52 citations · 286 across the 18 of their papers we have counts for
18 papers
Adaptive mesh refinement for electromagnetic simulation
Alexey Belokrys-Fedotov, Vladimir Garanzha, Lennard Kamenski +4
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the perfo…
Non-simplicial Delaunay meshing via approximation by radical partitions
Vladimir Garanzha, Liudmila Kudryavtseva, Lennard Kamenski
We consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (radical partitions). The dual Voronoi diagram is obtained as a limit o…
Stability of explicit Runge-Kutta methods for high order finite element approximation of linear parabolic equations
Weizhang Huang, Lennard Kamenski, Jens Lang
We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eige…
A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
Weizhang Huang, Lennard Kamenski, Jens Lang
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform on…
Sharp bounds on the smallest eigenvalue of finite element equations with arbitrary meshes without regularity assumptions
Lennard Kamenski
A proof for the lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes. The bound has a similar form as the one…
Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method
Klaus Gärtner, Lennard Kamenski
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary confo…
Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
Franco Dassi, Lennard Kamenski, Patricio Farrell +1
Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve t…
Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes
Weizhang Huang, Lennard Kamenski, Jens Lang
The conditioning of implicit Runge-Kutta (RK) integration for linear finite element approximation of diffusion equations on general anisotropic meshes is investigated. Bounds are e…
Stability of explicit one-step methods for P1-finite element approximation of linear diffusion equations on anisotropic meshes
Weizhang Huang, Lennard Kamenski, Jens Lang
We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissi…
On the mesh nonsingularity of the moving mesh PDE method
Weizhang Huang, Lennard Kamenski
The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained m…
A comparative numerical study of meshing functionals for variational mesh adaptation
Weizhang Huang, Lennard Kamenski, Robert D. Russell
We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalisation of Winslow's variable diffusion functional whil…
A geometric discretization and a simple implementation for variational mesh generation and adaptation
Weizhang Huang, Lennard Kamenski
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the J…
A study on the conditioning of finite element equations with arbitrary anisotropic meshes via a density function approach
Lennard Kamenski, Weizhang Huang
The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix an…
How a nonconvergent recovered Hessian works in mesh adaptation
Lennard Kamenski, Weizhang Huang
Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian…
Adaptive finite elements with anisotropic meshes
Weizhang Huang, Lennard Kamenski, Jens Lang
The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anis…
Conditioning of Finite Element Equations with Arbitrary Anisotropic Meshes
Lennard Kamenski, Weizhang Huang, Hongguo Xu
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The fi…
A Study on Using Hierarchical Basis Error Estimates in Anisotropic Mesh Adaptation for the Finite Element Method
Lennard Kamenski
A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M…
Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases
Weizhang Huang, Lennard Kamenski, Xianping Li
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper,…