Numerical Analysis and Scientific Computation

The Numerical Analysis and Scientific Computation group is primarily concerned with the efficient numerical approximation of solutions of partial differential equations. 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 and scientific applications.

The group consists of about a dozen permanent faculties and numerous graduate students, postdoc and visiting faculty. 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 on the development of large scale scientific simulations.

The graduate program in numerical analysis includes courses in basic numerical analysis, analysis of iterative methods, and finite element software. 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.

Regular events Numerical Analysis Seminar Applied Mathematics Seminar Finite Element Rodeo Resources See this page for a description of the compute resources available to members of the numerical analysis group.

Projects Advances in Numerical Analysis Computational Fluid Dynamics. Contaminant Transport in Porous Media Mobil Project

Faculty

	Andrea Bonito 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.		Matthias Maier Assistant Professor of Mathematics Multiscale effects in optical metamaterials, Multiscale methods, asymptotic analysis and homogenization theory, Finite element methods and finite element software.
	Alan Demlow Associate Professor of Mathematics Numerical analysis of partial differential equations, especially in the mathematical theory of finite element methods.		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		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

Prof. Peter Oswald (Fall 2016) Visiting Professor

Prof. Vivette Girault (Spring 2017) Visiting Professor

Graduate Students

Peng Wei	Justin Owen	Eric Tovar
Yuchen Hua	Min Wang	Jiuhua Hu
Salih Kilicli	Bennett Clayton	Siu Wun Cheung

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
	Wolfgang Bangerth Professor of Mathematics Numerical algorithms, finite element software, adaptive finite element schemes and error estimation, applications in fluid dynamics.

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.
Timo Heister Assistant Professor Dept. of Math., Clemson University, South Carolina, USA	Markus Bürg	Adam Larios Assistant Professor, U. of Nebraska
Murtazo Nazarov Assistant Professor, Uppsala University	Sara Pollock	Ke Shi Assistant Professor, Old Dominion University
Bruno Turcksin

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	Jennifer Webster Defended Summer 2013 Research scientist, Idaho National Laboratory	Kainan Wang Defended Spring 2014 Postdoc, University of Texas at Austin
Fang Wang Defended Summer 2014 Researcher, Stata	Sanghyun Lee Defended Summer 2014 Postdoc, ICES University of Texas at Austin	Seul-Ki Kang Defended Summer 2012 Analyst, Samsung Fire & Marine Insurance Co.
Vladimir Tomov Defended May 2014 Postdoc, Lawrence Livermore National Laboratory.	Youli Mao Defended August 2014	Daniel Castanon Defended May 2016 Postdoc, BCAM-Bilbao, Spain
Travis Thompson Defended August 2013 Research Associate, Joint Institute for Computational Sciences at Oak Ridge National Lab	Fahad Alrashed Defended May 2015 Computational Modeling Scientist, Dhahran, Saudi Arabia	Yong Yang Defended August 2016 Postdoc, Pennsylvania State University
Manuel Quezada de Luna Defended August 2016 Postdoc, US Army ERDC	Arezou Ghesmati Defended 2017	Spencer Patty Defended August 2017 Software Engineer, Intel Corporation
Wenyu Lei Defended 2018