133 citations · 248 across the 17 of their papers we have counts for
21 papers
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…
Wavelet-based Edge Multiscale Parareal Algorithm for subdiffusion equations with heterogeneous coefficients in a large time domain
Guanglian Li
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equatio…
Dispersion relation reconstruction for 2D Photonic Crystals based on polynomial interpolation
Yueqi Wang, Guanglian Li
Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and…
Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields
Seungchan Ko, Guanglian Li, Yi Yu
In this paper, we analyze the numerical approximation of the Navier-Stokes problem over a bounded polygonal domain in , where the initial condition is modeled by a lo…
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--different…
Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients
Guanglian Li, Jiuhua Hu
We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm to efficiently solve parabolic equations with heterogeneous coefficients. This algorithm combin…
On the Numerical Approximation of the Karhunen-Loève Expansion for Lognormal Random Fields
Michael Griebel, Guanglian Li
The Karhunen-Loève (KL) expansion is a popular method for approximating random fields by transforming an infinite-dimensional stochastic domain into a finite-dimensional parameter…
Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains
Shubin Fu, Guanglian Li, Richard Craster +1
We introduce a new efficient algorithm for Helmholtz problems in perforated domains with the design of the scheme allowing for possibly large wavenumbers. Our method is based upon…
Homogenization of time-fractional diffusion equations with periodic coefficients
Jiuhua Hu, Guanglian Li
We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data $a(x)\in…
Edge Multiscale Methods for elliptic problems with heterogeneous coefficients
Shubin Fu, Eric Chung, Guanglian Li
In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coeffic…
Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection
Guanglian Li, Yifeng Xu
In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2d cathodic protection problem governed by a steady-state…
On the Degree of Ill-Posedness of Multi-Dimensional Magnetic Particle Imaging
Tobias Kluth, Bangti Jin, Guanglian Li
Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparti…
Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
Guanglian Li, Daniel Peterseim, Mira Schedensack
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization…
Sparse Generalized Multiscale Finite Element Methods and their applications
Eric Chung, Yalchin Efendiev, Wing Tat Leung +1
In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, m…
Hierarchical multiscale modeling for flows in fractured media using Generalized Multiscale Finite Element Method
Yalchin Efendiev, Seong Lee, Guanglian Li +2
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), w…
Generalized Multiscale Finite Element Methods for problems in perforated heterogeneous domains
Eric T. Chung, Yalchin Efendiev, Guanglian Li +1
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see…
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Victor M. Calo, Y. Efendiev, Juan Galvis +1
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) frame…
A Generalized Multiscale Finite Element Method for the Brinkman Equation
Guanglian Li, Juan Galvis, Ke Shi
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Gener…
An adaptive GMsFEM for high-contrast flow problems
Eric T. Chung, Yalchin Efendiev, Guanliang Li
In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an…
Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations
Yalchin Efendiev, Juan Galvis, Guanglian Li +1
In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM) framework, introduced in [20], in order to solve nonlinear elliptic equations with high-contrast coeffi…
Generalized Multiscale Finite Element Methods. Oversampling Strategies
Yalchin Efendiev, Juan Galvis, Guanglian Li +1
In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], al…