Research

Work in Progress

• Two-level domain decomposition algorithms for neural network approximation (with Alexander Heinlein and Hee Jun Yang)

• Iterative algorithms for PNNs (Partitioned Neural Networks) with Robin interface condition (with Youngjae Jeon and Hee Jun Yang)

Published papers

• Yang, Hee Jun, and Hyea Hyun Kim. Iterative algorithms for partitioned neural network approximation to partial differential equations. (2024) Computers & Mathematics with Applications 170: 237-259. 

• Jang, Deok-Kyu, Kyungsoo Kim, and Hyea Hyun Kim. Partitioned neural network approximation for partial differential equations enhanced with Lagrange multipliers and localized loss functions. (2024) Computer Methods in Applied Mechanics and Engineering 429 : 117168. 

• Hyea Hyun Kim, et al. A staggered discontinuous Galerkin method for the Stokes problem on rectangular meshes. (2024), Computers & Mathematics with Applications, 162: 180-195. 

• Hyea Hyun Kim, and Hee Jun Yang. Domain decomposition algorithms for physics-informed neural networks. (2023) Domain Decomposition Methods in Science and Engineering XXVI. Cham: Springer International Publishing, 697-704. 

• Youngje Jeon,  Hea Hyun Kim, and Hee Jun Yang. A data-driven approach for a macroscopic conductivity model utilizing finite element approximation. (2021) Journal of Computational Physics, v.466,

• Eric Chung, Hyea Hyun Kim, Ming-Fai Lam, Lina Zhao. Learning adaptive coarse spaces of BDDC algorithms for stochastic elliptic problems with oscillatory and high contrast coefficients. (2021) Mathematical and Computational Applications, 26(2), 44. 

• Hyea Hyun Kim, C.-Y. Jung, and  T. B. Nguyen. A staggered discontinuous Galerkin method for elliptic problems on rectangular grids. (2021) Computers and Mathematics with Applications, v.99, no.1, pp.133-154. 

• Hee Jun Yang and Hyea Hyun Kim. Two-level domain decomposition algorithms for physics-informed neural networks. (2021) Proceedings of the 26th International Conference on Domain Decomposition Methods.

• Hee Jun Yang,  Hyea Hyun Kim, and Kiwan Jeon. Efficient mesh generation utilizing an adaptive body centered cubic mesh. (2021) Journal of Computational Physics.

• Hyea Hyun Kim and Junxian Wang. An adaptive BDDC method enhanced with prior selected primal constraints. (2021) Computers & Mathematics with Applications, v.80, no.8, pp.1928-1943.

• Junxian Wang, Eric Chung, and Hyea Hyun Kim. A two-level overlapping Schwarz method with energy-minimizing multiscale coarse basis functions. (2020) Journal of Computational and Applied Mathematics, v.370.

• Hyea Hyun Kim, Eric Chung, and Junxian Wang. Adaptive BDDC and FETI-DP methods with change of basis formulation. (2018) Lecture Notes in Computational Science and Engineering, v.125 , pp.445-453.

• Hee Jun Yang and Hyea Hyun Kim. A Hybrid Staggered Discontinuous Galerkin Method for KdV Equations. (2018) Journal of Scientific Computing. 

• Hyea Hyun Kim, Junxian Wang, and Eric Chung. BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints. (2018) Electronic Transcations on Numerical Analysis, v.49, pp.64-80.

• Siu Wun Cheung, Eric Chung, and Hyea Hyun Kim. A Mass Conservative Scheme for Fluid-Structure Interaction Problems by the Staggered Discontinuous Galerkin Method. (2018) Journal of Scientific Computing, v.74, no.3, pp.1423-1456.

• Hyea Hyun Kim, Eric Chung, and Junxian Wang. BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients. (2017) Journal of Computational Physics, v.349, pp.191-214.

• Ji Eun Kim and Hyea Hyun Kim. Approximation of macroscopic conductivity for a multiscale model by using mortar methods. (2017) Journal of Computational Physics, v.336, pp.275-287.

• Hyea Hyun Kim, Eric Chung, and Junxian Wang. A BDDC algorithm with adaptive primal constraints for staggered discontinuous Galerkin approximation of elliptic problems with highly oscillating coefficients. (2017) Journal of Computational and  Applied Mathematics, v.311, pp.599-617.

• Hyea Hyun Kim, Eric Chung, and Junxian Wang. BDDC and FETI-DP methods with enriched coarse spaces for elliptic problems with oscillatory and high contrast coefficients. (2017) Lecture Notes in Computational Science and Engineering, v.116, pp.179-186.