Washington University, St. LouisEngineering

Norman Katz

From 1959 to 1967, Professor Katz was at the AVCO Research and Advanced Development in Wilmington, Massachusetts, first as a Senior Scientist; then as a Section Chief; and finally as manager of the mathematics department. He studied numerical solutions of engineering problems, particularly ordinary and differential equations, on high speed computers. In 1967, Professor Katz joined Washington University in St. Louis as an associate professor in the Department of Applied Mathematics and Computer Science. In 1991, he became chair of the department. He also served as a consultant at McDonnell Aircraft Company from 1980 to 1990.
Numerical analysis and computational mathematics have become increasingly active and important disciplines pervading science, engineering, and mathematics. Professor Katz's primary research interests are in the numerical solution of ordinary and partial differential equations, reliable algorithms, parallel computation and finite element analysis. For more than 20 years, he has helped develop the p-version of the finite element method. This version is now widely accepted as a reliable computational tool in the finite element analysis of elastic structures, heat transfer, and related fields, and is implemented in many commercial computer codes. Other research interests include formulation and solution of location - equilibrium problems widely used in optimal facility location.
Selected Publications
"An Always Convergent Numerical Scheme for a Random Locational Equilibrium Problem", (with L. Cooper), SIAM J. Num. Anal., Vol. 11, No. 4, pp. 683-692, September 1974.

"The p-version of the Finite Element Method" (with I. Babuska and B. A. Szabo), SIAM J. Num. Anal., Vol. 18, No. 3, June 1981, pp. 515-545.

"The p-version of the Finite Element Method for Problems Requiring C1- continuity" (with D. W. Wang), in SIAM Journal of Numerical Analysis, Vol. 22, No. 6, December 1985, pp. 1082-1106.

"Multi-p Methods: Iterative Algorithms for the p-version of the Finite Element Method," (with N. Hu), SIAM Journal on Scientific Computing, Vol. 16, No. 6, pp. 1308-1332, (1995).

"Convergence of an Iterative Algorithm for Solving Hamilton-Jacobi Type Equation," (with J. Markman), Mathematics of Computation, Vol. 71, No. 237, pp. 77—103, ( 2001).

“An Iterative Algorithm for Solving Hamilton-Jacobi Type Equations,” (with J. Markman), SIAM Journal on Scientific Computing, Vol. 22, No. 1, pp. 312--329 (2000).

“Sequential Linear Quadratic Method for Differential Games,” H. Mukai, A. Tanikawa, I. Tunay, I. N. Katz, H. Schattler, P. Rinaldi, I. A. Ozcan, G. J. Wang, L. Yang and Y. Sawada, Proceedings of the 2nd DARPA-JFACC Symposium on Advances in Enterprise Control, pp. 159-168, Minneapolis, April 2000.

“Solution of a Differential Game Formulation of Military Air Operations by the Method of Characteristics”, I. N. Katz, H. Mukai, H. Schattler, M. Zhang, and M. Xu, Journal of Optimization Theory and Applications, Vol.125, No. 1 pp.113-135, April 2005.

“An Asymmetric Extension of the Generalized Fermat Location Problem”, I. N. Katz and S. R. Vogl, International Journal on Computers and Mathematics, Vol. 59, No. 1, pp.399-410, January 2010.

Selected Research
Air Force Office of Scientific Research Grant, "Research and Development of the p-Version of the Finite Element Method," 10/1/77 - 10/31/94

National Science Foundation Research Grant, “Iterative Algorithms for the p-version of the Finite Element Method: Parallel Multi-p Processes,” 9/1/96 - 8/31/99

Contact Norman Katz
Address 1 Brookings Drive
Campus Box 1127
City/St/Zip St. Louis, MO 63130

Bryan Hall, Room 309

Phone (314) 935-6083
Fax (314) 935-3248
Email katz@wustl.edu
Other Appt. Computer Science & Engineering

PhD, Massachusetts Institute of Technology, 1959
MS, Yeshiva University, 1954
BS, Yeshiva University, 1952

Washington University in St. Louis School of Engineering & Applied Science, Department of Electrical & Systems Engineering

Green Hall, CB 1042, 1 Brookings Drive, Saint Louis, MO, USA 63130
Phone: (314) 935-5565, Fax: (314) 935-7500

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