992: Multigrid solution of nonlinear balance equations in meteorology. Comm. Appl. Num. Meth., 8, 695-706.
• Fulton, S. R., and W. H. Schubert, 1991: Surface frontogenesis in isentropic coordinates. J. Atmos. Sci., 48, 2534-2541. Available online: and *
• Schubert, W. H., S. R. Fulton, and R. F. A. Hertenstein, 1989: Balanced atmospheric response to squall lines. J. Atmos. Sci., 46, 2478-2483. Available online: and*
• Fulton, S. R., 1989: Multigrid solution of the semigeostrophic invertibility relation. Mon. Wea. Rev., 117, 2059-2066. Available online: and *
• Fulton, S. R., and W. H. Schubert, 1987: Chebyshev spectral methods for limited-area models. Part I. Model problem analysis. Mon. Wea. Rev., 115, 1940-1953. Available online: and *
• Fulton, S. R., and W. H. Schubert, 1987: Chebyshev spectral methods for limited-area models. Part II. Shallow water model. Mon. Wea. Rev., 115, 1954-1965. Available online: and *
• Fulton, S. R., P. E. Ciesielski, and W. H. Schubert, 1986: Multigrid methods for elliptic problems: A review. Mon. Wea. Rev., 114, 943-959. Available online: and *
• Ciesielski, P. E., S. R. Fulton, and W. H. Schubert, 1986: Multigrid solution of an elliptic boundary value problem from tropical cyclone theory. Mon. Wea. Rev., 114, 797-807. Available online: and *
• Fulton, S. R., and W. H. Schubert, 1985: Vertical normal mode transforms: theory and application. Mon. Wea. Rev., 113, 647-658. Available online: and *
• Brandt, A., S. R. Fulton, and G. D. Taylor, 1985: Improved spectral multigrid methods for periodic elliptic problems. , 58, 96-112. Available online:
• Fulton, S. R. and G. D. Taylor, 1984: On the Gottlieb-Turkel time filter for Chebyshev spectral methods. , 55, 302-312. Available online:
• Schubert, W. H., J. J. Hack, P. L. Silva Dias, and S. R. Fulton, 1980: Geostrophic adjustment in an axisymmetric vortex. J. Atmos. Sci., 37, 1464-1484. Available online: and *

*Permission to place copies of work published by the American Meteorological Society (AMS) on this server has been provided by the AMS. The AMS does not guarantee that the copies provided here are accurate copies of the published work.

Selected Conference Preprints:

• Xenophontos, C., J. Kurtz, and S. R. Fulton: On the uniform approximation of the Reissner-Mindlin plate model by p/hp finite element methods. Fifth World Conference on Computational Mechanics, Vienna, Austria, July 2002 Preprint available in
• Xenophontos, C., J. Kurtz, and S. R. Fulton: On the Approximation of the Reissner-Mindlin Plate by the p/hp Version of the Finite Element Method. Fourth GRACM Congress on Computational Mechanics, Patra, Greece, June 2002. Preprint available in
• Fulton, S. R. and W. H. Schubert: Potential Vorticity Mixing in Shallow-Water Vortices. Twenty-Fifth Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, San Diego, California, April 2002. View abstract and preprint or download
• Schubert, W. H., B. D. McNoldy, R. Prieto, J. L. Vigh, S. R. Fulton, and R. M. Zehr: A Case Study of Tropical Cyclone Merger. Twenty-Fifth Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, San Diego, California, April 2002. View abstract and preprint
• Fulton, S. R.: Potential Vorticity Mixing and Tropical Cyclone Motion. Twenty-Fourth Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, Fort Lauderdale, Florida, May 2000.
• Mitchell, B. L., and S. R. Fulton, 2000: Experiments with an Adaptive Multigrid Shallow Water Tropical Cyclone Track Model. Twenty-Fourth Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, Fort Lauderdale, Florida, May 2000.
• Hu, M. and S. R. Fulton, 2000: Comparison of Discretization Accuracy in an Adaptive Multigrid Barotropic Tropical Cyclone Track Model. Twenty-Fourth Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, Fort Lauderdale, Florida, May 2000.
• Fulton, S. R., W. H. Schubert, and M. T. Montgomery: Potential vorticity mixing in hurricanes: comparison of nondivergent and divergent barotropic vortices. Twenty-Third Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, Dallas, Texas, January 1999, Preprints, 686-688.

Selected Technical Reports:

• Fulton, S. R., 2002: Semi-Implicit Time Differencing. Technical Report No. 2002-01, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 26 pp. (updated 1 June 2004)
• Hu, M. and S. R. Fulton, 2000: Higher Order Adaptive Multigrid Solution of a Fluid Flow Problem. Technical Report No. 2000-03, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 26 pp.
• Mitchell, B. L. and S. R. Fulton, 2000: Adaptive Multigrid Solution of the Shallow Water Equations. Technical Report No. 2000-02, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 28 pp.
• Burgess, N. M. and S. R. Fulton, 1999: Experiments with Higher-Order Multigrid Methods. Technical Report No. 99-02, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 23 pp.
• Fulton, S. R., and C. Xenophontos, 1999: Maple Tutorial #1: Getting Started. Technical Report No. 99-03, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 10 pp.
• Fulton, S. R., and C. Xenophontos, 1999: Maple Tutorial #2: Functions, Plots, and Equations. Technical Report No. 99-04, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 8 pp.
• Fulton, S. R., and C. Xenophontos, 1999: Maple Tutorial #3: Derivatives and Integrals. Technical Report No. 99-05, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 9 pp.
• Xenophontos, C., and S. R. Fulton, 1999: Maple Tutorial #4: Matrices and Vectors. Technical Report No. 99-06, Department of Mathematics and Computer Science, ÐÓ°ÉÂÛ̳, Potsdam, NY, 13699-5815, 15 pp.