3 papers
math.NA2025
Iterative Contact-resolving Hybrid Methods for Multiscale Contact Mechanics
Eric T. Chung, Hyea Hyun Kim, Xiang Zhong
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approxi…
math.NA2023
Partitioned neural network approximation for partial differential equations enhanced with Lagrange multipliers and localized loss functions
Deok-Kyu Jang, Kyungsoo Kim, Hyea Hyun Kim
Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and t…
math.NA2023
Enhanced physics-informed neural networks with domain scaling and residual correction methods for multi-frequency elliptic problems
Deok-Kyu Jang, Hyea Hyun Kim, Kyungsoo Kim
In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation meth…