Pilwon Kim

rs1114

Welcome!

Courses:

 

Spring 2008 Math 415: Ordinary and Partial Differential Equations

Spring 2008 Math 571: Linear Algebra with Applications

Research Interests:

 

My current interest is geometric integration, especially applications of Lie symmetry theory to numerical analysis for differential equations. In broad sense, geometric integration means numerical schemes that inherit structural and qualitative characteristics of the underlying system such as total energy, first integrals, symplecticity and Lie symmetries. I am developing several geometric integrators, invariantization by moving frames and the solution interpolation.

I am also interested in other practical applications of Lie groups. One of my long-term research plans is to establish an approximate equivalence theory by combining symmetry theory with other related fields, which brings a spark to computer vision, image processing, data compression, and so on.

 

Research Papers:

  • Geometric integration via multi-space (with P.J.Olver), Regular and Chaotic Dynamics, 2004, 9(3), 213-226
  • Numerical invariantization for morphological PDE schemes (with M.Welk and P.J.Olver), Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli and N. Paragios, eds., Lecture Notes in Computer Science, Springer--Verlag, New York, 2007.
  • Invariantization of Numerical Schemes Using Moving Frames  to appear in BIT
  • Invariantization of the Crank-Nicolson Method for Burgers' Equation  to appear in Physica D: Nonlinear Phenomena
  • Geometric Integration by Solution Interpolation  preprint

 

Talk and Presentations:

  • Invariantization of numerical schemes using moving frames, Mathematical Physics Seminar, School of Mathematics, University of Minnesota (April, 2004)
  • Error control for numerical schemes by invariantization, Mathematical Physics Seminar, School of Mathematics, University of Minnesota (Oct, 2004)
  • Invariant numerical schemes for differential equations, Applied Mathematics and Numerical Analysis Seminar, School of Mathematics, University of Minnesota (March, 2006)

Contact Information:

  • Phone: (614) 292-6597
  • Office: 456 Math Tower
  • Postal Address:  Math Tower 231 W. 18th Ave.
                                Columbus    , OH 43210
  • Email address: pwkim@math.ohio-state.edu

Last updated Aug, 2007