Overview

Tom DeLillo received his PhD from the Courant Institute, NYU, in 1985. He held postdoc and visiting positions at Exxon Research and Engineering, UNC Chapel Hill, and Duke University before coming to 麻豆破解版 State in 1988.

Tom DeLillo's research is in the numerical and theoretical study of conformal maps and in the development of computational methods for inverse problems in acoustics and gravimetry. He has developed several new methods, based on fast Fourier analysis, for computing conformal maps of simply and multiply connected domains in the complex plane, studied the ill-conditioning of those methods, and applied the methods to problems in fluid flow and plane stress and strain. He has extended the well-known Schwarz-Christoffel formula to multiply connected domains and implemented the formula numerically. He has also worked on inverse problems in acoustics, developing efficient computational methods to reconstruct boundary vibrations from interior pressure measurements. These methods can be applied to help locate sources of noise in aircraft and automobile cabins. In addition, Dr. DeLillo is interested in the mathematics of elementary particles physics and quantum field theory and he occasionally teaches courses on these topics. Recently he has been developing teaching material for the department's new programs in the mathematical foundations of data analytics.

Information

Academic Interests and Expertise
  • Numerical Conformal Mapping and Computational Complex Analysis
  • Inverse Problems
  • Quantum Field Theory
Areas of Teaching Interest
  • Numerical Analysis
  • Applied Mathematics and Fluid Dynamics
  • Mathematical Foundations of Data Analytics
  • Theoretical Physics
Publications
  • K. DeLillo, On some relations among numerical conformal mapping methods, Journal of Computational and Applied Mathematics, 19 (1987), pp. 363鈥377.
  • K. DeLillo, A note on Rengel鈥檚 inequality and the crowding phenomenon in conformal mapping, Applied Mathematics Letters, 3, 2, (1990), pp. 25鈥27.
  • K. DeLillo, A. R. Elcrat, and K. G. Miller, Constant vorticity Riabouchinsky flows from a variational principle, Journal of Applied Mathematics and Physics (ZAMP), 41 (1990), pp. 755鈥765.
  • K. DeLillo and A. R. Elcrat, A comparison of some numerical conformal mapping methods for exterior regions, Society for Industrial and Applied Mathematics (SIAM) Journal on Scientific and Statistical Computing, 12, 2 (1991), pp. 399鈥422.
  • K. DeLillo and A. R. Elcrat, A Fornberg-like conformal mapping method for slender regions, Journal of Computational and Applied Mathematics, 46, 1鈥2 (1993), pp. 49鈥 64.
  • K. DeLillo and J. A. Pfaltzgra铿, Extremal distance, harmonic measure, and numerical conformal mapping, Journal of Computational and Applied Mathematics, 46, 1鈥2 (1993), pp. 103鈥113.
  • K. DeLillo and A. R. Elcrat, Numerical conformal mapping methods for exterior regions with corners, Journal of Computational Physics, 108 (1993), pp. 199鈥208.
  • K. DeLillo, The accuracy of numerical conformal mapping methods: a survey of examples and results, SIAM Journal on Numerical Analysis, 31 (1994), pp. 788鈥812.
  • H. Chan, T. K. DeLillo, and M. A. Horn, The numerical solution of the biharmonic equation by conformal mapping, SIAM Journal on Scientific Computing, 18 (1997), pp. 1571鈥1582.
  • K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgra铿, Numerical conformal mapping methods based on Faber series, Journal of Computational and Applied Mathematics, 83 (1997), pp. 205鈥236.
  • H. Chan, T. K. DeLillo, and M. A. Horn, Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation, SIAM Journal on Scientific Computing Special Issue on Iterative Methods, 19 (1998), pp. 139鈥147.
  • K. DeLillo and J. A. Pfaltzgra铿, Numerical conformal mapping methods for simply and doubly connected regions, SIAM Journal on Scientific Computing Special Issue on Iterative Methods, 19 (1998), pp. 155鈥171.
  • K. DeLillo, M. A. Horn, and J. A. Pfaltzgra铿, Numerical conformal mapping of multiply connected regions by Fornberg-like methods, Numerische Mathematik, 83, 2 (1999), pp. 205鈥232.
  • DeLillo, V. Isakov, N. Valdivia, and L. Wang, The detection of the source of acoustical noise in two dimensions, SIAM Journal on Applied Mathematics, 61 (2001), pp. 2104鈥2121.
  • K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgra铿, Schwarz-Christo铿el mapping of the annulus, SIAM Review, 43 (2001), pp. 469鈥477.
  • DeLillo, V. Isakov, N. Valdivia, and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), pp. 507鈥524.
  • Benchama and T. K. DeLillo, A brief overview of Fornberg-like methods for conformal mapping of simply and multiply connected regions, Bulletin of the Malaysian Mathematical Sciences Society (Second Series) 26 (2003), pp. 1鈥10.
  • K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgra铿, Schwarz-Christo铿el mapping of multiply connected domains, Journal d鈥橝nalyse Mathematique, 94 (2004), pp. 17鈥47.
  • K. DeLillo, A. Elcrat, and C. Hu, Computation of the Helmholtz-Kirchho铿 and reentrant jet flows using Fourier series, Applied Mathematics and Computation, 163 (2005), pp. 397鈥422.
  • DeLillo, T. Hyrcak, and V. Isakov, Theory and boundary element methods for nearfield acoustic holography, Journal of Computational Acoustics, 13, 1 (2005), pp. 163鈥185.
  • K. DeLillo, Schwarz-Christo铿el mapping of bounded, multiply connected domains, Computational Methods and Function Theory Journal, 6, No. 2 (2006), pp. 275鈥300.
  • K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgra铿, Computation of multiply connected Schwarz-Christo铿el maps for exterior domains, Computational Methods and Function Theory Journal, 6, No. 2 (2006), pp. 301鈥315.
  • DeLillo and T. Hrycak, A stopping rule for the conjugate gradient regularization method applied to inverse problems in acoustics, Journal of Computational Acoustics, 14, No. 4 (2006), pp. 397鈥414.
  • Benchama, T. DeLillo, T. Hrycak, and L. Wang, A simplified Fornberg-like method for the conformal mapping of multiply connected regions - Comparisons and crowding, Journal of Computational and Applied Mathematics, 209 (2007), pp. 1鈥21.
  • K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgra铿, Radial and circular slit maps of unbounded multiply circle connected domains, Proceedings of the Royal Society A, 464 (2008), pp. 1719鈥1737.
  • K. DeLillo and E. H. Kropf, Slit maps and Schwarz-Christo铿el maps for multiply connected domains, Electronic Transactions on Numerical Analysis, 36 (2010), pp. 195鈥223.
  • K. DeLillo and E. H. Kropf, Numerical computation of the Schwarz-Christo铿el transformation for multiply connected domains, SIAM J. Sci. Comput., 33, 3 (2011), pp. 1369鈥1394.
  • K. DeLillo, A. R. Elcrat, and E. H. Kropf, Calculation of resistances for multiply connected domains using the Schwarz-Christo铿el transformations, Comput. Methods Function Theory, 11 (2) (2011), pp. 725鈥745.
  • K. DeLillo, A. R. Elcrat, E. H. Kropf, and J. A. Pfaltzgra铿, E铿僣ient calculation of Schwarz-Christo铿el transformations for multiply connected domains using Laurent series, Comput. Methods Funct. Theory, 13 (2013), pp. 307鈥336. D. G. Crowdy, S. Tanveer and T. DeLillo, Hybrid basis scheme for computing electrostatic fields exterior to close-to-touching discs, IMA Journal of Numerical Analysis, 36 (2) (2016), pp. 743鈥769.
  • Balu and T. K. DeLillo, Numerical methods for Riemann-Hilbert problems in multiply connected circle domains, Journal of Computational and Applied Mathematics, 307 (2016), pp. 248鈥261.
  • Badreddine, T. K. DeLillo, and S. Sahraei, A Comparison of Some Numerical Conformal Mapping Methods for Simply and Multiply Connected Domains, Dis crete and Continuous Dynamical Systems - B, 24, 1 (Jan. 2019), pp. 55鈥82, doi: 10.3934/dcdsb.2018100.
  • K. DeLillo and S. Sahraei, Computation of plane potential flow past multi-element airfoils using conformal mapping, revisited, Journal of Computational and Applied Mathematics, 362 (2019), pp. 246鈥261.