@Article{CiCP-38-248,
author = {Sun , QiXu , Xuejun and Yi , Haotian},
title = {Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {1},
pages = {248--284},
abstract = {<p style="text-align: justify;">Non-overlapping domain decomposition methods are well-suited for addressing interface problems across various disciplines, where traditional numerical
simulations often require the use of interface-fitted meshes or technically designed basis functions. To remove the burden of mesh generation and to effectively tackle with
the flux transmission condition, a novel mesh-free scheme, i.e., the Dirichlet-Neumann
learning algorithm, is studied in this work for solving the benchmark elliptic interface
problems with high-contrast coefficients and irregular interfaces. By resorting to the
variational principle, we carry out a rigorous error analysis to evaluate the discrepancy
caused by the boundary penalty treatment for each decomposed subproblem, which
paves the way for realizing the Dirichlet-Neumann algorithm using neural network
extension operators. Through experimental validation on a series of testing problems
in two and three dimensions, our methods demonstrate superior performance over
other alternatives even in scenarios with inaccurate flux predictions at the interface.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0046},
url = {http://global-sci.org/intro/article_detail/cicp/24258.html}
}