7 papers
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…
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situati…
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 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…
On Sparse Grid Interpolation for American Option Pricing with Multiple Underlying Assets
Jiefei Yang, Guanglian Li
In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach…