Thomas DeLillo PhD, Dr.

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 Wichita 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.

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. 363–377.
• K. DeLillo, A note on Rengel’s inequality and the crowding phenomenon in conformal mapping, Applied Mathematics Letters, 3, 2, (1990), pp. 25–27.
• 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. 755–765.
• 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. 399–422.
• K. DeLillo and A. R. Elcrat, A Fornberg-like conformal mapping method for slender regions, Journal of Computational and Applied Mathematics, 46, 1–2 (1993), pp. 49– 64.
• K. DeLillo and J. A. Pfaltzgraff, Extremal distance, harmonic measure, and numerical conformal mapping, Journal of Computational and Applied Mathematics, 46, 1–2 (1993), pp. 103–113.
• K. DeLillo and A. R. Elcrat, Numerical conformal mapping methods for exterior regions with corners, Journal of Computational Physics, 108 (1993), pp. 199–208.
• K. DeLillo, The accuracy of numerical conformal mapping methods: a survey of examples and results, SIAM Journal on Numerical Analysis, 31 (1994), pp. 788–812.
• 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. 1571–1582.
• K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, Numerical conformal mapping methods based on Faber series, Journal of Computational and Applied Mathematics, 83 (1997), pp. 205–236.
• 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. 139–147.
• K. DeLillo and J. A. Pfaltzgraff, Numerical conformal mapping methods for simply and doubly connected regions, SIAM Journal on Scientific Computing Special Issue on Iterative Methods, 19 (1998), pp. 155–171.
• K. DeLillo, M. A. Horn, and J. A. Pfaltzgraff, Numerical conformal mapping of multiply connected regions by Fornberg-like methods, Numerische Mathematik, 83, 2 (1999), pp. 205–232.
• 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. 2104–2121.
• K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, Schwarz-Christoffel mapping of the annulus, SIAM Review, 43 (2001), pp. 469–477.
• DeLillo, V. Isakov, N. Valdivia, and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), pp. 507–524.
• 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. 1–10.
• K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, Schwarz-Christoffel mapping of multiply connected domains, Journal d’Analyse Mathematique, 94 (2004), pp. 17–47.
• K. DeLillo, A. Elcrat, and C. Hu, Computation of the Helmholtz-Kirchhoff and reentrant jet flows using Fourier series, Applied Mathematics and Computation, 163 (2005), pp. 397–422.
• DeLillo, T. Hyrcak, and V. Isakov, Theory and boundary element methods for nearfield acoustic holography, Journal of Computational Acoustics, 13, 1 (2005), pp. 163–185.
• K. DeLillo, Schwarz-Christoffel mapping of bounded, multiply connected domains, Computational Methods and Function Theory Journal, 6, No. 2 (2006), pp. 275–300.
• K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, Computation of multiply connected Schwarz-Christoffel maps for exterior domains, Computational Methods and Function Theory Journal, 6, No. 2 (2006), pp. 301–315.
• 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. 397–414.
• 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. 1–21.
• K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, Radial and circular slit maps of unbounded multiply circle connected domains, Proceedings of the Royal Society A, 464 (2008), pp. 1719–1737.
• K. DeLillo and E. H. Kropf, Slit maps and Schwarz-Christoffel maps for multiply connected domains, Electronic Transactions on Numerical Analysis, 36 (2010), pp. 195–223.
• K. DeLillo and E. H. Kropf, Numerical computation of the Schwarz-Christoffel transformation for multiply connected domains, SIAM J. Sci. Comput., 33, 3 (2011), pp. 1369–1394.
• K. DeLillo, A. R. Elcrat, and E. H. Kropf, Calculation of resistances for multiply connected domains using the Schwarz-Christoffel transformations, Comput. Methods Function Theory, 11 (2) (2011), pp. 725–745.
• K. DeLillo, A. R. Elcrat, E. H. Kropf, and J. A. Pfaltzgraff, Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series, Comput. Methods Funct. Theory, 13 (2013), pp. 307–336. 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. 743–769.
• 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. 248–261.
• 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. 55–82, 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. 246–261.