Professor Qin (Tim) Sheng
 
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Different splitting methods have played important roles in the numerical solution of differential equations. Since the pioneering work on ADI and exponential splitting formulae, many new concepts and strategies have been developed and utilized. Splitting methods associated with finite differences, finite elements, or adaptations have been used widely and have been shown to have powerful capabilities in solving different differential equation problems in various applications.

Please email your comments and suggestions to Q. Sheng (qin_sheng@baylor.edu).


Research References:

  Baker-Campbell-Hausdorff Formula in Wikipedia.

  Trotter Product Formula in Wolfram.

  The Pioneering Paper by Peaceman and Rachford, Jr. ( Journal of the SIAM, Vol. 3, 1955, pages 28 - 41 ).

  Nineteen Dubious Ways to Compute a Matrix Exponential, I, by Moler and Van Loan ( SIAM Review, Vol. 20, 1978, pages 801 - 836 ).

  Splitting Methods, by McLachlan and Quispel ( Acta Numerica, Vol. 11, 2002, pages 341 - 434 ).

  Nineteen Dubious Ways to Compute a Matrix Exponential, II, by Moler and Van Loan ( SIAM Review, Vol. 45, 2003, pages 3 - 46 ).

  Strang Splitting -- Want to see a list of citations in Google? ( Google Search ).

  Geometric Numerical Integration, by Hairer, Lubich and Wanner ( Book by Springer, 2006, ISBN: 3-540-30663-3 ).

  From Exponential Functions to Exponential Splitting Computations -- Workshop, by Sheng ( Humboldt-University in Berlin, SUMMER 2007 ).

  Decompositions--A Journey of the Exponential Splitting Method for Solving Singular PDEs -- Mathematics Colloquium, by Sheng ( National Taiwan University, FALL 2009 ).



Recent Position Announcements:

  One Faculty Position and One Postdoctoral Position at Baylor, USA, posted September 2013

  Two Faculty Positions and One Postdoctoral Position at Baylor, USA, posted September 2011

  Faculty Position in University of Texas, USA, posted March 2011

  Research Positions in Britain, posted May 2010

  Postdoctoral Position in Montpellier, France, posted March 2008

  Postdoctoral Position in Berlin, Germany, posted September 2007

  Postdoctoral Position in Paris, France, posted September 2007



Recent Activities:

  Special Issue on Splitting Methods for Differential Equations (published!)

  Special Issue on Novel Difference and Hybrid Methods for Differential and Integro-Differential Equations (published!)

  Special Issue on Financial Derivatives (published!)

  Special Issue on Recent Advances in Numerical Solutions of Stochastic Partial Differential Equations

  LMS Minisymposium on Advanced Decomposition Methods for Partial Differential Equations, London, UK, September 2013

  DCABES 2013, London, UK, September 2013

  CMMSE2013, Cabo de Gata, Almería, Spain, June 2013

  Seventh M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, USA, June 2013

  TBA, Alejandro Aceves (SMU), Baylor Math Colloquium, USA, May 2013

  Fourteenth International Conference on Numerical Combustion, San Antonio, TX, USA, April 2013

  Eighth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, GA, USA, March 2013

  A new class of massively parallel direction splitting for the incompressible Navier-Stokes equations, Jean-Luc Guermond (Texas A&M), Baylor Math Colloquium, USA, Feb 2013

  Sixth European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, Austria, September 2012

  SIAM Annual Meeting, Minneapolis, MN, USA, July 2012

  CMMSE2012, Marcia, Spain, July 2012

  CASPER Spring Seminar, Waco, TX, USA, April 2012

  Finite Element Rodeo, Rice University, Houston, TX, USA, March 2012

  Baylor Workshop on Splitting and Multiscale Methods for Computational PDEs, Baylor University, Waco, TX, USA, September 2011

  CMMSE2011, Alicante, Spain, June 2011

  Highly Oscillatory Problems: From Theory to Applications, I. Newton Institute, Cambridge, UK, September 2010

  A Symposium on Splitting Methods for Differential Equations, Institut de Matemŕtiques i Aplicacions de Castelló, Castellón, Spain, September 2010

  SIAM Annual Meeting, Pittsburgh, PA, USA, July 2010

  CMMSE2010, Almeria , Andalucia, Spain, June 2010

  Minisymposium for the 8th AIMS Conference on Dynamical Systems, Dresden, Germany, May 2010

  Special Sessions for the Joint AMS Annual Meeting, San Francisco, CA, USA, January 2010

  2009 Fall AMS Sectional Meeting, Waco, TX, USA, October 2009

  CMMSE2009, Gijón (Asturias), Spain, June-July 2009

  Minisymposium for the Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, USA, June 2009

  International Workshop on Beam Propagation Methods for Nonlinear Refractive and Absorptive Media, Dayton, USA, June 2009

  Third International Conference on Scientific Computing and Partial Differential Equations, Hong Kong, December 2008

  Workshop on Splitting Methods in Time Integration, Innsbruck, Austria, October 2008

  International Workshop on Numerical Mathematics for Engineering Problems, in conjunction with the IEEE CSE 2008, Săo Paulo, Brazil, July 2008

  Minisymposium for the WCCM VIII-ECCOMAS, Italy, June-July 2008

  CMMSE2008 in Murcia, Spain, June 2008

  Minisymposium for the 7th AIMS International Conference on Dynamical Systems and Differential Equations, Arlington, Texas, 18-21 May 2008

  2008 Spring AMS Sectional Meeting, Courant Institute, NYC, NY, USA, March 2008

  Minisymposium in the USNCCM IX in San Francisco, USA, July 2007

  Minisymposiums in the ICIAM07 in Zurich, Switzerland, July 2007

  Minisymposiums in the CMMSE2007 in Chicago, USA, June 2007

  HOP Program in Isaac Newton Institute for Mathematical Sciences, Britain, January-July 2007

  Castellon Conference on Geometric Integration in University Jaume I, Spain, September 2006

  Minisymposium in the SIAM Annual Meeting in Boston, USA, July 2006

  50 Years of ADI Method, a Celebration Conference in Rice University, USA, Nov. 2005



Links in the Study:

Researchers: Reference Words:
Matthew A. Beauregard
Clarkson University, USA
http://www.clarkson.edu/math/
Dimensional and operator splitting,
adaptive finite difference methods,
iterative splitting for multiphysical problems
Sergio Blanes
Universitat Politécnica de Valencia, Spain
http://personales.upv.es/~serblaza/
Symplectic and operator splitting,
adaptive geometric integrators, Hamiltonian
problems, Lie group methods
R. Phillip Bording
Memorial University of Newfoundland, Canada
http://www.esd.mun.ca/faculty/members/bording_p.html
Itertive operator-splitting,
applied splitting algorithms,
parallel computing
Chris Budd
University of Bath, UK
http://www.bath.ac.uk/~mascjb/
adaptive splitting,
scale invariant adaptive mesh methods,
singular elliptic and parabolic PDEs
Mari Paz Calvo
Universidad de Valladolid, Spain
http://www.mac.cie.uva.es/~maripaz/
Symplectic and exponential splitting,
numerical Hamiltonians,
numerical differential equations
Fernando Casas
Universitat Jaume I, Spain
http://www.gicas.uji.es
Symplectic and operator splitting,
adaptive geometric integrators,
differential equations
Siu A. Chin
Texas A&M University, USA
http://www.physics.tamu.edu/
Geometric integration,
stable high order splitting,
applied and quantum physics
Moody T. Chu
North Carolina State University, USA
http://www4.ncsu.edu/~mtchu/
Geometric integration,
differential equations,
SVD and matrix analysis
Paul Clifford
University of Warwick, UK
http://www.maths.warwick.ac.uk
High dimensional integrals,
splitting methods for PDEs,
ADI and LOD schemes
Stéphane Descombes
Université de Nice - Sophia Antipolis, France
http://math.unice.fr/~sdescomb/
Operator splitting and applications,
mathematical biology
 
Bjorn Engquist
University of Texas at Austin, USA
http://www.ma.utexas.edu/text/webpages/engquist.html
Multiscale modeling,
HOP numerical solution,
CFD computations
Graeme Fairweather
Colorado School of Mines, USA
http://www.mines.edu/fs_home/gfairwea/
ADI methods and analysis,
finite element methods
 
I. Farago
Eötvös Loránd University, Hungary
http://www.elte.hu/
Iterative splitting,
operator splitting methods,
differential equations
Martin Gander
Universite de Geneve, Switzerland
http://www.unige.ch/~gander/
Domain decomposition methods,
waveform relaxation methods,
parallel space time methods
Jürgen Geiser
Humboldt-Universität zu Berlin, Germany
http://www.mathematik.hu-berlin.de/~geiser/
Itertive operator-splitting,
applied math algorithms
 
Glen Gillen
California Polytechnic State University, USA
http://www.calpoly.edu/~phys/ggillen.html
Finite difference algorithms,
computational physics,
e-optics and optimizations
Roland Glowinski
University of Houston, USA
http://www.math.uh.edu/~roland/
Newtonian and non-Newtonian fluids,
domain decomposition methods,
operator splitting
Leonel Gonzalez
USAF Research Laboratory, USA
http://www.afrl.af.mil/
E-optics computations,
experimental optics and modeling,
linear and nonlinear systems
Jean-Luc Guermond
Texas A&M University, USA
http://www.math.tamu.edu/~guermond
Partial differential equations,
numerical methods in fluid dynamics,
finite element method
Shekhar Guha
USAF Research Laboratory, USA
http://www.afrl.af.mil/
ADI and splitting computations,
computational physics, mathematical modeling,
linear and nonlinear e-optics
Ernst Hairer
Universite de Geneve, Switzerland
http://www.unige.ch/~hairer/welcome.html
Geometric numerical integration,
numerical ODEs,
exponential splitting
Eskil Hansen
Lund University, Sweden
http://www.maths.lu.se/avdelningar/numerisk-analys/medarbetare/#0
Galerkin/Runge-Kutta discretizations,
nonlinear parabolic equations,
dimensional splitting
Jialin Hong
Chinese Academy of Sciences, China
http://www.cc.ac.cn/staff/hjl.html
Structure-preserving algorithms,
dynamical systems
 
Thomas J.R. Hughes
University of Texas at Austin, USA
http://www.ae.utexas.edu/faculty/members/hughes.html
Operator splitting methods,
computational mechanics,
complex fluids
Daan Huybrechs
Katholieke Universiteit Leuven, Belgium
http://people.cs.kuleuven.be/~daan.huybrechs/
oscillatory integrals and
oscillatory integral equations,
function approximations, splitting methods
Arieh Iserles
University of Cambridge, UK
http://www.damtp.cam.ac.uk/user/na/people/Arieh/
Geometric integration, complex dynamics,
foundations of computational mathematics,
orthogonality and ODEs
Abdul M. Khaliq
Middle Tenessee State University, USA
http://www.mtsu.edu/~akhaliq/
Operator and dimensional splitting,
nonlinear PDE analysis,
advanced financial computations
Sanjay K. Khattri
Stord Haugesund University College, Norway
http://ans.hsh.no/home/skk/
Numerical PDEs, reservoir simulation,
finite volume, mesh generations,
ADI methods
Choi-Hong Lai
University of Greenwich, UK
http://www.cms.gre.ac.uk/staff/details.asp?id=243
Image processing, inverse problems,
split and parallel computing,
computational medical biology
Ming-Chih Lai
National Chiao Tung University, Taiwan
http://jupiter.math.nctu.edu.tw/~mclai/
Computational fluid dynamics,
split and adaptive numerical methods,
mathematical modeling with applications
Che-Rung Lee
National Tsing Hua University, Taiwan
http://www.cs.nthu.edu.tw/~cherung/
Quantum Monte Carlo simulations,
solutions of large linear systems,
split solvers and parallel computing
Ping Lin
University of Dundee, UK
http://www.maths.dundee.ac.uk/~plin/
Decomposition schemes,
adaptive finite element methods,
computational fluid mechanics
Xinfeng Liu
University of South Carolina, USA
www.math.sc.edu/~xfliu
alternate direction and operator splitting,
compact schemes and stability,
stiff system solvers
Christian Lubich
Universität Tübingen, Germany
http://na.uni-tuebingen.de/~lubich/
Geometric numerical integration,
numerical ODES and PDEs,
operator splitting
Marc Massot
École Centrale Paris, France
http://www.em2c.ecp.fr/
Numerical combustion,
operator and dimensional splitting
 
Robert McLachlan
Massey University, New Zealand
http://www.massey.ac.nz/~rmclachl/
Geometric integration,
foundations of computational mathematics
 
Per Christian Moan
Universitet i Oslo, Norway
http://www.math.uio.no/
Symplectic splitting,
geometric, Nagnus integrators
 
Syvert P. Nřrsett
Norges teknisk-naturvitenskapelige universitet, Norway
http://www.math.ntnu.no/~norsett/
Geometric integration,
numerical ODEs on and off manifolds
 
Alexander Ostermann
Universität Innsbruck, Austria
http://techmath.uibk.ac.at/numbau/alex/
Exponential integrators,
nonlinear parabolic problems,
geometric theory, nonlinear analysis
Reinout Quispel
La Trobe University, Australia
http://www.latrobe.edu.au/mathstats/staff/quispel.html
Geometric integration,
splitting methods, dynamical systems,
integrable systems
Béatrice Rivičre
Rice University, USA
http://www.caam.rice.edu/~riviere/
Discontinuous Galerkin (DG) methods,
multiphase flow, error analysis,
numerical differential equations
Jesus M. Sanz-Serna
Universidad de Valladolid, Spain
http://www.sanzserna.org/intro.php
Geometric integration,
HOP numerical integrators,
mollified impulse methods
John N. Shadid
Sandia National Laboratories, USA
http://www.sandia.gov/
Stability of operator splitting,
multidimensional CFDs
 
Qin Sheng
Baylor University, USA
http://bearspace.baylor.edu/Qin_Sheng/www/index.html
Exponential and operator splitting,
adaptive difference methods,
hybrid and meshless methods
Andrew Sornborger
University of Georgia, USA
http://www.math.uga.edu/
High order operator splitting,
quantum computations
 
Gilbert Strang
MIT, USA
http://www-math.mit.edu/~gs/
Exponential and operator splitting,
finite element and difference methods
 
Andrew Stuart
University of Warwick, UK
http://www.warwick.ac.uk/~masdr/
Applied and computational mathematics,
finite element and difference methods
 
Haiwei Sun
University of Macau, Macau
http://www.fst.umac.mo/en/staff/fsthws.html
Matrix exponential computations,
solutions of large linear systems,
fractional differential equations
Zhizhong Sun
Southeast University, China
http://math.seu.edu.cn/Portal/101001322/
Theory and methods of finite differences,
numerical analysis and ADI applications,
fractional differential equations
M. Suzuki
University of Tokyo, Japan
--
Operator and exponential splitting,
quantum physics and algorithms
matrix exponential products
Xuecheng Tai
Universitetet i Bergen, Norway
http://www.mi.uib.no/~tai/
Domain decomposition methods,
parallel operator splitting,
image analysis and levelset
Roger Choon Ee Tan
National University of Singapore, Singapore
http://www.math.nus.edu.sg/~mattance/
Numerical partial differential equations,
matrix eigensystems and sensitivity analysis,
control theory
Yi-fa Tang
Chinese Academy of Sciences, China
http://www.cc.ac.cn/staff/tyf.html
Geometric numerical integration,
dynamical systems
 
Tao Tang
Hong Kong Baptist University, Hong Kong
http://www.math.hkbu.edu.hk/~ttang/
Spectral and high-order methods,
adaptive computations,
parallel splitting schemes
Richard A. Tapia
Rice University, USA
http://www.caam.rice.edu/~rat/
Interior-point methodology,
quasi-Newton methods,
constrained optimization
John Trangenstein
Duke University, USA
http://www.math.duke.edu/faculty/trangenstein/
Operator splitting,
adaptive mesh refinement,
flow in porous media
Gerhard Wanner
Universite de Geneve, Switzerland
http://www.unige.ch/~wanner/
Geometric numerical integration,
numerical ODEs,
splitting methods
Musheng Wei
Shanghai Normal University, China
http://mathsc.shnu.edu.cn/Default.aspx?tabid=1032
Pseudoinverses and least squares,
numerical linear algebra,
nonlinear PDE analysis
Mary F. Wheeler
University of Texas, USA
http://users.ices.utexas.edu/~mfw/
Subsurface mathematical modeling,
finite element methods for PDEs,
time stepping procedures
Xinyuan Wu
Nanjing University, China
http://math.nju.edu.cn/~XYWUMATHNJU/
Geometric algorithms for differential equations,
stiff problem solvers,
numerical algebraic systems
Haruo Yosida
National Astronomical Observatory, Japan
http://www.nao.ac.jp/E/index.html
Symplectic integration methods,
quantum physics and algorithms,
Hamiltonian systems
Antonella Zanna
University of Bergen, Norway
http://www.mi.uib.no/~anto/
Symplectic integration,
Hamiltonian systems,
error of splitting formulae

 

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