# The Department of Mathematics

Anita Mayo received a BA from Barnard College and a Ph.D. in mathematics from the Courant Institute, NYU. Her areas of specialization are numerical analysis, applied mathematics and, more recently, computational finance. In her work she has developed rapid and highly accurate methods for solving a variety of differential equations on general regions. She has applied these techniques to solving problems in elasticity, electrodynamics and fluid mechanics, including ones directly arising in the manufacture of IBM chips and recording devices. In particular she has helped engineers develop programs used for modeling deposition in CMOS manufacture and programs that were widely used for modeling thin film recording heads. She has also developed rapid methods for pricing certain financial options.

** Publications **

Mayo, A, * On the numerical evaluation of option prices in the Variance* *Gamma model*, International Journal of Computer Mathematics, 86(2) Feb. 2009, pp. 86-99.

Mayo, A., *Methods for the pricing of PIDEs in Exponential and Merton Models, *Journal of Computational and Applied Math., vol. 222, issue 1, December 2008, 128-143.

P. Carr and A. Mayo, On the numerical evaluation of option prices in jump diffusion models European Journal of Finance, vol.13, issue 4 June 2007, 353- 369.

Mayo, A. and Greenbaum, A. *Fourth order accurate evaluation of integrals in potential theory on exterior 3d regions,* J. of Computational Phys., vol 220, Issue 2, January 2006, pp. 900-914.

Mayo, A., *Rapid fourth order accurate solution of the steady Navier Stokes ** equations on general regions,* Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 12, 2005, pp.59-72.

Mayo, A*., High Order Accurate Implicit Method for Valuing American Options *The European Journal of Finance, vol. 10, no.3, 2004, pp. 212-237.

Ruehli, A., Antonini, G., Esch, J., Mayo, A. and Orlandi, A., *Non Orthogonal PEEC Formulation for Time and Frequency Domain EM and Circuit Modeling*, IEEE Transactions Electro-Magnetic Compatibility, vol. 45, no.2, 2003, 167-.179.

Mayo, A.,* Rapid, fourth order accurate evaluation of particular solutions of the biharmonic equation on general regions*, Contemporary Mathematics, American Mathematical Association (AMS), vol.323, 2003, pp 233-245.

Greenbaum, A. and Mayo, A., *Rapid Parallel Evaluation of Integrals in Potential Theory** on General Three Dimensional Regions*, J. of Computational Phys, 145, 1998, pp. 731-742.

Mayo,A.,* Deferred Correction Finite Difference Methods for the Evaluation of Integrals in Potential Theory and Low Frequency Scattering,* Integral methods in Science and Engineering,Vol. 2, Addison Wesley, 1997, pp.165-170.

Mayo, A., Hamaguchi , S., Rossnagel, S. and Joo, J., *Across wafer nonuniformity of long throw sputter deposition systems*, Journal of the Vacuum Society B. Vol. 15, October 1997, pp. 1788-1793.

Hamaguchi, S., Mayo, A., Rossnagel, S., Kotecki, D. and Milkove, K, *Numerical Simulation of Etching and Deposition Processes*, J. Journal Applied Physics,Vol. 36, No. 7B, 1997, pp. 4762 - 4768.

Greengard, L., Kropinski, M. C. and Mayo, A., *Integral equation methods for Stokes flow and isotropic elasticity in the plane*, J. of Computational Physics, v. 125, May 1996, pp. 403-41

McKenney, A., Greengard, L. and Mayo, A., *A fast Poisson solver for complex geometries,* J. of Computational Physics, Vol. 118, 1995, pp. 348-355.

** **Li, Z. and Mayo, A., *ADI Methods for heat equations with discontinuities along an arbitrary interface*, Symposia in Applied Mathematics, American Mathematics Society (AMS), Vol. 48, 1994, pp.311-333.

Mayo, A., and. Peskin, C., *An implicit numerical method for fluid dynamics problems with immersed elastic boundaries*, Contemporary Mathematics, American Mathematical Society (AMS), Vol. 141, 1993, pp. 261-277.

Mayo, A., *The rapid evaluation of volume integrals of potential theory on genera regions,* J. of Computational Physics, Vol. 100, No. 2, June 1992, pp.236- 245.

Greenbaum, A., Greengard, L. and Mayo, A., *On the numerical solution of the **biharmonic equation in the plane,* Physica D, 60, 1992, pp. 216-225.

PATENTS

__ __Mayo, A. and Rubin, B., Method for determining voltage, current and/or power distributions in a resistive structure using a rectangular grid algorithm modified for nonrectangular holes and contacts, Patent No. US 6,704, 669B2, Date of patent: May 9, 2004.

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