We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust preconditioner for problems defined by different geometries without further fine-tuning or additional data mining. We demonstrate our method for the Helmholtz equation, which is used to solve problems in electromagnetics and acoustics; the Helmholtz equation is not positive definite, and with absorbing boundary conditions, it is not symmetric.
@article{arxiv.2411.13341,
title = {Attention-based hybrid solvers for linear equations that are geometry aware},
author = {Idan Versano and Eli Turkel},
journal= {arXiv preprint arXiv:2411.13341},
year = {2024}
}