Reduced Krylov Basis Methods for Parametric Partial Differential Equations - Yuwen Li; Ludmil T. Zikatanov; Cheng Zuo (SIAM J. Numer. Anal., 2025)

Oscillation-Free Numerical Schemes for Biot's Model and Their Iterative Coupling Solution - Álvaro Pé de la Riva; Francisco José Gaspar; Xiaozhe Hu; James H. Adler; Carmen Rodrigo; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2025)

Parameter-free preconditioning for nearly-incompressible linear elasticity - James H. Adler; Xiaozhe Hu; Yuwen Li; Ludmil T. Zikatanov (Comput. Math. Appl., 2024)

A local Fourier analysis for additive Schwarz smoothers - Álvaro Pé de la Riva; Carmen Rodrigo; Francisco José Gaspar; James H. Adler; Xiaozhe Hu; Ludmil T. Zikatanov (Comput. Math. Appl., 2024)

Algebraic Multigrid Methods for Metric-Perturbed Coupled Problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2024)

A Reduced Conjugate Gradient Basis Method for Fractional Diffusion - Yuwen Li; Ludmil T. Zikatanov; Cheng Zuo (SIAM J. Sci. Comput., 2024)

Weakly Coupled Systems of Eikonal Equations in Path-Planning Problems - Maria Teresa Chiri; Kenneth D. Czuprynski; Ludmil T. Zikatanov (American Control Conference, ACC 2024, Toronto, ON, Canada, July 10-12, 2024, 2024)

Reduced Krylov Basis Methods for Parametric Partial Differential Equations - Yuwen Li; Ludmil T. Zikatanov; Cheng Zuo (CoRR, 2024)

Oscillation-free numerical schemes for Biot's model and their iterative coupling solution - Álvaro Pé de la Riva; Francisco José Gaspar; Xiaozhe Hu; James H. Adler; Carmen Rodrigo; Ludmil T. Zikatanov (CoRR, 2024)

Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations - Pasqua D'Ambra; Fabio Durastante; Salvatore Filippone; Ludmil T. Zikatanov (Comput. Math. Appl., 2023)

HAZniCS - Software Components for Multiphysics Problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil T. Zikatanov (ACM Trans. Math. Softw., 2023)

Parameter-free preconditioning for nearly-incompressible linear elasticity - James H. Adler; Xiaozhe Hu; Yuwen Li; Ludmil T. Zikatanov (CoRR, 2023)

Algebraic multigrid methods for metric-perturbed coupled problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil Tomov Zikatanov (CoRR, 2023)

A reduced conjugate gradient basis method for fractional diffusion - Yuwen Li; Ludmil T. Zikatanov; Cheng Zuo (CoRR, 2023)

A Local Fourier Analysis for Additive Schwarz Smoothers - Álvaro Pé de la Riva; Carmen Rodrigo; Francisco José Gaspar; James H. Adler; Xiaozhe Hu; Ludmil T. Zikatanov (CoRR, 2023)

Locking-Free Enriched Galerkin Method for Linear Elasticity - Son-Young Yi; Sanghyun Lee; Ludmil T. Zikatanov (SIAM J. Numer. Anal., 2022)

Rational Approximation Preconditioners for Multiphysics Problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil T. Zikatanov (Numerical Methods and Applications - 10th International Conference, NMA 2022, Borovets, Bulgaria, August 22-26, 2022, Proceedings, 2022)

Rational approximation preconditioners for multiphysics problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil T. Zikatanov (CoRR, 2022)

HAZniCS - Software Components for Multiphysics Problems - Ana Budisa; Xiaozhe Hu; Miroslav Kuchta; Kent-André Mardal; Ludmil T. Zikatanov (CoRR, 2022)

A posteriori error estimates of finite element methods by preconditioning - Yuwen Li; Ludmil T. Zikatanov (Comput. Math. Appl., 2021)

Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations - Chunmei Wang; Ludmil T. Zikatanov (J. Comput. Appl. Math., 2021)

Energetic stable discretization for non-isothermal electrokinetics model - Simo Wu; Chun Liu; Ludmil T. Zikatanov (J. Comput. Phys., 2021)

A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations - James H. Adler; Casey Cavanaugh; Xiaozhe Hu; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2021)

A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians - Xiaozhe Hu; Kaiyi Wu; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2021)

New stabilized P\(_1\) exttimesP\(_0\) finite element methods for nearly inviscid and incompressible flows - Yuwen Li; Ludmil T. Zikatanov (CoRR, 2021)

Neural networks with trainable matrix activation functions - Yuwen Li; Zhengqi Liu; Ludmil T. Zikatanov (CoRR, 2021)

An Enriched Galerkin Method for the Stokes Equations - Son-Young Yi; Xiaozhe Hu; Sanghyun Lee; James H. Adler; Ludmil T. Zikatanov (CoRR, 2021)

Auxiliary space preconditioning for mixed finite element discretizations of Richards' equation - Juan Batista; Xiaozhe Hu; Ludmil T. Zikatanov (Comput. Math. Appl., 2020)

Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations - J. H. Adler; Francisco José Gaspar; Xiaozhe Hu; Peter Ohm; Carmen Rodrigo; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2020)

A posteriori error estimates of finite element methods by preconditioning - Yuwen Li; Ludmil T. Zikatanov (CoRR, 2020)

On the unisolvence for the quasi-polynomial spaces of differential forms - Shuonan Wu; Ludmil T. Zikatanov (CoRR, 2020)

A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians - Xiaozhe Hu; Kaiyi Wu; Ludmil T. Zikatanov (CoRR, 2020)

Nodal auxiliary a posteriori error estimates - Yuwen Li; Ludmil T. Zikatanov (CoRR, 2020)

Fast auxiliary space preconditioners on surfaces - Yuwen Li; Ludmil T. Zikatanov (CoRR, 2020)

A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations - James H. Adler; Casey Cavanaugh; Xiaozhe Hu; Ludmil T. Zikatanov (CoRR, 2020)

An Adaptive Multigrid Method Based on Path Cover - Xiaozhe Hu; Junyuan Lin; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2019)

Residual-based a posteriori error estimates of mixed methods in Biot's consolidation model - Yuwen Li; Ludmil T. Zikatanov (CoRR, 2019)

Adaptive aggregation on graphs - Wenfang Xu; Ludmil T. Zikatanov (J. Comput. Appl. Math., 2018)

New Stabilized Discretizations for Poroelasticity Equations - Francisco José Gaspar; Carmen Rodrigo; Xiaozhe Hu; Peter Ohm; James H. Adler; Ludmil T. Zikatanov (Numerical Methods and Applications - 9th International Conference, NMA 2018, Borovets, Bulgaria, August 20-24, 2018, Revised Selected Papers, 2018)

Algebraic multigrid methods - Jinchao Xu; Ludmil T. Zikatanov (Acta Numer., 2017)

Arbitrary dimension convection-diffusion schemes for space-time discretizations - Randolph E. Bank; Panayot S. Vassilevski; Ludmil T. Zikatanov (J. Comput. Appl. Math., 2017)

A nonconforming finite element method for the Biot's consolidation model in poroelasticity - Xiaozhe Hu; Carmen Rodrigo; Francisco José Gaspar; Ludmil T. Zikatanov (J. Comput. Appl. Math., 2017)

A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems - Paola F. Antonietti; Marco Sarti; Marco Verani; Ludmil T. Zikatanov (J. Sci. Comput., 2017)

Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions - J. H. Adler; Xiaozhe Hu; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2017)

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator - Yangqingxiang Wu; Ludmil T. Zikatanov (High Performance Computing in Science and Engineering - Third International Conference, HPCSE 2017, Karolinka, Czech Republic, May 22-25, 2017, Revised Selected Papers, 2017)

Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach - James H. Adler; Ilya Lashuk; Scott P. MacLachlan; Ludmil T. Zikatanov (Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers, 2017)

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations - Qingguo Hong; Johannes Kraus; Jinchao Xu; Ludmil T. Zikatanov (Numerische Mathematik, 2016)

Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications - Johannes K. Kraus; Raytcho D. Lazarov; Maria Lymbery; Svetozar Margenov; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2016)

A finite element framework for some mimetic finite difference discretizations - Carmen Rodrigo; Francisco José Gaspar; Xiaozhe Hu; Ludmil T. Zikatanov (Comput. Math. Appl., 2015)

A two-level method for mimetic finite difference discretizations of elliptic problems - Paola F. Antonietti; Marco Verani; Ludmil T. Zikatanov (Comput. Math. Appl., 2015)

Fast Constrained Image Segmentation Using Optimal Spanning Trees - Stanislav Harizanov; Svetozar Margenov; Ludmil T. Zikatanov (Large-Scale Scientific Computing - 10th International Conference, LSSC 2015, Sozopol, Bulgaria, June 8-12, 2015. Revised Selected Papers, 2015)

A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem - Blanca Ayuso de Dios; Franco Brezzi; L. Donatella Marini; Jinchao Xu; Ludmil T. Zikatanov (J. Sci. Comput., 2014)

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients - Blanca Ayuso de Dios; Michael J. Holst; Yunrong Zhu; Ludmil T. Zikatanov (Math. Comput., 2014)

Commuting projections on graphs - Panayot S. Vassilevski; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2014)

Combined Preconditioning with Applications in Reservoir Simulation - Xiaozhe Hu; Shuhong Wu; Xiao-hui Wu; Jinchao Xu; Chen-Song Zhang; Shiquan Zhang; Ludmil T. Zikatanov (Multiscale Model. Simul., 2013)

Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids - Guozhu Yu; Jinchao Xu; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2013)

Algebraic Multilevel Preconditioners for the Graph Laplacian Based on Matching in Graphs - James J. Brannick; Yao Chen; Johannes Kraus; Ludmil T. Zikatanov (SIAM J. Numer. Anal., 2013)

Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations - J. H. Adler; V. Petkov; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2013)

An Algebraic Multigrid Method Based on Matching in Graphs - James J. Brannick; Yao Chen; Johannes Kraus; Ludmil T. Zikatanov (Domain Decomposition Methods in Science and Engineering XX, 2013)

A Subspace Correction Method for Nearly Singular Linear Elasticity Problems - Erwin Karer; Johannes K. Kraus; Ludmil T. Zikatanov (Domain Decomposition Methods in Science and Engineering XX, 2013)

Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients - Blanca Ayuso de Dios; Michael J. Holst; Yunrong Zhu; Ludmil T. Zikatanov (Domain Decomposition Methods in Science and Engineering XX, 2013)

A Block Solver for the Exponentially Fitted IIPG-0 Method - Blanca Ayuso de Dios; Ariel L. Lombardi; Paola Pietra; Ludmil T. Zikatanov (Domain Decomposition Methods in Science and Engineering XX, 2013)

Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-level Methods - Johannes Kraus; Panayot S. Vassilevski; Ludmil T. Zikatanov (Comput. Methods Appl. Math., 2012)

Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses - Petia T. Boyanova; Ivan Georgiev; Svetozar Margenov; Ludmil T. Zikatanov (Math. Comput. Simul., 2012)

An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching - James J. Brannick; Yao Chen; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2012)

Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids - Robert Scheichl; Panayot S. Vassilevski; Ludmil T. Zikatanov (SIAM J. Numer. Anal., 2012)

First-order system least squares and the energetic variational approach for two-phase flow - J. H. Adler; James J. Brannick; Chun Liu; Thomas A. Manteuffel; Ludmil T. Zikatanov (J. Comput. Phys., 2011)

Weak Approximation Properties of Elliptic Projections with Functional Constraints - Robert Scheichl; Panayot S. Vassilevski; Ludmil T. Zikatanov (Multiscale Model. Simul., 2011)

A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations - Blanca Ayuso de Dios; Ivan Georgiev; Johannes Kraus; Ludmil T. Zikatanov (Numerical Methods and Applications - 7th International Conference, NMA 2010, Borovets, Bulgaria, August 20-24, 2010. Revised Papers, 2010)

Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations - Blanca Ayuso de Dios; Ludmil T. Zikatanov (J. Sci. Comput., 2009)

A sharp convergence estimate for the method of subspace corrections for singular systems of equations - Young-Ju Lee; Jinbiao Wu; Jinchao Xu; Ludmil T. Zikatanov (Math. Comput., 2008)

Uniform convergence of the multigrid V-cycle on graded meshes for corner singularities - James J. Brannick; Hengguang Li; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2008)

Advanced multigrid methods for systems of PDEs - Panayot S. Vassilevski; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2008)

Two-sided bounds on the convergence rate of two-level methods - Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2008)

Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials - Shi Shu; Ivo Babuska; Yingxiong Xiao; Jinchao Xu; Ludmil T. Zikatanov (SIAM J. Sci. Comput., 2008)

A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes - Durkbin Cho; Ludmil T. Zikatanov (J. Num. Math., 2007)

Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations - Veselin Dobrev; Raytcho D. Lazarov; Panayot S. Vassilevski; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2006)

Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid - Panayot S. Vassilevski; Ludmil T. Zikatanov (SIAM J. Matrix Anal. Appl., 2006)

On the Convergence of Iterative Methods for Semidefinite Linear Systems - Young-Ju Lee; Jinbiao Wu; Jinchao Xu; Ludmil T. Zikatanov (SIAM J. Matrix Anal. Appl., 2006)

Partition of unity method on nonmatching grids for the Stokes problem - Constantin Bacuta; Jinru Chen; Yunqing Huang; Jinchao Xu; Ludmil T. Zikatanov (J. Num. Math., 2005)

On two-grid convergence estimates - Robert D. Falgout; Panayot S. Vassilevski; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2005)

Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps - Constantin Bacuta; Victor Nistor; Ludmil T. Zikatanov (Numerische Mathematik, 2005)

Uniformly Convergent Multigrid Methods for Convection-Diffusion Problems without Any Constraint on Coarse Grids - Hwanho Kim; Jinchao Xu; Ludmil T. Zikatanov (Adv. Comput. Math., 2004)

A multigrid method based on graph matching for convection-diffusion equations - Hwanho Kim; Jinchao Xu; Ludmil T. Zikatanov (Numer. Linear Algebra Appl., 2003)

Some observations on Babu\vs\ - Jinchao Xu; Ludmil T. Zikatanov

A monotone finite element scheme for convection-diffusion equations - Jinchao Xu; Ludmil T. Zikatanov (Math. Comput., 1999)

Circulant Block-Factorization Preconditioning of Anisotropic Elliptic Problems - Ivan Lirkov; Svetozar Margenov; Ludmil T. Zikatanov (Computing, 1997)