58 citations · 216 across the 16 of their papers we have counts for
16 papers
Transformer Meets Boundary Value Inverse Problems
Ruchi Guo, Shuhao Cao, Long Chen
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-ti…
A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian
Mary Barker, Shuhao Cao, Ari Stern
We introduce a nonconforming hybrid finite element method for the two-dimensional vector Laplacian, based on a primal variational principle for which conforming methods are known t…
How to Understand Masked Autoencoders
Shuhao Cao, Peng Xu, David A. Clifton
"Masked Autoencoders (MAE) Are Scalable Vision Learners" revolutionizes the self-supervised learning method in that it not only achieves the state-of-the-art for image pre-training…
Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
Shuhao Cao, Long Chen, Ruchi Guo +1
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh m…
Choose a Transformer: Fourier or Galerkin
Shuhao Cao
In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need for the first time to a data-driven operator learning problem related…
A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh
Shuhao Cao, Long Chen, Ruchi Guo
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal me…
Error analysis of a decoupled finite element method for quad-curl problems
Shuhao Cao, Long Chen, Xuehai Huang
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the…
A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions
Shuhao Cao, Chunmei Wang, Junping Wang
This paper presents a numerical method for div-curl systems with normal boundary conditions by using a finite element technique known as primal-dual weak Galerkin (PDWG). The PDWG…
Convergence and optimality of an adaptive modified weak Galerkin finite element method
Yingying Xie, Shuhao Cao, Long Chen +1
An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinea…
A simple virtual element-based flux recovery on quadtree
Shuhao Cao
In this paper, we introduce a simple local flux recovery for finite element of a scalar coefficient diffusion equation on quadtree meshes, with no restriction on th…
A note on the error estimate of the virtual element methods
Shuhao Cao, Long Chen, Frank Lin
This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error…
Anisotropic Error Estimates of The Linear Virtual Element Method on Polygonal Meshes
Shuhao Cao, Long Chen
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geo…
A Discretization-Accurate Stopping Criterion for Iterative Solvers for Finite Element Approximation
Zhiqiang Cai, Shuhao Cao, Robert D. Falgout
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element appro…
A Bootstrap Multigrid Eigensolver
James Brannick, Shuhao Cao
This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by the full bootstrap…
Robust A Posteriori Error Estimation for Finite Element Approximation to H(curl) Problem
Zhiqiang Cai, Shuhao Cao, Rob Falgout
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-…
A Recovery-Based A Posteriori Error Estimator for H(curl) Interface Problems
Zhiqiang Cai, Shuhao Cao
This paper introduces a new recovery-based a posteriori error estimator for the lowest order Nedelec finite element approximation to the H(curl) interface problem. The error estima…