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DEPARTMENT OF MATHEMATICS, STATISTICS, AND PHYSICS

Thomas DeLillo, Professor and Chairman

Numerical Conformal Mapping; PhD, New York University, 1985

 

Contact

 

Awards

WSU President's Distinguished Service Award, 2004

 

PhD Students

  • Mark A. Horn, "Iterative Methods Applied to Some Problems in Conformal Mapping and Potential Theory", PhD thesis, 1997.
  • Lianju Wang, "Computational Methods for Two Problems in Potential Theory", PhD thesis, 2000.
  • Nourredine Benchama, "A simplified Fornberg-Like Method for the Conformal Mapping of Multiply Connected Regions", PhD thesis, 2003.
  • T. Mark Harder, "Some remarks on constructive Yukawa theory in four dimensions", PhD thesis, 2008.
  • Everett H. Kropf, "A Fornberg-like method for the numerical conformal mapping of bounded multiply connected domains", MS thesis(won WSU Graduate School Outstanding Thesis Award for Spring 2009), PhD thesis (2012) "Numerical Computation of Schqarz-Christoffel transformations and slit maps for multiply connedted domains."
  • Badreddine, M.  “Comparison of Some Numerical Conformal Mapping Methods for Simply and Multiply Connected Domains”  PhD thesis, May 2016 
  • Justin Mears (Current)
  • Saman Sahraei (Current)


Research

Dr. 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 coures on these topics.

 

Selected Publications

  • T.K. DeLillo and E.H. Kropf, Numerical Computation of the Schwarz-Christoffel transformation for multiply connected domains, SIAM J. Sci. Comput., 33 (2011, pp. 1369-1394.
  • T.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; http://etna.mcs.kent.edu/
  • N. Benchama, T. DeLillo, T. Hrycak, and L. Wang, A simplified Fornberg-like methods for the conformal mapping of multiply connected regions-Comparisons and crowding, Journal of Computational and Applied Mathematics, 209 (2007), pp. 1-21.
  • T.K. DeLillo, Schwarz-Christoffel mapping of bounded, multiply connected domains, Computational Methods and Function Theory Journal, 6, No.2 (2006), pp. 275-300.
  • T.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.
  • T.K. DeLillo, V. Isakov, N. Valdivia, and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), pp. 507-524.