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

Projects
ResourcesA description of the compute resources available to members of the numerical analysis group can be found on this page. 
Faculty
Wolfgang Bangerth
Professor of Mathematics Numerical algorithms, finite element software, adaptive finite element schemes and error estimation, applications in fluid dynamics. 
Andrea Bonito
Associate 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 
JeanLuc Guermond
Professor of Mathematics Partial differential equations, numerical methods for PDEs, finite element aproximation, computational fluid dynamics 

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
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
Professor of Mathematics Conservation laws, linear transport equations, approximation theory, numerical analysis of PDEs. 
Visiting Faculty and Research Staff
Markus Bürg
Visiting Assistant Professor 
Adam Larios
Visiting Assistant Professor 
Murtazo Nazarov
Visiting Assistant Professor 
Sara Pollock
Visiting Assistant Professor 
Ke Shi
Visiting Assistant Professor 
Bruno Turcksin
Postdoctoral Researcher 
Graduate Students
SeulKi Kang  Sanghyun Lee  Spencer Patty 
Fang Wang  Kainan Wang  Arezou Ghesmati 
Vladimir Tomov  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. 
Guido Kanschat
Associate Professor of Mathematics Finite elements, discontinuous Galerkin methods, iterative solvers, computational fluid dynamics, radiative transfer, neutron transport 
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 FugroJason 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. 
Timo Heister
Assistant Professor Dept. of Math., Clemson University, South Carolina, USA 
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 KLATencor 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 
Jennifer Webster
Defended Summer 2013 Research scientist, Idaho National Laboratory 