# 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## ResourcesSee this page for a description of the compute resources available to members of the numerical analysis group. |
## Projects |

## 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. |
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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 |
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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 |
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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

Hung-Chieh Chu | Arezou Ghesmati |

Seul-Ki Kang | Spencer Patty |

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 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 |
Sanghyun Lee
Defended Summer 2014 Postdoc, ICES University of Texas at Austin |