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Numerical Analysis and Scientific Computation

Groundwater Contaminant Flow

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

Resources

A description of the compute resources available to members of the numerical analysis group can be found on this page.

Faculty

Wolfgang Bangerth Wolfgang Bangerth
Professor of Mathematics
Numerical algorithms, finite element software, adaptive finite element schemes and error estimation, applications in fluid dynamics.
Andrea Bonito 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 Prabir Daripa
Associate Professor of Mathematics
Computational fluid dynamics, inverse problems, scientific computing, applied mathematics and engineering.
Ron DeVore Ronald DeVore
Koss Professor of Mathematics, Distinguished Professor,
Approximation theory, numerical analysis
Yalchin Efendiev Yalchin Efendiev
Professor of Mathematics
Numerical analysis, multiscale finite element method, flow in porous media
Jean-Luc Guermond Jean-Luc Guermond
Professor of Mathematics
Partial differential equations, numerical methods for PDEs, finite element aproximation, computational fluid dynamics
Raytcho Lazarov Raytcho Lazarov
Professor of Mathematics
Numerical analysis, finite difference, finite volume, and finite element approximations of PDEs, scientific computing.
Joseph Pasciak Joseph Pasciak
Professor of Mathematics
Finite element approximation, preconditioned iterative methods including domain decomposition and multigrid, large scale scientific computation
Guergana Petrova Guergana Petrova
Professor of Mathematics
Numerical methods for PDEs, approximation theory, wavelets
Michael Pilant Michael Pilant
Professor of Mathematics
Inverse problems in PDE, parallel and distributed computation, numerical algorithms, iterative methods for nonlinear equations.
Bojan Popov 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

Seul-Ki Kang Sanghyun Lee Spencer Patty
Arezou Ghesmati
Vladimir Tomov Youli Mao

Former Faculty

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

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