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Discrete Edge Multiscale Space based Hybrid Schwarz Preconditioner for High-Frequency Helmholtz Problems
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…
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…
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…
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…
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 for Dispersion Relation Reconstruction of 3D Photonic Crystals
Yueqi Wang, Richard Craster, Guanglian Li
In this work we investigate the computation of dispersion relation (i.e., band functions) for three-dimensional photonic crystals, formulated as a parameterized Maxwell eigenvalue…
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…
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…