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Research Output 1997 2019

  • 1309 Citations
  • 20 h-Index
  • 63 Article
  • 12 Conference contribution
  • 7 Chapter
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Article
2019

An adaptive multigrid method based on path cover

Hu, X., Lin, J. & Zikatanov, L. T., Jan 1 2019, In : SIAM Journal on Scientific Computing. 41, 5, p. S220-S241

Research output: Contribution to journalArticle

Multigrid Method
Adaptive Method
Agglomeration
Cover
Algebraic multigrid

Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation

Batista, J., Hu, X. & Zikatanov, L. T., Jan 1 2019, (Accepted/In press) In : Computers and Mathematics with Applications.

Research output: Contribution to journalArticle

Richards Equation
Mixed Finite Elements
Finite Element Discretization
Preconditioning
Mathematical operators
3 Citations (Scopus)

On the validity of the local Fourier analysis*

Rodrigo, C., Gaspar, F. J. & Zikatanov, L. T., Jan 1 2019, In : Journal of Computational Mathematics. 37, 3, p. 340-348 9 p.

Research output: Contribution to journalArticle

Fourier analysis
Fourier Analysis
Boundary conditions
Fourier Method
Multigrid Method

Optimal spatial-dynamic management to minimize the damages caused by aquatic invasive species

Zipp, K. Y., Wu, Y., Wu, K. & Zikatanov, L. T., Dec 1 2019, In : Letters in Spatial and Resource Sciences. 12, 3, p. 199-213 15 p.

Research output: Contribution to journalArticle

invasive species
damages
damage
lake
invasion

Randomized and fault-tolerant method of subspace corrections

Hu, X., Xu, J. & Zikatanov, L. T., Sep 1 2019, In : Research in Mathematical Sciences. 6, 3, 29.

Research output: Contribution to journalArticle

Iterative methods
Fault-tolerant
Subspace
Iteration
Convergence Rate
2018
1 Citation (Scopus)

Adaptive aggregation on graphs

Xu, W. & Zikatanov, L. T., Oct 1 2018, In : Journal of Computational and Applied Mathematics. 340, p. 718-730 13 p.

Research output: Contribution to journalArticle

Aggregation
Agglomeration
Graph Laplacian
A Posteriori Estimates
A Posteriori Error Estimators
7 Citations (Scopus)

New stabilized discretizations for poroelasticity and the Stokes’ equations

Rodrigo, C., Hu, X., Ohm, P., Adler, J. H., Gaspar, F. J. & Zikatanov, L. T., Nov 1 2018, In : Computer Methods in Applied Mechanics and Engineering. 341, p. 467-484 18 p.

Research output: Contribution to journalArticle

bubbles
degrees of freedom
Consolidation
formulations
perturbation
2017
25 Citations (Scopus)

Algebraic multigrid methods

Xu, J. & Zikatanov, L., May 1 2017, In : Acta Numerica. 26, p. 591-721 131 p.

Research output: Contribution to journalArticle

Algebraic multigrid Method
Eigenvalues and eigenfunctions
Multigrid Method
Minimization Problem
Eigenvector
16 Citations (Scopus)

A nonconforming finite element method for the Biot's consolidation model in poroelasticity

Hu, X., Rodrigo, C., Gaspar, F. J. & Zikatanov, L. T., Jan 15 2017, In : Journal of Computational and Applied Mathematics. 310, p. 143-154 12 p.

Research output: Contribution to journalArticle

Poroelasticity
Nonconforming Finite Element Method
Mass Lumping
Consolidation
Finite element method
9 Citations (Scopus)

Arbitrary dimension convection–diffusion schemes for space–time discretizations

Bank, R. E., Vassilevski, P. S. & Zikatanov, L. T., Jan 15 2017, In : Journal of Computational and Applied Mathematics. 310, p. 19-31 13 p.

Research output: Contribution to journalArticle

Convection-diffusion
Convergence of numerical methods
Error analysis
Discretization
Space-time
1 Citation (Scopus)

A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems

Antonietti, P. F., Sarti, M., Verani, M. & Zikatanov, L. T., Feb 1 2017, In : Journal of Scientific Computing. 70, 2, p. 608-630 23 p.

Research output: Contribution to journalArticle

Additive Schwarz
Discontinuous Galerkin
Galerkin Approximation
Preconditioner
Elliptic Problems

On the approximation of Laplacian eigenvalues in graph disaggregation

Hu, X., Urschel, J. C. & Zikatanov, L. T., Sep 2 2017, In : Linear and Multilinear Algebra. 65, 9, p. 1805-1822 18 p.

Research output: Contribution to journalArticle

Laplacian Eigenvalues
Disaggregation
Graph Laplacian
Vertex Degree
Approximation
2016
7 Citations (Scopus)

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations

Hong, Q., Kraus, J., Xu, J. & Zikatanov, L. T., Jan 1 2016, In : Numerische Mathematik. 132, 1, p. 23-49 27 p.

Research output: Contribution to journalArticle

Discontinuous Galerkin
Linear Elasticity
Multigrid Method
Poisson ratio
Robust Methods
2 Citations (Scopus)

On the maximal error of spectral approximation of graph bisection

Urschel, J. C. & Zikatanov, L. T., Oct 2 2016, In : Linear and Multilinear Algebra. 64, 10, p. 1972-1979 8 p.

Research output: Contribution to journalArticle

Spectral Approximation
Bisection
Graph in graph theory
Graph Partitioning
Complete Graph
8 Citations (Scopus)

Preconditioning heterogeneous h(div) problems by additive schur complement approximation and applications

Kraus, J., Lazarov, R., Lymbery, M., Margenov, S. & Zikatanov, L., Jan 1 2016, In : SIAM Journal on Scientific Computing. 38, 2, p. A875-A898

Research output: Contribution to journalArticle

Schur Complement
Preconditioning
Preconditioner
Approximation
Factorization
37 Citations (Scopus)

Stability and monotonicity for some discretizations of the Biot's consolidation model

Rodrigo, C., Gaspar, F. J., Hu, X. & Zikatanov, L. T., Jan 1 2016, In : Computer Methods in Applied Mechanics and Engineering. 298, p. 183-204 22 p.

Research output: Contribution to journalArticle

consolidation
Consolidation
oscillations
Stabilization
permeability
2015
11 Citations (Scopus)

A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians

Urschel, J. C., Xu, J., Hu, X. & Zikatanov, L. T., Mar 1 2015, In : Journal of Computational Mathematics. 33, 2, p. 209-226 18 p.

Research output: Contribution to journalArticle

Graph Laplacian
Computing
Graph Drawing
Graph Partitioning
Smallest Eigenvalue
2 Citations (Scopus)

A finite element framework for some mimetic finite difference discretizations

Rodrigo, C., Gaspar, F. J., Hu, X. & Zikatanov, L., Dec 2015, In : Computers and Mathematics with Applications. 70, 11, p. 2661-2673 13 p.

Research output: Contribution to journalArticle

Fourier analysis
Finite Difference
Discretization
Multigrid Method
Finite Element
4 Citations (Scopus)

A two-level method for mimetic finite difference discretizations of elliptic problems

Antonietti, P. F., Verani, M. & Zikatanov, L., Dec 2015, In : Computers and Mathematics with Applications. 70, 11, p. 2674-2687 14 p.

Research output: Contribution to journalArticle

Two-level Method
Elliptic Problems
Boundary value problems
Finite Difference
Discretization
3 Citations (Scopus)

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

Brannick, J., Hu, X., Rodrigo, C. & Zikatanov, L., Jan 1 2015, In : Numerical Mathematics. 8, 1, p. 1-21 21 p.

Research output: Contribution to journalArticle

Fourier analysis
Multigrid Method
Fourier Analysis
Coarsening
Polynomials
2014
11 Citations (Scopus)

A simple preconditioner for a Discontinuous Galerkin method for the Stokes problem

De Dios, B. A., Brezzi, F., Marini, L. D., Xu, J. & Zikatanov, L., Mar 2014, In : Journal of Scientific Computing. 58, 3, p. 517-547 31 p.

Research output: Contribution to journalArticle

Divergence-free
Discontinuous Galerkin
Stokes Problem
Galerkin Approximation
Discontinuous Galerkin Method
6 Citations (Scopus)

Commuting projections on graphs

Vassilevski, P. S. & Zikatanov, L. T., May 2014, In : Numerical Linear Algebra with Applications. 21, 3, p. 297-315 19 p.

Research output: Contribution to journalArticle

Graph Laplacian
Projection
Graph in graph theory
Factorization
Mathematical operators
13 Citations (Scopus)

Multilevel preconditioners for discontinuous Galerkin approximations of elliptic problems with jump coefficients

De Dios, B. A., Holst, M., Zhu, Y. & Zikatanov, L., May 1 2014, In : Mathematics of Computation. 83, 287, p. 1083-1120 38 p.

Research output: Contribution to journalArticle

Multilevel Preconditioners
Discontinuous Galerkin
Galerkin Approximation
Elliptic Problems
Jump
7 Citations (Scopus)

Spectral bisection of graphs and connectedness

Urschel, J. C. & Zikatanov, L. T., May 15 2014, In : Linear Algebra and Its Applications. 449, p. 1-16 16 p.

Research output: Contribution to journalArticle

Bisection
Connectedness
Graph in graph theory
Graph Laplacian
Irreducible Matrix
2013
10 Citations (Scopus)

Algebraic multilevel preconditioners for the graph laplacian based on matching in graphs

Brannick, J., Chen, Y., Kraus, J. & Zikatanov, L., Oct 9 2013, In : SIAM Journal on Numerical Analysis. 51, 3, p. 1805-1827 23 p.

Research output: Contribution to journalArticle

Multilevel Preconditioners
Graph Laplacian
Vector spaces
Convergence Rate
Vector space
2 Citations (Scopus)
Two-level Method
Anisotropic Diffusion
Diffusion equation
Anisotropy
Grid
3 Citations (Scopus)

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

Ayuso De Dios, B., Georgiev, I., Kraus, J. & Zikatanov, L., Sep 1 2013, In : ESAIM: Mathematical Modelling and Numerical Analysis. 47, 5, p. 1315-1333 19 p.

Research output: Contribution to journalArticle

Discontinuous Galerkin
Linear Elasticity
Preconditioner
Elasticity
Discretization
12 Citations (Scopus)

Combined preconditioning with applications in reservoir simulation

Hu, X., Wu, S., Wu, X. H., Xu, J., Zhang, C. S., Zhang, S. & Zikatanov, L., Jul 9 2013, In : Multiscale Modeling and Simulation. 11, 2, p. 507-521 15 p.

Research output: Contribution to journalArticle

multigrid methods
Reservoir Simulation
preconditioning
Preconditioning
Iterative methods
1 Citation (Scopus)

Numerical approximation of asymptotically disappearing solutions of maxwell's equations

Adler, J. H., Petkov, V. & Zikatanov, L. T., Nov 7 2013, In : SIAM Journal on Scientific Computing. 35, 5, p. S386-S401

Research output: Contribution to journalArticle

Maxwell equations
Numerical Approximation
Maxwell's equations
Electric fields
Initial conditions
2012
10 Citations (Scopus)
Multilevel Methods
Algebraic Methods
Elliptic Equations
Subgraph
Coarsening
17 Citations (Scopus)

Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids

Scheichl, R., Vassilevski, P. S. & Zikatanov, L. T., Sep 5 2012, In : SIAM Journal on Numerical Analysis. 50, 3, p. 1675-1694 20 p.

Research output: Contribution to journalArticle

Multilevel Methods
Varying Coefficients
Elliptic Problems
Boundary value problems
Grid
1 Citation (Scopus)

Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses

Boyanova, P., Georgiev, I., Margenov, S. & Zikatanov, L., Jun 1 2012, In : Mathematics and Computers in Simulation. 82, 10, p. 1964-1971 8 p.

Research output: Contribution to journalArticle

Multilevel Preconditioning
Graph Laplacian
Polynomial approximation
Pivot
Polynomial Approximation
13 Citations (Scopus)

Polynomial of best uniform approximation to 1/x and smoothing in two-level methods

Kraus, J., Vassilevski, P. & Zikatanov, L., Oct 1 2012, In : Computational Methods in Applied Mathematics. 12, 4, p. 448-468 21 p.

Research output: Contribution to journalArticle

Two-level Method
Uniform Approximation
Best Approximation
Smoothing
Polynomials
2011
7 Citations (Scopus)

First-order system least squares and the energetic variational approach for two-phase flow

Adler, J. H., Brannick, J., Liu, C., Manteuffel, T. & Zikatanov, L., Jul 20 2011, In : Journal of Computational Physics. 230, 17, p. 6647-6663 17 p.

Research output: Contribution to journalArticle

two phase flow
Two phase flow
Magnetohydrodynamics
Flow of fluids
magnetohydrodynamics
15 Citations (Scopus)

Weak approximation properties of elliptic projections with functional constraints

Scheichl, R., Vassilevski, P. S. & Zikatanov, L. T., Dec 1 2011, In : Multiscale Modeling and Simulation. 9, 4, p. 1677-1699 23 p.

Research output: Contribution to journalArticle

Weak Approximation
Approximation Property
projection
Projection
pulse detonation engines
2010
7 Citations (Scopus)

Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems

Brannick, J. J., Frommer, A., Kahl, K., MacLachlan, S. & Zikatanov, L. T., Dec 1 2010, In : Electronic Transactions on Numerical Analysis. 37, p. 276-295 20 p.

Research output: Contribution to journalArticle

Interpolate
Sparse Approximation
Algebraic multigrid
Singular matrix
Convergence Theory
2009
23 Citations (Scopus)

A posteriori error estimator and AMR for discrete ordinates nodal transport methods

Duo, J. I., Azmy, Y. Y. & Zikatanov, L. T., Apr 1 2009, In : Annals of Nuclear Energy. 36, 3, p. 268-273 6 p.

Research output: Contribution to journalArticle

Fluxes
Spatial distribution
37 Citations (Scopus)

Uniformly convergent iterative methods for discontinuous Galerkin discretizations

Ayuso De Dios, B. & Zikatanov, L. T., Jul 1 2009, In : Journal of Scientific Computing. 40, 1-3, p. 4-36 33 p.

Research output: Contribution to journalArticle

Interior Penalty
Discontinuous Galerkin
Iterative methods
Linear systems
Discretization
2008

Advanced multigrid methods for systems of PDEs

Vassilevski, P. S. & Zikatanov, L. T., Jun 1 2008, In : Numerical Linear Algebra with Applications. 15, 5 SPEC. ISS., 1 p.

Research output: Contribution to journalArticle

Multigrid Method
15 Citations (Scopus)

A sharp convergence estimate for the method of subspace corrections for singular systems of equations

Lee, Y. J., Wu, J., Xu, J. & Zikatanov, L., Apr 1 2008, In : Mathematics of Computation. 77, 262, p. 831-850 20 p.

Research output: Contribution to journalArticle

Convergence Estimates
Laplace equation
Singular Systems
System of equations
Subspace
6 Citations (Scopus)

Convergence analysis on iterative methods for semidefinite systems

Wu, J., Lee, Y. J., Xu, J. & Zikatanov, L. T., Nov 1 2008, In : Journal of Computational Mathematics. 26, 6, p. 797-815 19 p.

Research output: Contribution to journalArticle

Iterative methods
Convergence Analysis
Convergence Rate
Computer systems
Iteration
22 Citations (Scopus)

Two-sided bounds on the convergence rate of two-level methods

Zikatanov, L. T., Jun 1 2008, In : Numerical Linear Algebra with Applications. 15, 5 SPEC. ISS., p. 439-454 16 p.

Research output: Contribution to journalArticle

Two-level Method
Rate of Convergence
Optimal Convergence Rate
Curl
Multigrid Method
18 Citations (Scopus)

Uniform convergence of the multigrid V -cycle on graded meshes for corner singularities

Brannick, J. J., Li, H. & Zikatanov, L. T., Mar 1 2008, In : Numerical Linear Algebra with Applications. 15, 2-3 SPEC. ISS., p. 291-306 16 p.

Research output: Contribution to journalArticle

Corner Singularity
Graded Meshes
Poisson equation
Uniform convergence
Poisson's equation
2007
6 Citations (Scopus)

A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes

Cho, D. & Zikatanov, L. T., Oct 10 2007, In : Journal of Numerical Mathematics. 15, 3, p. 163-180 18 p.

Research output: Contribution to journalArticle

Multilevel Preconditioning
Generalized Finite Element Method
Preconditioner
Mesh
Finite element method
23 Citations (Scopus)

Improving the rate of convergence of high-order finite elements on polyhedra II: Mesh refinements and interpolation

Bacuta, C., Nistor, V. & Zikatanov, L. T., Jul 1 2007, In : Numerical Functional Analysis and Optimization. 28, 7-8, p. 775-824 50 p.

Research output: Contribution to journalArticle

High-order Finite Elements
Mesh Refinement
Polyhedron
Interpolation
Rate of Convergence
31 Citations (Scopus)

Mathematical models for the deformation of electrolyte droplets

Ryham, R., Liu, C. & Zikatanov, L. T., Oct 1 2007, In : Discrete and Continuous Dynamical Systems - Series B. 8, 3, p. 649-661 13 p.

Research output: Contribution to journalArticle

Phase Field
Electrolyte
Droplet
Free energy
Electrostatics
22 Citations (Scopus)

Robust subspace correction methods for nearly singular systems

Lee, Y. J., Wu, J., Xu, J. & Zikatanov, L. T., Nov 1 2007, In : Mathematical Models and Methods in Applied Sciences. 17, 11, p. 1937-1963 27 p.

Research output: Contribution to journalArticle

Singular Systems
Subspace
Decomposition
kernel
Two-level Method
2006
5 Citations (Scopus)

Extending the applicability of multigrid methods

Brannick, J., Brezina, M., Falgout, R., Manteuffel, T., McCormick, S., Ruge, J., Sheehan, B., Xu, J. & Zikatanov, L., Oct 1 2006, In : Journal of Physics: Conference Series. 46, 1, p. 443-452 10 p., 061.

Research output: Contribution to journalArticle

multigrid methods
TOPS (spacecraft)
radiation transport
degrees of freedom
quantum chromodynamics
12 Citations (Scopus)

Multiple vector preserving interpolation mappings in algebraic multigrid

Vassilevski, P. S. & Zikatanov, L. T., Oct 25 2006, In : SIAM Journal on Matrix Analysis and Applications. 27, 4, p. 1040-1055 16 p.

Research output: Contribution to journalArticle

Algebraic multigrid
Interpolation
Interpolate
Algebraic multigrid Method
Set of vectors
22 Citations (Scopus)

On the convergence of iterative methods for semidefinite linear systems

Lee, Y. J., Wu, J., Xu, J. & Zikatanov, L. T., Dec 1 2006, In : SIAM Journal on Matrix Analysis and Applications. 28, 3, p. 634-641 8 p.

Research output: Contribution to journalArticle

Regularity
Linear Systems
Iteration
Norm
Necessary Conditions