128 citations · 346 across the 59 of their papers we have counts for
9 papers · 1 filter
Some Applications of the Hahn-Banach Separation Theorem
Frank Deutsch, Hein Hundal, Ludmil Zikatanov
We show that a single special separation theorem (namely, a consequence of the geometric form of the Hahn-Banach theorem) can be used to prove Farkas type theorems, existence theor…
On the validity of the local Fourier analysis
Carmen Rodrigo, Francisco J. Gaspar, Ludmil T. Zikatanov
Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic bou…
Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach
J. H. Adler, I. Lashuk, S. P. MacLachlan +1
This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the he…
Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
Yangqingxiang Wu, Ludmil T Zikatanov
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz e…
New stabilized discretizations for poroelasticity and the Stokes' equations
Carmen Rodrigo, Xiaozhe Hu, Peter Ohm +3
In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisf…
Robust Block Preconditioners for Biot's Model
James H. Adler, Francisco J. Gaspar, Xiaozhe Hu +2
In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot's consolidation model, where stabilized finite-element discretizations are…
A unified approach to the design and analysis of AMG
Jinchao Xu, Hongxuan Zhang, Ludmil Zikatanov
In this work, we present a general framework for the design and analysis of two-level AMG methods. The approach is to find a basis for locally optimal or quasi-optimal coarse space…
On the Weyl's law for discretized elliptic operators
Jinchao Xu, Hongxuan Zhang, Ludmil Zikatanov
In this paper we give an estimate on the asymptotic behavior of eigenvalues of discretized elliptic boundary values problems. We first prove a simple min-max principle for selfadjo…
Adaptive aggregation on graphs
Wenfang Xu, Ludmil T. Zikatanov
We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical…