7 papers
Edge Multiscale Finite Element Methods
Shubin Fu, Guanglian Li
The objective of this paper is to review recent developments in Edge Multiscale Finite Element Methods (EMsFEM) for partial differential equations with heterogeneous coefficients o…
A POD-DeepONet Framework for Forward and Inverse Design of 2D Photonic Crystals
Yueqi Wang, Guanglian Li, Guang Lin
We develop a reduced-order operator-learning framework for forward and inverse band-structure design of two-dimensional photonic crystals with binary, pixel-based -symmetric u…
Edge multiscale finite element methods for semilinear parabolic problems with heterogeneous coefficients
Leonardo A. Poveda, Shubin Fu, Guanglian Li +1
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth ini…
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…
Wavelet-based Edge Multiscale Finite Element Methods for Singularly Perturbed Convection-Diffusion Equations
Shubin Fu, Eric Chung, Guanglian Li
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convectio…
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…