1 citations · 1 across the 11 of their papers we have counts for
11 papers
Wavenumber-explicit stability and preasymptotic error analysis of UPML finite element method for obstacle scattering problems
Yuhao Wang, Weiying Zheng
This paper develops a wavenumber-explicit stability and preasymptotic error analysis for finite element approximation of the two-dimensional Helmholtz scattering problem with a uni…
hp-Optimal DG Approximation and Robust Schwarz Decompositions on One-Irregular Cubical Meshes
Situan Li, Weiying Zheng
We study hp approximation and additive Schwarz decompositions for variable-order cubical finite element spaces on one-irregular meshes. For fitted homogeneous diffusion interface p…
Stable Triangle Projections for Variable-Degree Tetrahedral Spaces and Uniform IPDG Preconditioning
Situan Li, Weiying Zheng
The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two…
Weighted hp-Uniform Decompositions for H^k-Type Tensor-Product Spaces in Arbitrary Dimension
Situan Li, Weiying Zheng
We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces,…
Owner-selected bubble transforms and coefficient-robust Schwarz preconditioners for variable-degree finite elements
Situan Li, Weiying Zheng
We construct - and -robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree finite element discretizations of conforming…
Trace-Preserving hp Interpolation and Polynomial Liftings on Conforming Hexahedral Meshes
Situan Li, Weiying Zheng
Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed e…
Boundary-preserving hp interpolation and p-robust discrete harmonic extensions on tetrahedral meshes
Situan Li, Weiying Zheng
We construct a boundary-preserving hp interpolation operator on three-dimensional tetrahedral meshes with locally variable polynomial degrees. If the trace of an H^1 function on th…
p-multigrid method for the discontinuous Galerkin discretization of elliptic problems
Nuo Lei, Donghang Zhang, Weiying Zheng
In this paper, we propose a -cycle -multigrid method for solving the -version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems…
Topological Invariants in Nonlinear Thouless Pumping of Solitons
Fei-Fei Wu, Xian-Da Zuo, Qing-Qing Zhu +8
Recent explorations of quantized solitons transport in optical waveguides have thrust nonlinear topological pumping into the spotlight. In this work, we introduce a unified topolog…
A new framework of high-order unfitted finite element methods using ALE maps for moving-domain problems
Wenhao Lu, Chuwen Ma, Weiying Zheng
As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic f…
Local Multigrid in H(curl)
Ralf Hiptmair, Weiying Zheng
We consider H(curl)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume…