Research Articles
Shin, J., Park, J., Ji, M., and Lee, S. (2026). Exploring potential of Turing pattern classification through convolution maps. Scientific Reports, 16: 3008.
Ji, M. and Shin, J. (2025). Energy-stable linear convex splitting methods for the parabolic sine-Gordon equation. Computers & Mathematics with Applications, 198, 24-37.
Yoo, C., Ji, M. and Shin, J. (2025). Second-order operator splitting method for solving heterogeneous diffusion equations. Journal of the Korean Society for Industrial and Applied Mathematics, 29, 229-245.
Shin, J. and Lee, J.Y. (2023). Energy-conserving successive multi-stage method for the linear wave equation with forcing terms. Journal of Computational Physics, 489, 112255.
Lee, H. G., Shin, J., and Lee, J. Y. (2022). Energy quadratization Runge-Kutta scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier. Applied Mathematics Letters, 132, 108161.
Shin, J. and Lee, J. Y. (2022). Energy conserving successive multi-stage method for the linear wave equation. Journal of Computational Physics, 458, 111098.
Shin, J., Lee, H. G., and Lee, J. Y. (2022). Energy quadratization Runge-Kutta method for the modified phase field crystal equation. Modelling and Simulation in Materials Science and Engineering, 30(2), 024004.
Lee, H. G., Shin, J., and Lee, J. Y. (2022). A high-order and unconditionally energy stable scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier. Journal of Scientific Computing, 90(1), 1-12.
Shin, J. and Lee, H. G. (2021). A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection. Applied Numerical Mathematics, 163, 30-42.
Shin, J, Lee, H. G., and Lee, J. Y. (2020). Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methods. Computer Methods in Applied Mechanics and Engineering 364, 112981.
Shin, J., Yang, J., Lee, C., and Kim, J. (2020). The Navier–Stokes–Cahn–Hilliard model with a high-order polynomial free energy. Acta Mechanica 231, 2425-2437.
Shin, J. and Lee, J. Y. (2020). An energy stable Runge-Kutta method for convex gradient problems. Journal of Computational and Applied Mathematics, 367, 112455.
Lee, H. G., Shin, J., and Lee, J. Y. (2019). A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional. Mathematics, 7(12), 1242.
Shin, J., Choi, Y., and Kim, J. (2019). The Cahn-Hilliard Equation with Generalized Mobilities in Complex Geometries. Mathematical Problems in Engineering, 2019.
Lee, H. G., Lee, J. Y., and Shin, J. (2019). A constrained convex splitting scheme for the vector-valued Cahn-Hilliard equation. Journal of the Korean Society for Industrial and Applied Mathematics, 23(1), 1-18.
Lee, S. and Shin, J. (2019). Energy stable compact scheme for Cahn-Hilliard equation with periodic boundary condition. Computers & Mathematics with Applications, 77(1), 189-198.
Shin, J., Lee, H. G., and Lee, J. Y. (2017). Unconditionally stable methods for gradient flow using Convex Splitting Runge-Kutta scheme. Journal of Computational Physics, 347, 367-381.
Lee, H. G., Shin, J., and Lee, J. Y. (2017). First- and second-order energy stable methods for the modified phase field crystal equation. Computer Methods in Applied Mechanics and Engineering, 321, 1-17.
Lee, S., Li, Y., Shin, J., and Kim, J. (2017). Phase-field simulations of crystal growth in a two-dimensional cavity flow. Computer Physics Communications, 216, 84-94.
Shin, J., Lee, H. G., and Lee, J. Y. (2017). Convex Splitting Runge-Kutta methods for phase-field models. Computers & Mathematics with Applications, 73(11), 2388-2403.
Lee, H. G., Shin, J., and Lee, J. Y. (2017). A Second-Order Operator Splitting Fourier Spectral Method for Models of Epitaxial Thin Film Growth. Journal of Scientific Computing, 71(3), 1303-1318.
Shin, J., Lee, H. G., and Lee, J. Y. (2017). Higher order operator splitting Fourier spectral methods for the Allen-Cahn equation. The journal of the Korean Society for Industrial and Applied Mathematics, 21(1), 1-16.
Kim, J. and Shin, J. (2017). An unconditionally gradient stable numerical method for the Ohta-Kawasaki model. Bulletin of the Korean Mathematical Society, 54, 145-158.
Shin, J., Lee, H. G., and Lee, JY. (2016). First and second order numerical methods based on a new convex splitting for phase-field crystal equation. Journal of Computational Physics, 327, 519-542.
Jeong, D., Lee, S., Lee, D., Shin, J., and Kim, J. (2016). Comparison study of numerical methods for solving the Allen-Cahn equation. Computational Materials Science, 111, 131-136.
Lee, H. G., Shin, J., and Lee, JY. (2015). First and second order operator splitting methods for the phase field crystal equation. Journal of Computational Physics, 299, 82-91.
Li, Y., Shin, J., Choi, Y., and Kim, J. (2015). Three-dimensional volume reconstruction from slice data using phase-field models. Computer Vision and Image Understanding. 137, 115-124.
Yun, A., Shin, J., Li, Y., Lee, S., and Kim, J. (2015). Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features. International Journal of Bifurcation and Chaos, 25(09), 1550117.
Shin, J., Jeong, D., Li, Y., Choi, Y., and Kim, J. (2015). A hybrid numerical method for the phase-field model of fluid vesicles in three-dimensional space. International Journal for Numerical Methods in Fluids, 78(2), 63-75.
Hua, H., Shin, J., and Kim, J. (2014). Dynamics of a compound droplet in shear flow. International Journal of Heat and Fluid Flow, 50, 63-71.
Shin, J., Park, S. K., and Kim, J. (2014). A hybrid FEM for solving the Allen-Cahn equation. Applied Mathematics and Computation, 244, 606-612.
Lee, C., Jeong, D., Shin, J., Li, Y., and Kim, J. (2014). A fourth-order spatial accurate and practically stable compact scheme for the Cahn-Hilliard equation. Physica A: Statistical Mechanics and its Applications, 409, 17-28.
Jeong, D., Shin, J., Li, Y., Choi, Y., Jung, J. H., Lee, S., and Kim, J. (2014). Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers. Current Applied Physics. 14(9), 1263-1272
Jeong, D., Ha, T., Kim, M., Shin, J., Yoon, I. H., and Kim, J. (2014). An adaptive finite difference method using far-field boundary conditions for the Black-Scholes equation. Bulletin of the Korean Mathematical Society, 51(4), 1087-1100.
Shin, J., Choi, Y., and Kim, J. (2014). An unconditionally stable numerical method for the viscous Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems-Series B, 19(6) 1734-1747.
Hua H., Shin. J., and Kim J., (2014). Level set, phase-field, and immersed boundary methods for two-phase fluid flows, ASME-Journal of Fluids Engineering, 136, 021301.
Lee, D., Huh, J. Y., Jeong, D., Shin, J., Yun, A., and Kim, J. (2014). Physical, mathematical, and numerical derivations of the Cahn-Hilliard equation. Computational Materials Science, 81, 216-225.
Hua H., Li Y., Shin J., Song H-K., and Kim J., (2013). Effect of confinement on droplet deformation in shear flow, International Journal of Computational Fluid Dynamics, 27, 317-331.
Li, Y., Yun, A., Lee, D., Shin, J., Jeong, D., and Kim, J. (2013). Three-dimensional volume conserving immersed boundary model for two-phase fluid flows. Computer Methods in Applied Mechanics and Engineering, 257, 36-46.
Shin, J., Kim, S., Lee, D., and Kim, J. (2013). A parallel multigrid method of the Cahn-Hilliard equation. Computational Materials Science, 71, 89-96.
Li, Y., Jeong, D., Shin, J., and Kim, J. (2013). A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains. Computers & Mathematics with Applications, 65(1), 102-115.
Lee, C. H., Shin, J., and Kim, J. (2013). A numerical characteristic method for probability generating functions on stochastic first-order reaction networks. Journal of Mathematical Chemistry, 51(1), 316-337.
Shin, J., Kim, S., Jeong, D., Lee, H. G., Lee, D., Lim, J. Y., and Kim, J. (2012). Finite Element Analysis of Schwarz P Surface Pore Geometries for Tissue-Engineered Scaffolds. Mathematical Problems in Engineering, 2012.
Shin, J., Jeong, D., and Kim, J. (2011). A conservative numerical method for the Cahn-Hilliard equation in complex domains. Journal of Computational Physics, 230(19), 7441-7455.
Shin, J., Lee, D., Kim, S., Jeong, D., Lee, H. G., and Kim, J. (2011). The effects of mesh style on the finite element analysis for artificial hip joints. The journal of the Korean Society for Industrial and Applied Mathematics, 15(1), 57-65
Presentations
High-order energy stable schemes for gradient flows, The 18th East Asia SIAM Section Conference, June 2025, Manila, Philippines
Linear Convex Splitting Strategies for Stable Simulation of the Parabolic Sine-Gordon Equation, The 2025 International Conference of the Honam Mathematical Society, June 2025, Gwangju, Korea
Exploring Turing Pattern Classification through Convolutional Neural Networks and Feature Engineering, The Third Vietnam-Korea Workshop on Selected Topics in Mathematics, January 2025, Hanoi, Vietnam
Energy stable methods for gradient flows by invariant energy quadratization approach, 2023 KMS Annual Meeting, October 2023, Seoul, Korea
High-order energy stable schemes for the phase-field model by the Convex Splitting Runge–Kutta methods, International Congress for Industrial and Applied Mathematics, August 2023, Tokyo, Japan
Energy stable methods for the phase-field crystal equations, 2021 EIMS International Conference on Computational Mathematics, August 2021, Online
Energy stable methods for convex gradient problems, KSIAM 2019 Annual Meeting, November 2019, Yeosu, Korea.
Convex Splitting Runge–Kutta Methods to Solve the Phase Field Equations, WCCM XIII, July 2018, New York, USA
High Order and Energy Stable Numerical Methods to Solve the Phase Field Equations, 2018 SIAM Conference, July 2018, Portland, USA
Application of Convex Splitting Runge–Kutta method to the phase-field crystal equation, KSIAM 2015 Spring Conference, May 2018, Daejeon, Korea.
Convex splitting Runge–Kutta methods for gradient flows, KSIAM 2017 Annual Meeting, November 2017, Busan, Korea.
Energy stable and high-order methods for gradient flows based on the Convex Splitting Runge–Kutta methods, ACOMEN 2017, September, Ghent, Belgium
Convex splitting methods for phase field models, KSIAM 2017 Spring Conference, June 2017, Seoul, Korea.
Numerical methods for phase field crystal equation using a new convex splitting, KSIAM 2016 Annual Meeting, Nov 2016, Jeju, Korea.
Operator splitting method for phase-field-crystal equation, KSIAM 2015 Spring Conference, May 2015, Suwon, Korea.
Energy stable scheme for Ohta–Kawasaki model, KSIAM 2014 Annual Meeting, November 2014, Jeju, Korea.
Immersed boundary method for a droplet under shear flow, KSIAM 2014 Spring Conference, May 2014, Seoul, Korea
A numerical scheme for viscous Cahn-Hilliard equation, KMS Spring Meeting, April 2014, Gangneung, Korea.
Finite difference solver on GPUs: parallel cyclic reduction method, KMS Annual Meeting, October 2013, Seoul, Korea.
Immersed boundary method for two-phase fluid flows, KSIAM, May 2013, Daejeon, Korea.
Study of the mean curvature flow using the Allen–Cahn equation, KSIAM, November 2012, Daejeon, Korea.
Two phase fluid flow using the phase-field method in the complex domain, KMS Fall Meeting, October 2011, Daegu, Korea.
A conservative numerical method for the Cahn–Hilliard equations in complex domains, KSIAM, May 2011, Daejeon, Korea.