Email: leeh1@kw.ac.kr; leeh@korea.ac.kr.

Address: Department of Mathematics, Kwangwoon University, Seoul 01897, Republic of Korea.

Research interest

 

My primary research interest is in the field of scientific computing and numerical analysis. In particular, I am interested in developing mathematical models for problems arising in fluid dynamics and biology, and in applying accurate and efficient numerical methods for solving nonlinear partial differential equations.

Rayleigh-Taylor instability in a five-component fluid The red and blue regions represent the lightest and heaviest fluids, respectively. Initially heavier fluids are superposed over lighter fluids in a gravitational field. Any perturbation of the interface tends to grow with time, producing the phenomenon known as the Rayleigh-Taylor instability. As time goes by, the heaviest and lightest fluids go to the bottom and top, respectively.

Publications

 

1. A second-order accurate non-linear difference scheme for the N-component Cahn-Hilliard system ... Hyun Geun Lee and Junseok Kim. Physica A 387 (2008) 4787-4799. IF: 1.785.

2. An unconditionally gradient stable numerical method for solving the Allen-Cahn equation ... Jeong-Whan Choi, Hyun Geun Lee, Darae Jeong, and Junseok Kim. Physica A 388 (2009) 1791-1803. IF: 1.785.

3. Fast and automatic inpainting of binary images using a phase-field model ... Darae Jeong, Yibao Li, Hyun Geun Lee, and Junseok Kim. Journal of KSIAM 13 (2009) 225-236.

4. Phase-field model for the pinchoff of liquid-liquid jets ... Chang-Hun Kim, Seung-Ho Shin, Hyun Geun Lee, and Junseok Kim. Journal of the Korean Physical Society 55 (2009) 1451-1460. IF: 0.445.

5. A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint ... Seong-Deog Yang, Hyun Geun Lee, and Junseok Kim. Computer Physics Communications 181 (2010) 1037-1046. IF: 3.635.

6. An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation ... Yibao Li, Hyun Geun Lee, Darae Jeong, and Junseok Kim. Computers and Mathematics with Applications 60 (2010) 1591-1606. IF: 1.398.

7. The effects of mesh style on the finite element analysis for artificial hip joints ... Jaemin Shin, Dongsun Lee, Sungki Kim, Darae Jeong, Hyun Geun Lee, and Junseok Kim. Journal of KSIAM 15 (2011) 57-65.

8. On the long time simulation of the Rayleigh-Taylor instability ... Hyun Geun Lee, Kyoungmin Kim, and Junseok Kim. International Journal for Numerical Methods in Engineering 85 (2011) 1633-1647. IF: 2.100.

9. A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth ... Yibao Li, Hyun Geun Lee, and Junseok Kim. Journal of Crystal Growth 321 (2011) 176-182. IF: 1.462.

10. Accurate contact angle boundary conditions for the Cahn-Hilliard equations ... Hyun Geun Lee and Junseok Kim. Computers and Fluids 44 (2011) 178-186. IF: 1.891.

11. Numerical studies of the fingering phenomena for the thin film equation ... Yibao Li, Hyun Geun Lee, Daeki Yoon, Woonjae Hwang, Suyeon Shin, Youngsoo Ha, and Junseok Kim. International Journal for Numerical Methods in Fluids 67 (2011) 1358-1372. IF: 1.447.

12. Finite element analysis of Schwarz P surface pore geometries for tissue engineered scaffolds ... Jaemin Shin, Sungki Kim, Darae Jeong, Hyun Geun Lee, Dongsun Lee, Joong Yeon Lim, and Junseok Kim. Mathematical Problems in Engineering 2012 (2012) Article ID 694194. IF: 0.644.

13. A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system ... Hyun Geun Lee, Jeong-Whan Choi, and Junseok Kim. Physica A 391 (2012) 1009-1019. IF: 1.785.

14. A robust and accurate phase-field simulation of snow crystal growth ... Yibao Li, Dongsun Lee, Hyun Geun Lee, Darae Jeong, Chaeyoung Lee, Donggyu Yang, and Junseok Kim. Journal of KSIAM 16 (2012) 15-29.

15. Volume preserving immersed boundary methods for two-phase fluid flows ... Yibao Li, Eunok Jung, Wanho Lee, Hyun Geun Lee, and Junseok Kim. International Journal for Numerical Methods in Fluids 69 (2012) 842-858. IF: 1.447.

16. Regularized Dirac delta functions for phase-field models ... Hyun Geun Lee and Junseok Kim. International Journal for Numerical Methods in Engineering 91 (2012) 269-288. IF: 2.100.

17. A comparison study of the Boussinesq and the variable density models on buoyancy-driven flows ... Hyun Geun Lee and Junseok Kim. Journal of Engineering Mathematics 75 (2012) 15-27. IF: 0.665.

18. An efficient and accurate numerical algorithm for the vector-valued Allen-Cahn equations ... Hyun Geun Lee and Junseok Kim. Computer Physics Communications 183 (2012) 2107-2115. IF: 3.635.

19. Comparison of different numerical schemes for the Cahn-Hilliard equation ... Seunggyu Lee, Chaeyoung Lee, Hyun Geun Lee, and Junseok Kim. Journal of KSIAM 17 (2013) 197-207.

20. Buoyancy-driven mixing of multi-component fluids in two-dimensional tilted channels ... Hyun Geun Lee and Junseok Kim. European Journal of Mechanics B/Fluids 42 (2013) 37-46. IF: 1.418.

21. Numerical simulation of the three-dimensional Rayleigh-Taylor instability ... Hyun Geun Lee and Junseok Kim. Computers and Mathematics with Applications 66 (2013) 1466-1474. IF: 1.398.

22. A numerical method for the modified vector-valued Allen-Cahn phase-field model and its application to multiphase image segmentation ... Hyun Geun Lee and June-Yub Lee. Journal of KSIAM 18 (2014) 27-41.

23. A simple and robust boundary treatment for the forced Korteweg-de Vries equation ... Hyun Geun Lee and Junseok Kim. Communications in Nonlinear Science and Numerical Simulation 19 (2014) 2262-2271. IF: 2.834.

24. Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: A mathematical model ... Yangjin Kim, Hyun Geun Lee, Nina Dmitrieva, Junseok Kim, Balveen Kaur, and Avner Friedman. PLoS ONE 9 (2014) e102499. IF: 3.057.

25. A semi-analytical Fourier spectral method for the Allen-Cahn equation ... Hyun Geun Lee and June-Yub Lee. Computers and Mathematics with Applications 68 (2014) 174-184. IF: 1.398.

26. Two-dimensional Kelvin-Helmholtz instabilities of multi-component fluids ... Hyun Geun Lee and Junseok Kim. European Journal of Mechanics B/Fluids 49 (2015) 77-88. IF: 1.418.

27. An efficient numerical method for simulating multiphase flows using a diffuse interface model ... Hyun Geun Lee and Junseok Kim. Physica A 423 (2015) 33-50. IF: 1.785.

28. Numerical investigation of falling bacterial plumes caused by bioconvection in a three-dimensional chamber ... Hyun Geun Lee and Junseok Kim. European Journal of Mechanics B/Fluids 52 (2015) 120-130. IF: 1.418.

29. A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms ... Hyun Geun Lee and June-Yub Lee. Physica A 432 (2015) 24-34. IF: 1.785.

30. First and second order operator splitting methods for the phase field crystal equation ... Hyun Geun Lee, Jaemin Shin, and June-Yub Lee. Journal of Computational Physics 299 (2015) 82-91. IF: 2.556.

31. The role of the microenvironment in regulation of CSPG-driven invasive and non-invasive tumor growth in glioblastoma ... Hyun Geun Lee and Yangjin Kim. Japan Journal of Industrial and Applied Mathematics 32 (2015) 771-805. IF: 0.377.

32. Mathematical model and its fast numerical method for the tumor growth ... Hyun Geun Lee, Yangjin Kim, and Junseok Kim. Mathematical Biosciences and Engineering 12 (2015) 1173-1187. IF: 1.006.

33. A compact fourth-order finite difference scheme for the three-dimensional Cahn-Hilliard equation ... Yibao Li, Hyun Geun Lee, Binhu Xia, and Junseok Kim. Computer Physics Communications 200 (2016) 108-116. IF: 3.635.

34. A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces ... Hyun Geun Lee and Junseok Kim. Computer Methods in Applied Mechanics and Engineering 307 (2016) 32-43. IF: 3.467.

35. High-order and mass conservative methods for the conservative Allen-Cahn equation ... Hyun Geun Lee. Computers and Mathematics with Applications 72 (2016) 620-631. IF: 1.398.

36. First and second order numerical methods based on a new convex splitting for phase-field crystal equation ... Jaemin Shin, Hyun Geun Lee, and June-Yub Lee. Journal of Computational Physics 327 (2016) 519-542. IF: 2.556.

37. A second-order operator splitting Fourier spectral method for models of epitaxial thin film growth ... Hyun Geun Lee, Jaemin Shin, and June-Yub Lee. Journal of Scientific Computing, accepted, 2017. IF: 1.946.

38. Higher order operator splitting Fourier spectral methods for the Allen-Cahn equation ... Jaemin Shin, Hyun Geun Lee, and June-Yub Lee. Journal of KSIAM, accepted, 2017.

39. First- and second-order energy stable methods for the modified phase field crystal equation ... Hyun Geun Lee, Jaemin Shin, and June-Yub Lee. Computer Methods in Applied Mechanics and Engineering, accepted, 2017. IF: 3.467.

40. Convex Splitting Runge-Kutta methods for phase-field models ... Jaemin Shin, Hyun Geun Lee, and June-Yub Lee. Computers and Mathematics with Applications, accepted, 2017. IF: 1.398.

41. A second-order operator splitting Fourier spectral method for fractional-in-space reaction-diffusion equations ... Hyun Geun Lee, submitted, 2017.

42. A new conservative vector-valued Allen-Cahn equation and its fast numerical method ... Junseok Kim and Hyun Geun Lee, submitted, 2017.

43. A semi-analytical Fourier spectral method for the Swift-Hohenberg equation ... Hyun Geun Lee, submitted, 2017.

44. Unconditionally stable methods for gradient flow using Convex Splitting Runge-Kutta scheme ... Jaemin Shin, Hyun Geun Lee, and June-Yub Lee, submitted, 2017.

Awards

 

  • KSIAM Young Researcher Award, KSIAM, 2012.
  • Presentations

     

    1. A phase-field approach for surface area minimization of triply-periodic surfaces. KSIAM 2007 Spring Conference, May 25-26, 2007.

    2. An unconditionally stable hybrid numerical method for the Allen-Cahn equation. KSIAM 2009 Annual Meeting, November 27-28, 2009.

    3. Schwartz P surfaces for tissue scaffolds. KSIAM 2010 Annual Meeting, December 3-4, 2010.

    4. Volume preserving immersed boundary methods for two-phase fluid flows. KSIAM 2011 Spring Conference, May 27-28, 2011.

    5. Sinking, merging, and stationary plumes in a coupled chemotaxis-fluid model. KSMB 2011 Annual Meeting, August 25-26, 2011.

    6. A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system. International Conference on Applied Mathematics, May 28-June 1, 2012.

    7. Buoyancy-driven mixing of multi-component fluids in two-dimensional tilted channels. KSIAM 2013 Annual Meeting, November 22-24, 2013.

    8. Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: Mathematical model and numerical simulation. KSIAM 2013 Annual Meeting, November 22-24, 2013.

    9. Chase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: Numerical simulation. KMS 2014 Spring Meeting, April 24-26, 2014.

    10. A numerical method for the modified vector-valued Allen-Cahn model and its application to multiphase image segmentation. KSIAM 2014 Spring Conference, May 23-24, 2014.

    11. Mathematical model and its fast numerical method for the tumor growth. KSIAM 2015 Spring Meeting, May 29-30, 2015.

    12. Kelvin-Helmholtz instabilities of multi-component fluids. KSIAM 2015 Annual Meeting, November 20-22, 2015.