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

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

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

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

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

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

Weakly Coupled Systems of Eikonal Equations in Path-Planning Problems. - Chiri, Maria Teresa; Czuprynski, Kenneth D.; Zikatanov, Ludmil T. (2024)

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

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

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

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

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

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

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

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

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

Rational Approximation Preconditioners for Multiphysics Problems. - Budisa, Ana; Hu, Xiaozhe; Kuchta, Miroslav; Mardal, Kent-André; Zikatanov, Ludmil T. (2022)

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

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

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

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

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

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

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

New stabilized P1×P0 finite element methods for nearly inviscid and incompressible flows. - Li, Yuwen; Zikatanov, Ludmil T. (CoRR, 2021)

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

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

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

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

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

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

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

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

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

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

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

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

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

New Stabilized Discretizations for Poroelasticity Equations. - Gaspar, Francisco José; Rodrigo, Carmen; Hu, Xiaozhe; Ohm, Peter; Adler, James H.; Zikatanov, Ludmil T. (2018)

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

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

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

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

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

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator. - Wu, Yangqingxiang; Zikatanov, Ludmil T. (2017)

Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach. - Adler, James H.; Lashuk, Ilya; MacLachlan, Scott P.; Zikatanov, Ludmil T. (2017)

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

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

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

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

Fast Constrained Image Segmentation Using Optimal Spanning Trees. - Harizanov, Stanislav; Margenov, Svetozar; Zikatanov, Ludmil T. (2015)

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

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

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

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

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

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

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

An Algebraic Multigrid Method Based on Matching in Graphs. - Brannick, James J.; Chen, Yao; Kraus, Johannes; Zikatanov, Ludmil T. (2013)

A Subspace Correction Method for Nearly Singular Linear Elasticity Problems. - Karer, Erwin; Kraus, Johannes K.; Zikatanov, Ludmil T. (2013)

Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. - Dios, Blanca Ayuso de; Holst, Michael J.; Zhu, Yunrong; Zikatanov, Ludmil T. (2013)

A Block Solver for the Exponentially Fitted IIPG-0 Method. - Dios, Blanca Ayuso de; Lombardi, Ariel L.; Pietra, Paola; Zikatanov, Ludmil T. (2013)

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

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

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

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

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

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

A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations. - Dios, Blanca Ayuso de; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil T. (2010)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Some observations on Babu\vs}ka and Brezzi theories. - Xu, Jinchao; Zikatanov, Ludmil T. (Numerische Mathematik, 2003)

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

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