arXiv subjects

Yunying Fan

Publications and source records attributed to Yunying Fan.

2 recordsLinked to original sources

arXiv2024

Subspace method based on neural networks for eigenvalue problems

In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality reduction technique, and then calculate the Galerkin projection of the eigenvalue problem onto the subspace spanned by the orthogonal basis and obtain an approximate solution. Numerical experiments show that we can obtain approximate eigenvalues and eigenfunctions with very high accuracy but low cost.

math.NA↗

arXiv2023

Weak Galerkin methods for the Stokes eigenvalue problem

In this paper, we rewrite the Stokes eigenvalue problem as an Elliptic eigenvalue problem restricted to subspace, and introduce an abstract framework of solving abstract elliptic eigenvalue problem to give the WG scheme, error estimates and asymptotic lower bounds. Besides, we introduce a new stabilizer and several inequalities to prove GLB properties. Some numerical examples are provided to validate our theoretical analysis.

math.NA↗