Area of Research:

• Numerical method for partial differential equations
• Finite element approximation
• High-order absorbing boundary condition, PML method
• Wave propagation, scattering problems, acoustic and photonic resonances

Publications:

21. Optimal rational approximation of operator functions : Fractional diffusion problems (in preparation)
20. Complete radiation boundary conditions for the Helmholtz equation II: domains with corners
    • Numer. Math. 153 (4) (2023) 775-825
    • T. Hagstrom and S. Kim
    • preprint
19. Hybrid absorbing boundary conditions of PML and CRBC
    • J. Comput. Appl. Math. 399 (2022) 113713
    • S. Kim
    • preprint
18. Convergence analysis of the continuous and discrete non-overlapping double sweep domain decomposition method based on PMLs for the Helmholtz equation
    • J. Sci. Comput. 89 (2) (2021) 37
    • S. Kim and H. Zhang
    • preprint
17. Dirichlet-to-Neumann boundary conditions for multiple scattering in waveguides
    • Comput. Math. Appl. 79 (6) (2020), 1661-1686
    • Y. Min and S. Kim
    • preprint
16. Application of a complete radiation boundary condition for the Helmholtz equation in locally perturbed waveguides
    • J. Comput. Appl. Math. 367 (2020) 112458
    • S. Kim
    • preprint
15. Fractional order Sobolev spaces for the Neumann Laplacian and the vector Laplacian
    • J. Korean. Math. Soc. 57(3) (2020) 721-745
    • S. Kim
    • preprint
14. Error analysis of PML-FEM approximations for the Helmholtz equation in waveguides
    • ESAIM Math. Model. Numer. Anal. 53 (4) (2019), 1191-1222
    • S. Kim
    • preprint
13. Complete radiation boundary conditions for the Helmholtz equation I: waveguides
    • Numer. Math. 141(4) (2019), 917-966
    • T. Hagstrom and S. Kim
    • preprint
12. Analysis of the non-reflecting boundary condition for the time-harmonic electromagnetic wave propagation in waveguides
    • J. Math. Anal. Appl. 453(1) (2017), 82-103
    • S. Kim
    • preprint
11. Optimized double sweep Schwarz method by complete radiation boundary conditions
    • Comput. Math. Appl. 72(6) (2016), 1573-1589
    • S. Kim and H. Zhang
    • preprint
10. Convergence of the supercell method for computation of defect modes in one-dimensional photonic crystals
    • Appl. Math. Lett. 49 (2015), 159-165
    • S. Kim and T. Kwon
    • preprint
9. Optimized Schwarz method with complete radiation transmission conditions for the Helmholtz equation in waveguides
   • SIAM J. Numer. Anal. 53(3) (2015), 1537-1558
   • S. Kim and H. Zhang
   • preprint
8. Cartesian PML approximation to resonances in open systems in R^2
   • Appl. Numer. Math. 81 (2014), 50-75
   • S. Kim
   • preprint
7. Suppression of the resonant scattering in imperfect acoustic cloaking with a lossy medium in R^3
   • Chin. Phys. Lett. 31(5) (2014), 054301
   • M. Li and S. Kim
   • preprint
6. Analysis of an approximate cloaking for acoustic scattering problems in R^3
   • Appl. Math. Comput. 232(1) (2014), 117-131
   • S. Kim
   • preprint
5. Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions
   • J. Math. Anal. Appl. 410(1) (2014), 275-291
   • S. Kim
   • preprint
4. Analysis of Imperfect Acoustic Cloaking Resonances
   • Chin. Phys. Lett. 29(12) (2012), 124301
   • S. Kim
   • preprint
3. Analysis of a Cartesian PML approximation to acoustic scattering problems in R^2
   • J. Math. Anal. Appl. 370(1) (2010), 168-186
   • S. Kim and J. E. Pasciak
   • preprint
2. Analysis of the spectrum of a Cartesian perfectly matched layer (PML) approximation to acoustic scattering problems
   • J. Math. Anal. Appl. 361(2) (2010), 420-430
   • S. Kim and J. E. Pasciak
   • preprint
1. The computation of resonances in open systems using a perfectly matched layer
   • Math. Comp. 78 (2009), 1375-1398
   • S. Kim and J. E. Pasciak
   • preprint