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Numerical homogenization for indefinite time-harmonic Maxwell equations
Yueqi Wang, Wing Tat Leung, Guanglian Li
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wa…
Adaptive Crouzeix-Raviart finite elements for the first eigenpair of -Laplacian
Guanglian Li, Yueqi Wang, Yifeng Xu
In this paper, we propose and analyze an adaptive Crouzeix-Raviart finite element method for computing the first Dirichlet eigenpair of the -Laplacian problem. We prove that the…
Predicting band structures for 2D Photonic Crystals via Deep Learning
Yueqi Wang, Richard Craster, Guanglian Li
Photonic crystals (PhCs) are periodic dielectric structures that exhibit unique electromagnetic properties, such as the creation of band gaps where electromagnetic wave propagation…
On Edge Multiscale Space based Hybrid Schwarz Preconditioner for Helmholtz Problems with Large Wavenumbers
Shubin Fu, Shihua Gong, Guanglian Li +1
In this work, we develop a novel hybrid Schwarz method, termed as edge multiscale space based hybrid Schwarz (EMs-HS), for solving the Helmholtz problem with large wavenumbers. The…
An hp-Adaptive Sampling Algorithm on Dispersion Relation Reconstruction for 2D Photonic Crystals
Yueqi Wang, Guanglian Li
Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high…