2.2k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Center for Astrophysics Harvard & SmithsonianUS71 papers
- Space Telescope Science InstituteUS70 papers
- University of MichiganUS65 papers
- University of California, DavisUS55 papers
- University of ArizonaUS53 papers
- Max Planck Institute for Extraterrestrial PhysicsDE52 papers
- University of FloridaUS51 papers
- California Institute of TechnologyUS49 papers
- Jet Propulsion LaboratoryUS49 papers
- University of ChicagoUS46 papers
- Massachusetts Institute of TechnologyUS44 papers
- University of California, Santa CruzUS42 papers
12 papers · 1 filter
Solver-in-the-Loop joint operator learning: fractional Laplace-Beltrami features for interface reconstruction
Yangyang Zheng, Huayi Wei, Shuhao Cao +1
In this work, we propose a joint operator learning method for reconstructing images of conductivity coefficients from boundary data. Inspired by the idea of employing partial diffe…
Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
Shuhao Cao, Long Chen, Seulip Lee
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a…
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…
Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions
Shuhao Cao, Long Chen, Ruchi Guo
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may…
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…
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…
Anisotropic Mesh Adaptation for Finite Element Solution of Anisotropic Porous Medium Equation
Xianping Li
Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived fo…
Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of newton's iteration
Fei Zhang, Weizhang Huang, Xianping Li +1
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is emp…
A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations
Xianping Li, Weizhang Huang
Preservation of nonnengativity and boundedness in the finite element solution of Nagumo-type equations with general anisotropic diffusion is studied. Linear finite elements and the…
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…
Anisotropic mesh adaptation for 3D anisotropic diffusion problems with application to fractured reservoir simulation
Xianping Li, Weizhang Huang
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The M-uniform mesh approach is used, where an anisotropic adaptive m…
Lebesgue Constants Arising in a Class of Collocation Methods
William W. Hager, Hongyan Hou, Anil V. Rao
Estimates are obtained for the Lebesgue constants associated with the Gauss quadrature points on augmented by the point and with the Radau quadrature points on eith…