Thomas DeLillo

Thomas DeLillo, Professor

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.

Research

Dr. DeLillo's research is in the numerical computation and theoretical study of conformal maps and in the development of computational methods for inverse problems in acoustics. 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, quantum field theory, and string theory.

Selected Publications

  • T. K. DeLillo, "The accuracy of numerical conformal mapping methods: a survey of examples and results", SIAM Journal on Numerical Analysis, 31 (1994) 788-812.
  • R. 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) 1571-1582.
  • T. 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) 205-236.
  • T. K. DeLillo, M. A. Horn, and J. A. Pfaltzgraff, "Numerical conformal mapping of multiply connected regions by Fornberg-like methods", Numerische Mathematik, 83 (1999) 2, 205-232.
  • T. DeLillo, V. Isakov, N. Valdivia, and L. Wang, "The detection of surface vibrations from interior acoustical pressure", Inverse Problems, 19 (2003) 507-524.
  • T. K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, "Schwarz-Christoffel mapping of multiply connected domains", Journal d'Analyse Mathematique, 94 (2004) 17-47.