Courses | Prospective Students: Undergraduate - Graduate | Positions Available

Numerical Analysis and Scientific Computation

The numerical methods group is primarily concerned with the efficient numerical approximation of solutions of partial differential equations. The techniques and expertise include the development and analysis of iterative methods, stability and error analysis for finite element, finite difference and finite volume approximations, and large scale scientific computation with industrial application.

The group consists of eight permanent faculties, graduate students and numerous visitors. As well as doing research into theoretical numerical analysis, the group works closely with the Institute for Scientific Computatation and the Institute for Applied Mathematics and Computational Science in the development of large scale scientific simulations for serial and parallel computing architectures.

The graduate program in numerical analysis includes courses in basic numerical analysis and analysis of iterative methods. More advanced courses concerning the theory of finite elements, domain decomposition, multigrid, and mixed finite elements are also offered on a regular basis. Several of the past Numerical Analysis Qualifying Exams are available.

Events

Numerical Analysis Seminar
Applied Mathematics Seminar
Texas Finite Element Rodeo
Eighth IMACS International Symposium on Iterative Methods in Scientific Computation
November 15-17, 2006.
A Scientific Celebration of the 60th Birthday of Professor Richard E. Ewing
November 17-18, 2006.
James Bramble – Half a Century in Mathematics
May 2-3, 2008.

Projects

Faculty

Wolfgang Bangerth Associate Professor of Mathematics Inverse and imaging problems in PDE, numerical algorithms, finite element software, adaptive finite element schemes and error estimation.	Andrea Bonito Assistant Professor of Mathematics Adaptive Numerical Methods for Standard and Geometric PDEs, Free Boundary Problems, Computational Fluid Dynamics including Viscoelastic Flows.	James Bramble Distinguished Professor of Mathematics (retired) Partial differential equations, numerical methods for PDE, multigrid methods, domain decomposition methods.
Prabir Daripa Associate Professor of Mathematics Computational fluid dynamics, inverse problems, scientific computing, applied mathematics and engineering.	Ronald DeVore Koss Professor of Mathematics Approximation theory, numerical analysis	Yalchin Efendiev Professor of Mathematics Numerical analysis, multiscale finite element method, flow in porous media
Richard Ewing (November 24, 1946 - December 5, 2007) Distinguished Professor of Mathematics Numerical analysis, finite difference, finite volume, and finite element approximations of PDEs, scientific computing.	Jean-Luc Guermond Professor of Mathematics Partial differential equations, numerical methods for PDEs, finite element aproximation, computational fluid dynamics	Guido Kanschat Associate Professor of Mathematics Finite elements, discontinuous Galerkin methods, iterative solvers, computational fluid dynamics, radiative transfer, neutron transport
Raytcho Lazarov Professor of Mathematics Numerical analysis, finite difference, finite volume, and finite element approximations of PDEs, scientific computing.	Joseph Pasciak Professor of Mathematics Finite element approximation, preconditioned iterative methods including domain decomposition and multigrid, large scale scientific computation	Guergana Petrova Associate Professor of Mathematics Numerical methods for PDEs, approximation theory, wavelets
Michael Pilant Professor of Mathematics Inverse problems in PDE, parallel and distributed computation, numerical algorithms, iterative methods for nonlinear equations.	Bojan Popov Associate Professor of Mathematics Conservation laws, linear transport equations, approximation theory, numerical analysis of PDEs.

Visiting Faculty and Research Staff

Juan Galvis Visiting Assistant Professor	Jean Marie Linhart Visiting Assistant Professor	Miguel Sebastian Pauletti Visiting Assistant Professor
Shuguang Tan Visiting Assistant Professor	Jörg Willems Visiting Assistant Professor

Graduate Students

Moritz Allmaras	Yan Li	Javier Polanco
Abner Salgado	Fang Wang	Kainan Wang
Jennifer Webster

Former Numerical Analysis Visiting Faculty

Mohammed Aiffa Sessional Instructor Dept. of Mathematics and Statistics, U. of Calgary	Panagiotis Chatzipantelidis Assistant Professor Dept. of Mathematics, University of Crete, Greece	Oleg Iliev Research Associate Inst. for Industrial Math. (ITWM), Kaiserslautern
Sungkwon Kang Research Scientist Chosun University, Korea	Jeongwook Kim Visiting Associate Professor Junnam University, Korea	Fabien Marpeau Visiting Assistant Professor Department of Mathematics, University of Houston
Patrick O'Leary Assistant Professor of Computer Science, Dept. of Math. Science, U. of Alaska Anchorage	Hao Lu Senior Computer Scientist Fugro-Jason Netherlands BV	Giancarlo Sangalli Associate Professor Dept. of Math., Università di Pavia, Italy
Joachim Schöberl Assistant Professor Johannes Kepler University Linz, Austria	Anna Spagnuolo Associate Professor Dept. of Math. and Statistics, Oakland U., Rochester, Michigan	Olaf Steinbach Univ.-Prof. Inst. für Numerische Mathematik, Graz University of Technology, Austria
Hong Wang Professor Dept. of Mathematics, University of South Carolina	Victor Ginting Postdoctoral Associate Dept. of Mathematics, Colorado State Univ.	Jiangguo Liu Assistant Professor Dept. of Mathematics, Colorado State Univ.
Rajen Sinha Associate Professor Dept. of Mathematics, Indian Inst. of Tech. Guwahati	Craig Douglas Professor Departments of Computer Science and Mechanical Engineering, University of Kentucky. Senior Research Scientist, Department of Computer Science, Yale University.

Former Numerical Analysis Ph.D. Students

Sergey Malyasov Defended Spring 1996 ExxonMobil Upstream Research Co., Houston, TX	Ilya Mishev Defended Spring 1996 ExxonMobil Upstream Research Co., Houston, TX	Apostol Vassilev Defended Spring 1996 Founder and CEO NetIDSys, Inc.
Tong Sun Defended Spring 1997 Associate Prof., Dept. of Math., Bowling Green State U.	Yan Zheng Defended Summer 1997	Jayadeep Gopalakrishnan Defended Spring 1999 Associate Prof., Dept. of Mathematics, U. of Florida
Hong Huang Defended Fall 1999	Constantin Bacuta Defended Fall 2000 Assistant Prof., Math. Sciences, U. Delaware	Chisup Kim Defended Summer 2001 Assistant Professor of Mathematics The Catholic University of America
Stanimire Tomov Defended Spring 2002 Research Scientist and Adjunct Assistant Professor, at the Innovative Computing Laboratory Computer Science Department, University of Tennessee	Jun Zhao Defended Summer 2002 KLA-Tencor Corporation, San Jose, CA	Tzanio Kolev Defended Spring 2004 Computational mathematician at the Center for Applied Scientific Computing, LLNL
Yanqiu Wang Defended Spring 2004 Assistant Prof., Math. Dept., Oklahoma State University	Victor Ginting Defended Spring 2004 Assistant Professor, U. of Wyoming	Taejong Kim Defended Spring 2006 Processing Geophyisicist, VERITAS DGC Inc., Houston, TX
Dylan Copeland Defended Spring 2006 Research Scientist Direct Field Problems, RICAM, Austria	Veselin Dobrev Defended Summer 2007	Paul Dostert Defended Summer 2007 Postdoctoral Associate, University of Arizona
Dukjin Nam Defended Summer 2008	Lijian Jiang Defended Summer 2008 Institute for Mathematics and its Applications	Seungil Kim Defended Summer 2009 Southern Methodist University
Dimitar Trenev Defended Summer 2009 Institute for Mathematics and its Applications, University of Minnesota