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math.NA2026
A Parallel and Adaptive Mesh-Free Method for Discontinuous Coefficient Fields in Heterogeneous Porous Media
Kapil Chawla, Sanghyun Lee, Yeonjong Shin
Discontinuous coefficient fields arise in many computational physics problems and are often represented as cellwise constant data tied to a given spatial discretization. Such repre…
math.NA2026
Discontinuous Galerkin finite element operator network for solving non-smooth PDEs
Kapil Chawla, Youngjoon Hong, Jae Yong Lee +1
We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin…
math.NA2024
From Obstacle Problems to Neural Insights: Feed Forward Neural Network Modeling of Ice Thickness
Kapil Chawla, William Holmes, Roger Temam
In this study, we integrate the established obstacle problem formulation from ice sheet modeling with cutting-edge deep learning methodologies to enhance ice thickness predictions,…