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RESEARCH

 

 

 

 

RECENT RESEARCH TOPICS

 

  • Hidden mechanics on the time integration of Runge-Kutta methods

  • Iteration free Semi-Lagrangian method for nonlinear advection diffustion equations.

  • Iteration free Semi-Lagrangian method for solving incompressible Navier-Stokes equations

 

PUBLICATIONS

  • BEM for nonlinear boundary value problems using an auxiliary boundary integral equation" M.S. thesis(1994) in KAIST

  • P. Kim and S. Lee,  A piecewise linear quadrature of Caucy singular integrals, J. Comp. Appl. Math 95, (1998) 101 - 115.

  • P. Kim and U J. Choi,  A quadrature rule of interpolatory type for Cauchy integrals, J. Comp. Appl. Math. 126, (2000) 207 - 220.

  • P. Kim and U J. Choi,  A quadrature rule for weighted Cauchy integrals, J. Comp. Appl. Math., 126, (2000) 221 - 232.

  • Study on the numerical method for solving singular integral equations", Ph. D. thesis (2001) in KAIST

  • P. Kim, A Chebyshev quadrature rule for one sided finite part integrals, J. Approx. Theory, 111, (2001) 196 - 219.

  • P. Kim, A trigonometric quadrature rule for Cauchy integrals with Jacobi weight, J. Approx. Theory, 108, (2001), 18 - 35.

  • A survey for numerical method for singular integral equation", with U Jin Choi, Differential equations and applications(2002) vol 2, 81-107

  • P. Kim and B.I. Yun, On the convergence of interpolatory type quadrature rules for evaluating Cauchy integrals, J. Comp. Appl. Math., 149(2002) 381-395.

  • P. Kim and U J. Choi, Two trigonometric quadrature formulae for evaluating hypersingular integrals, Int. J. Numer. Methods in eng., 56 (2003) 469 - 486.

  • B.I Yun and P. Kim, A new sigmoidal transformation for weakly singular integrals in the boundary element method, SIAM J. Sci. Computing, 24, (2003) 1203 - 1217.

  • P.Kim and J.R. Kweon, A finite element method for convection-dominated compressible viscous Stokes system with inflow boundary, J. Comp. Appl. Math. 156 (2003) 319-343

  • P.Kim, Soyoung ahn and U Jin Choi, A note on the stability analysis of a quadrature rule of interpolatory type for Cauchy principal value integrals,  Intern. Math. Journal. vol 3, (2003) no 8, 825-835

  • Convergence theorems for an interplatory type quadrature rule for weighted Cauchy integrals, with B. Jang, East Asian Math. J 20(2004), no 1, 61-72

  • P.Kim,   S. Ahn and B. Jang,A uniform convergence of a quadrature rule for evaluating Cauchy integrals,  East Asian Math. J. 20(2004), no2 201-205

  • P. Kim, Soyoung Ahn and U J. Choi, On the stability analysis for the Chebyshev quadrature rule of a finite part integrals, J. Comp. Appl. Math., 180 (2005) 147 - 159.

  • Y. Do, S. D Kim and P. Kim, Stability of fixed points placed on the border in the piecewise linear systems, Chaos, Solitons and Fractals, 38 (2008) 391 - 399.

  • H. K. Baek, S.D. Kim and P. Kim, Permanence and stability of an Ivlev-type predator-prey system with impulsive control strategies, Math. and Comp. Modelling, 50 ( 2009 ) 1385 - 1393.

  • P. Kim and H. Kim, Point Ordering with Natural Distance Based on Brownian Motion, Math. Prob. Engng., (2010) 1 - 17.

  • S.D. Kim, S. Ahn and P. Kim, Local boundary element based a new finite difference representation for Poisson equations, Appl. Math. Comp. 217 (2011) 5186 - 5198.

  • ​P. Kim, X, Piao, S.D. Kim, An error corrected Euler method for solving stiff problems based on Chebyshev collocation, SIAM J. Numer. Anal. 49(6) (2011) 2211 - 2230.

  • J.K. Kwon, S. Ryu, P.Kim and S.D. Kim, Finite element preconditioning on spectral element discretizations for coupled elliptic equations, J. Appl. Math., (2012) 1 - 17.

  • G. Lee, P. Kim and Y. S. Kwon, Incompressible limit for the full magnetohydrodynamics flow under strong stratification, J. Math. Anal. Appl. 387 (2012) 221 - 240.

  • S.D. Kim, X. Piao, D.H. Kim and P. Kim, Convergence on error correction methods for solving initial value problems, J. Comp. Appl. Math. 236 (2012) 4448 - 4461.

  • X. Piao, H. J. Choi, S.D. Kim and P. Kim, A fast singly diagonally implicit Runge-Kutta method for solving 1D unsteady convection-diffusion equations, Numer. methods for partial differential equations 30(3) (2013) 788 - 812

  • X. Piao, S. Bu, S. Bak and P. Kim, An iteration free backward semi-Lagrangian scheme for solving incompressible Navier-Stokes equations,  J. Comp. Phy. 283 (2015) 189-204

  • J. Kwon, D. Yi, X. Piao and P. Kim, Development of semi-Lagrangian gyrokinetic code for full-f turbulence simulation in general tokamak geometry, J. Comp. Phy. 283 (2015) 518-540

  • X. Piao, S. D. Kim, P. Kim, J. Kwon and D. Yi, An Iteration Free Backward Semi-Lagrangian Scheme for Guiding Center Problems, SIAM J. Numer. Anal.  53(1) (2015) 619-643

  • P Kim, J Kim, WK Jung, S Bu, An error embedded method based on generalized Chebyshev polynomials, Journal of Computational Physics 306 (2016) 55-72

  • X Piao, S Bu, D Kim, P Kim, An embedded formula of the Chebyshev collocation method for stiff problems, Journal of Computational Physics 351(2017) 376-391

  • X Piao, P Kim, D Kim, One-step L (α)-stable temporal integration for the backward semi-Lagrangian scheme and its application in guiding center problems, Journal of Computational Physics 366(2018) 327-340

  • P Kim, X Piao, WK Jung, S Bu, A new approach to estimating a numerical solution in the error embedded correction framework, Advances in Difference Equations 2018 (1), 168​

  • S Bak, P Kim, X Piao, S Bu, Numerical solution of advection–diffusion type equation by modified error correction scheme, Advances in Difference Equations 2018 (1), 432

  • S Bak, P Kim, D Kim, A semi-Lagrangian approach for numerical simulation of coupled Burgers’ equations, Communications in Nonlinear Science and Numerical Simulation 69, (2019) 31-44

  • P Kim, D Kim, X Piao, S Bak, A completely explicit scheme of Cauchy problem in BSLM for solving the Navier–Stokes equations, Journal of Computational Physics 401(2020) 109028

  • P Kim, D Kim, Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions, Applied Mathematics and Computation 366(2020) 124744

  • X Piao, P Kim, An efficient trajectory tracking algorithm for the backward semi-Lagrangian method of solving the guiding center problems, Journal of Computational Physics(2020) 109664

SUBMITTED PAPER

 

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WORKING PAPER

 

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GRANT LIST

  • Convergence properties of a class of trigonometric quadrature rule for Cauchy singular integrals and its applications.

    • Period : July 2002. - June 2003.

    • Grant No. : Korea Research Foundation Grant KRF - 2002-003-C00010.

  • On the numerical method for Bio-electric magnetic system

    • Period : December 2003. - November 2005.

    • Grant No. : Korea Research Foundation Grant KRF- 2003-041-C00039

  • Computational control methods and properties for numerical solution of P.D.E

    • Period : September 2005. - August 2008.

    • Grant No. :  Korea Research Foundation Grant KRF-2005-070-C00017

  • Higher-order time stepping methods and simulation methods for solving Gyro-kinetic equations

    • Period : Sep 2001. - Aug 2014.

    • Grant No. : Korea Research Foundation Grant KRF-2011-0029013

  • Non-standard time stepping methods and its applications

    • Period : May 2011.  - April 2016.

    • Grant No. : Korea Research Foundation Grant KRF-2011-0009825

  • Nurture of Industry Mathematics Readers and Outstanding Individuals to Mathematical Computation

    • Period : July 2015. - February 2016.

  • ​Numerical method for solving partial differential equations with self-consistency and its applications

    • Period : June 2016 - May 2019

    • Grant No. : Korea Research Foundation Grant NRF-2016R1A2B2011326

  • Improvement of numerical algorithm used in BOUT++ code : BOUT++​

    • Period : February 2018 - December 2018

    • Grant No. : NFRI-EN1741-1

  • Semi-Lagrangian method for solving incompressible Navier-Stokes equation based on VSF

    • Period : June 2019 - May 2020

    • Grant No. : Korea Research Foundation Grant NRF-2019R1H1A2079997

  • Development of optimized algorithm of the Cauchy problem for the Semi-Lagrangian method and Plasma turbulence simulation​

    • Period : March 2020 - February 2023

    • Grant No. : Korea Research Foundation Grant NRF-2020R1A2C1A01008506​

  • Basic Research Laboratory for Analysis and Simulation of Solids and Plasma Flows

    • Period : July 2020 - February 2023

    • Grant No. : Korea Research Foundation Grant NRF-2020R1A4A1018190​

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