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Research Output 1997 2019

  • 1307 Citations
  • 20 h-Index
  • 63 Article
  • 12 Conference contribution
  • 7 Chapter
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

New stabilized discretizations for poroelasticity equations

Gaspar, F. J., Rodrigo, C., Hu, X., Ohm, P., Adler, J. & Zikatanov, L., Jan 1 2019, Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. Kolkovska, N., Georgiev, K. & Nikolov, G. (eds.). Springer Verlag, p. 3-14 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 11189 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Poroelasticity
Consolidation
Conservation
Mechanics
Discretization
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

Discrete energy laws for the first-order system least-squares finite-element approach

Adler, J. H., Lashuk, I., MacLachlan, S. P. & Zikatanov, L. T., Jan 1 2018, Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers. Lirkov, I. & Margenov, S. (eds.). Springer Verlag, p. 3-20 18 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 10665 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

First-order System
Partial differential equations
Least Squares
Finite Element
Energy

Fourier method for approximating eigenvalues of indefinite stekloff operator

Wu, Y. & Zikatanov, L., Jan 1 2018, High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers. Sistek, J., Tichy, P., Kozubek, T., Cermak, M., Lukas, D., Jaros, J. & Blaheta, R. (eds.). Springer Verlag, p. 34-46 13 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 11087 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Helmholtz equation
Fourier Method
Helmholtz Equation
Eigenvalue
Computing
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
5 Citations (Scopus)

Robust block preconditioners for biot’s model

Adler, J. H., Gaspar, F. J., Hu, X., Rodrigo, C. & Zikatanov, L. T., Jan 1 2018, Lecture Notes in Computational Science and Engineering. Springer Verlag, p. 3-16 14 p. (Lecture Notes in Computational Science and Engineering; vol. 125).

Research output: Chapter in Book/Report/Conference proceedingChapter

Preconditioner
Consolidation
Linear systems
Stabilized Finite Elements
Equivalent Norm
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
1 Citation (Scopus)

Fast constrained image segmentation using optimal spanning trees

Harizanov, S., Margenov, S. & Zikatanov, L., Jan 1 2015, Large-Scale Scientific Computing - 10th International Conference, LSSC 2015, Revised Selected Papers. Lirkov, I., Margenov, S. D. & Waśniewski, J. (eds.). Springer Verlag, p. 15-29 15 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 9374).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Spanning tree
Image segmentation
Image Segmentation
Voxel
Approximation Error
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

Space decompositions and solvers for discontinuous galerkin methods

de Dios, B. A. & Zikatanov, L., Jan 1 2014, Domain Decomposition Methods in Science and Engineering XXI. Sassi, T., Pichot, G., Gander, M. J., Erhel, J., Widlund, O. & Halpern, L. (eds.). Springer Verlag, p. 3-15 13 p. (Lecture Notes in Computational Science and Engineering; vol. 98).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Discontinuous Galerkin Method
Galerkin methods
Decomposition
Decompose
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
2 Citations (Scopus)

A Block Solver for the Exponentially Fitted IIPG-0 Method

de Dios, B. A., Lombardi, A., Pietra, P. & Zikatanov, L., Jul 25 2013, Domain Decomposition Methods in Science and Engineering XX. Bank, R., Holst, M., Xu, J. & Widlund, O. (eds.). p. 239-246 8 p. (Lecture Notes in Computational Science and Engineering; vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

Advection
Discontinuous Galerkin Method
Galerkin methods
Linear systems
Linear Systems
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
3 Citations (Scopus)

An Algebraic Multigrid Method Based on Matching in Graphs

Brannick, J., Chen, Y., Kraus, J. & Zikatanov, L., Jul 25 2013, Domain Decomposition Methods in Science and Engineering XX. Randolph, B., Michael, H. & Jinchao, X. (eds.). p. 143-150 8 p. (Lecture Notes in Computational Science and Engineering; vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

Algebraic multigrid Method
Graph in graph theory
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

A Subspace Correction Method for Nearly Singular Linear Elasticity Problems

Karer, E., Kraus, J. K. & Zikatanov, L. T., Jul 25 2013, Domain Decomposition Methods in Science and Engineering XX. Randolph, B., Michael, H. & Jinchao, X. (eds.). p. 159-166 8 p. (Lecture Notes in Computational Science and Engineering; vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

Elasticity Problem
Linear Elasticity
Elasticity
Subspace
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

Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients

De Dios, B. A., Holst, M., Zhu, Y. & Zikatanov, L., Jul 25 2013, Domain Decomposition Methods in Science and Engineering XX. Bank, R., Holst, M., Xu, J. & Widlund, O. (eds.). p. 183-190 8 p. (Lecture Notes in Computational Science and Engineering; vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

Preconditioner
Elliptic Problems
Linear systems
Jump
Discretization
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

Visible Points in Convex Sets and Best Approximation

Deutsch, F., Hundal, H. & Zikatanov, L., Jan 1 2013, Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday. Springer New York LLC, p. 349-364 16 p. (Springer Proceedings in Mathematics and Statistics; vol. 50).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Best Approximation
Convex Sets
Point Sets
Robotics
Concepts
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

A simple preconditioner for the SIPG discretization of linear elasticity equations

Ayuso, B., Georgiev, I., Kraus, J. & Zikatanov, L. T., Mar 1 2011, Numerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers. p. 353-361 9 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6046 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Interior Penalty
Discontinuous Galerkin
Linear Elasticity
Preconditioner
Elasticity
2 Citations (Scopus)

A simple uniformly convergent iterative method for the non-symmetric incomplete interior penalty discontinuous Galerkin Discretization

Ayuso, B. & Zikatanov, L. T., Jan 1 2011, Domain Decomposition Methods in Science and Engineering XIX. Springer Verlag, p. 335-342 8 p. (Lecture Notes in Computational Science and Engineering; vol. 78 LNCSE).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Interior Penalty
Discontinuous Galerkin
Iterative methods
Discretization
Iteration
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