Pilwon Kim

rs1114

Welcome!

Courses:

 

Spring 2009 Math 255: Differential Equations and Their Applications

Spring 2009 Math 571: Linear Algebra with Applications

Research Interests:

 

My interest lies in mathematical modelling for complex, nonlinear phenomena. I am especially interested in self-organization process, which increases in complexity spontaneously without being guided by an external system. I have recently developed scale interaction equations, as a mathematical framework to describe scale-dependent behaviors of general systems.

The research I have been working on in more conventional mathematics is geometric integration. 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 developed several geometric integrators, invariantization by moving frames and the solution interpolation.

 

Research Papers:

  • Geometric integration via multi-space - P. Kim and P. J. Olver, Regular and Chaotic Dynamics, 9(3), p213-226, 2004.  pdf
  • Numerical invariantization for morphological PDE schemes - M. Welk, P. Kim 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.  pdf
  • Invariantization of Numerical Schemes Using Moving Frames – P. Kim, BIT Numerical Mathematics Bit Numerical Mathematics 47(3) p. 525. 2007.  pdf
  • Invariantization of the Crank-Nicolson Method for Burgers' Equation – P. Kim,  Physica D: Nonlinear Phenomena, 237(2) p. 243. 2008.  pdf
  • Geometric Integration by Solution Interpolation – P. Kim  International Journal of Modern Physics C vol. 20, No. 2, 2009.  pdf
  • Scale-dependent Behavior of Scale Equations – P. Kim, submitted to Chaos.  pdf
  • A Moment Closure Method for Stochastic Reaction Networks - C. Lee, P. Kim and  K. Kim,  Journal of Chemical Physics, vol. 130, issue 13, 134107, 2009.  pdf

 

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 Dec, 2008