### Thomas DeLillo, Professor

Numerical Conformal Mapping; PhD, New York University, 1985

### 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 (in progress).
### 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

- 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), pp. 1571-1582.
- T. DeLillo, V. Isakov, N. Valdivia, and L. Wang, "The detection of surface vibrations from interior acoustical pressure", Inverse Problems, 19 (2003), pp. 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) pp. 17-47.
- T.K. DeLillo, "Schwarz-Christoffel mapping of bounded, multiply connected domains", Computational Methods and Function Theory Journal, 6, No.2 (2006), pp. 275-300.
- 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 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/