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 twelve 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 Computation 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 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 Advances in Numerical Analysis Computational Fluid Dynamics. Contaminant Transport in Porous Media Inverse problems and biomedical imaging Mobil Project Software for Finite Element Simulations and Scientific Computing Resources A description of the compute resources available to members of the numerical analysis group can be found on this page.

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.		Prabir Daripa Associate Professor of Mathematics Computational fluid dynamics, inverse problems, scientific computing, applied mathematics and engineering.
	Ronald DeVore Koss Professor of Mathematics, Distinguished Professor, Approximation theory, numerical analysis		Yalchin Efendiev Professor of Mathematics Numerical analysis, multiscale finite element method, flow in porous media		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	Timo Heister Visiting Assistant Professor	Adam Larios Visiting Assistant Professor
Miguel Sebastian Pauletti Visiting Assistant Professor	Sarah Zedler Research Associate (IAMCS)

Graduate Students

Seul-Ki Kang	Sanghyun Lee	Orhan Mehmetoglu
Fang Wang	Kainan Wang	Jennifer Webster
Vladimir Tomov	Habiballah Talavatifard	Youli Mao

Former Faculty

Richard Ewing (Nov. 24, 1946 - Dec. 5, 2007) Distinguished Professor of Mathematics Numerical analysis, finite volume and finite element approximations of PDEs, scientific computing.

James Bramble Distinguished Professor of Mathematics (retired) Partial differential equations, numerical methods for PDE, multigrid methods, domain decomposition methods.

Former Numerical Analysis Visiting Faculty and Postdocs

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	Jean Marie Linhart Lecturer Department of Mathematics, Texas A&M
Fabien Marpeau Visiting Assistant Professor Department of Mathematics, U. of Houston	Patrick O'Leary Director, Center for Advanced Modeling and Simulation at Idaho National Laboratory	Hao Lu Senior Computer Scientist Fugro-Jason Netherlands BV
Giancarlo Sangalli Associate Professor Dept. of Math., Università di Pavia, Italy	Joachim Schoeberl Professor Institute for Analysis and Scientific Computing, Vienna U. of Technology, 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 S. Carolina	Victor Ginting Postdoctoral Associate Assistant Prof. of Mathematics, U. of Wyoming
Jiangguo Liu Assistant Professor Dept. of Mathematics, Colorado State U.	Rajen Sinha Professor Head, Dept. of Mathematics, Indian Institute of Tech., Guwahati, India	Craig Douglas Distinguished Professor School of Energy Resources, Dept. of Mathematics, Director, Inst. Sci. Computation, U. of Wyoming.
Peter Minev Professor Dept. of Math.&Stat. Sciences, U. Alberta, Edmonton, Canada	Jörg Willems Research Scientist Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria	Shuguang Tan Bloomberg L.P.

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 Professor, Portland State University
Hong Huang Defended Fall 1999	Constantin Bacuta Defended Fall 2000 Associate 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 Prof., Innovative Comp. Lab CS Dept., U. 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 U.	Victor Ginting Defended Spring 2004 Assistant Professor, U. of Wyoming	Taejong Kim Defended Spring 2006 Processing Geophysicist, VERITAS DGC Inc., Houston
Dylan Copeland Defended Spring 2006 Research Scientist, IAMCS Texas A&M University	Veselin Dobrev Defended Summer 2007 Visiting Scientist, CASC, LLNL	Paul Dostert Defended Summer 2007 Assistant Professor, Coker College, Hartsville, SC
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 Research scientist, ExxonMobile, New York	Yan Li Defended Summer 2010	Abner Salgado Defended Summer 2010 Department of Mathematics at the U. Maryland
Moritz Allmaras Defended Winter 2011 Research scientist, Siemens, Munich, Germany