Ludmil T. Zikatanov

  • Penn State, University Park, USA

According to our database1, Ludmil T. Zikatanov authored at least 68 papers between 1997 and 2022.

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PhD thesis 


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Locking-Free Enriched Galerkin Method for Linear Elasticity.
SIAM J. Numer. Anal., 2022

HAZniCS - Software Components for Multiphysics Problems.
CoRR, 2022

Rational approximation preconditioners for multiphysics problems.
CoRR, 2022

A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians.
SIAM J. Sci. Comput., 2021

A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations.
SIAM J. Sci. Comput., 2021

Energetic stable discretization for non-isothermal electrokinetics model.
J. Comput. Phys., 2021

Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations.
J. Comput. Appl. Math., 2021

An Enriched Galerkin Method for the Stokes Equations.
CoRR, 2021

Neural networks with trainable matrix activation functions.
CoRR, 2021

New stabilized P<sub>1</sub>×P<sub>0</sub> finite element methods for nearly inviscid and incompressible flows.
CoRR, 2021

A posteriori error estimates of finite element methods by preconditioning.
Comput. Math. Appl., 2021

Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations.
SIAM J. Sci. Comput., 2020

Fast auxiliary space preconditioners on surfaces.
CoRR, 2020

Nodal auxiliary a posteriori error estimates.
CoRR, 2020

On the unisolvence for the quasi-polynomial spaces of differential forms.
CoRR, 2020

Auxiliary space preconditioning for mixed finite element discretizations of Richards' equation.
Comput. Math. Appl., 2020

An Adaptive Multigrid Method Based on Path Cover.
SIAM J. Sci. Comput., 2019

Residual-based a posteriori error estimates of mixed methods in Biot's consolidation model.
CoRR, 2019

Adaptive aggregation on graphs.
J. Comput. Appl. Math., 2018

New Stabilized Discretizations for Poroelasticity Equations.
Proceedings of the Numerical Methods and Applications - 9th International Conference, 2018

Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions.
SIAM J. Sci. Comput., 2017

A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems.
J. Sci. Comput., 2017

A nonconforming finite element method for the Biot's consolidation model in poroelasticity.
J. Comput. Appl. Math., 2017

Arbitrary dimension convection-diffusion schemes for space-time discretizations.
J. Comput. Appl. Math., 2017

Algebraic multigrid methods.
Acta Numer., 2017

Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach.
Proceedings of the Large-Scale Scientific Computing - 11th International Conference, 2017

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator.
Proceedings of the High Performance Computing in Science and Engineering, 2017

Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications.
SIAM J. Sci. Comput., 2016

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations.
Numerische Mathematik, 2016

A finite element framework for some mimetic finite difference discretizations.
Comput. Math. Appl., 2015

A two-level method for mimetic finite difference discretizations of elliptic problems.
Comput. Math. Appl., 2015

Fast Constrained Image Segmentation Using Optimal Spanning Trees.
Proceedings of the Large-Scale Scientific Computing - 10th International Conference, 2015

Commuting projections on graphs.
Numer. Linear Algebra Appl., 2014

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients.
Math. Comput., 2014

A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem.
J. Sci. Comput., 2014

A Subspace Correction Method for Nearly Singular Linear Elasticity Problems.
Proceedings of the Domain Decomposition Methods in Science and Engineering XX, 2013

A Block Solver for the Exponentially Fitted IIPG-0 Method.
Proceedings of the Domain Decomposition Methods in Science and Engineering XX, 2013

Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients.
Proceedings of the Domain Decomposition Methods in Science and Engineering XX, 2013

An Algebraic Multigrid Method Based on Matching in Graphs.
Proceedings of the Domain Decomposition Methods in Science and Engineering XX, 2013

Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations.
SIAM J. Sci. Comput., 2013

Algebraic Multilevel Preconditioners for the Graph Laplacian Based on Matching in Graphs.
SIAM J. Numer. Anal., 2013

Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids.
Numer. Linear Algebra Appl., 2013

Combined Preconditioning with Applications in Reservoir Simulation.
Multiscale Model. Simul., 2013

Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids.
SIAM J. Numer. Anal., 2012

An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching.
Numer. Linear Algebra Appl., 2012

Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses.
Math. Comput. Simul., 2012

Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-level Methods.
Comput. Methods Appl. Math., 2012

Weak Approximation Properties of Elliptic Projections with Functional Constraints.
Multiscale Model. Simul., 2011

First-order system least squares and the energetic variational approach for two-phase flow.
J. Comput. Phys., 2011

A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations.
Proceedings of the Numerical Methods and Applications - 7th International Conference, 2010

Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations.
J. Sci. Comput., 2009

Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials.
SIAM J. Sci. Comput., 2008

Two-sided bounds on the convergence rate of two-level methods.
Numer. Linear Algebra Appl., 2008

Advanced multigrid methods for systems of PDEs.
Numer. Linear Algebra Appl., 2008

Uniform convergence of the multigrid <i>V</i>-cycle on graded meshes for corner singularities.
Numer. Linear Algebra Appl., 2008

A sharp convergence estimate for the method of subspace corrections for singular systems of equations.
Math. Comput., 2008

A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes.
J. Num. Math., 2007

Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid.
SIAM J. Matrix Anal. Appl., 2006

On the Convergence of Iterative Methods for Semidefinite Linear Systems.
SIAM J. Matrix Anal. Appl., 2006

Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations.
Numer. Linear Algebra Appl., 2006

Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps.
Numerische Mathematik, 2005

On two-grid convergence estimates.
Numer. Linear Algebra Appl., 2005

Partition of unity method on nonmatching grids for the Stokes problem.
J. Num. Math., 2005

Uniformly Convergent Multigrid Methods for Convection-Diffusion Problems without Any Constraint on Coarse Grids.
Adv. Comput. Math., 2004

Some observations on Babu\vs}ka and Brezzi theories.
Numerische Mathematik, 2003

A multigrid method based on graph matching for convection-diffusion equations.
Numer. Linear Algebra Appl., 2003

A monotone finite element scheme for convection-diffusion equations.
Math. Comput., 1999

Circulant Block-Factorization Preconditioning of Anisotropic Elliptic Problems.
Computing, 1997