128 citations · 346 across the 59 of their papers we have counts for
8 papers · 1 filter
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +1
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of t…
Fast auxiliary space preconditioners on surfaces
Yuwen Li
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning…
Nodal auxiliary a posteriori error estimates
Yuwen Li, Ludmil T. Zikatanov
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert s…
A Posteriori Error Estimates for Solving Graph Laplacians
Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed…
On the unisolvence for the quasi-polynomial spaces of differential forms
Shuonan Wu, Ludmil T. Zikatanov
We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the u…
A posteriori error estimates of finite element methods by preconditioning
Yuwen Li, Ludmil Zikatanov
We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods…
Discrete Trace Theorems and Energy Minimizing Spring Embeddings of Planar Graphs
John C. Urschel, Ludmil T. Zikatanov
Tutte's spring embedding theorem states that, for a three-connected planar graph, if the outer face of the graph is fixed as the complement of some convex region in the plane, and…
Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations
Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone +1
In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, na…