128 citations · 346 across the 59 of their papers we have counts for
6 papers · 1 filter
Algebraic Multigrid Methods
Jinchao Xu, Ludmil T Zikatanov
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often…
Constructing Frequency Domains on Graphs in Near-Linear Time
John C. Urschel, Wenfang Xu, Ludmil T. Zikatanov
Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domai…
On the Approximation of Laplacian Eigenvalues in Graph Disaggregation
Xiaozhe Hu, John C. Urschel, Ludmil T. Zikatanov
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple…
Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions
James H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov
In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a…
A Nonconforming Finite Element Method for the Biot's Consolidation Model in Poroelasticity
Xiaozhe Hu, Carmen Rodrigo, Francisco J. Gaspar +1
A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid…
Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations
Randolph E. Bank, Panayot S. Vassilevski, Ludmil T. Zikatanov
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the c…