Stochastic approach for elliptic problems in perforated domains

arXiv:2403.11385v1 Announce Type: cross
Abstract: A wide range of applications in science and engineering involve a PDE model in a domain with perforations, such as perforated metals or air filters. Solving such perforated domain problems suffers from computational challenges related to resolving the scale imposed by the geometries of perforations. We propose a neural network-based mesh-free approach for perforated domain problems. The method is robust and efficient in capturing various configuration scales, including the averaged macroscopic behavior of the solution …

abstract applications arxiv challenges computational cs.ce cs.lg cs.na domain domains engineering filters math.na math.pr metals scale science stochastic type