Ludmil T. Zikatanov

Publication Activity (10 Years)

Years Active: 1997-2024
Publications (10 Years): 46

Top Topics

Error Estimates

Software Components

Partial Differential Equations

Top Venues

Comput. Math. Appl.

SIAM J. Sci. Comput.

J. Comput. Appl. Math.

Publications

Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
Algebraic Multigrid Methods for Metric-Perturbed Coupled Problems. SIAM J. Sci. Comput. 46 (3) (2024)
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco José Gaspar, James H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov
A local Fourier analysis for additive Schwarz smoothers. Comput. Math. Appl. 158 (2024)
James H. Adler, Xiaozhe Hu, Yuwen Li, Ludmil T. Zikatanov
Parameter-free preconditioning for nearly-incompressible linear elasticity. Comput. Math. Appl. 154 (2024)
Álvaro Pé de la Riva, Francisco José Gaspar, Xiaozhe Hu, James H. Adler, Carmen Rodrigo, Ludmil T. Zikatanov
Oscillation-free numerical schemes for Biot's model and their iterative coupling solution. CoRR (2024)
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
Reduced Krylov Basis Methods for Parametric Partial Differential Equations. CoRR (2024)
James H. Adler, Xiaozhe Hu, Yuwen Li, Ludmil T. Zikatanov
Parameter-free preconditioning for nearly-incompressible linear elasticity. CoRR (2023)
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
HAZniCS - Software Components for Multiphysics Problems. ACM Trans. Math. Softw. 49 (4) (2023)
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
A reduced conjugate gradient basis method for fractional diffusion. CoRR (2023)
Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone, Ludmil T. Zikatanov
Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations. Comput. Math. Appl. 144 (2023)
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar, James H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov
A Local Fourier Analysis for Additive Schwarz Smoothers. CoRR (2023)
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
Rational approximation preconditioners for multiphysics problems. CoRR (2022)
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
HAZniCS - Software Components for Multiphysics Problems. CoRR (2022)
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
Rational Approximation Preconditioners for Multiphysics Problems. NMA (2022)
Son-Young Yi, Sanghyun Lee, Ludmil T. Zikatanov
Locking-Free Enriched Galerkin Method for Linear Elasticity. SIAM J. Numer. Anal. 60 (1) (2022)
Yuwen Li, Ludmil T. Zikatanov
A posteriori error estimates of finite element methods by preconditioning. Comput. Math. Appl. 91 (2021)
Simo Wu, Chun Liu, Ludmil T. Zikatanov
Energetic stable discretization for non-isothermal electrokinetics model. J. Comput. Phys. 425 (2021)
Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James H. Adler, Ludmil T. Zikatanov
An Enriched Galerkin Method for the Stokes Equations. CoRR (2021)
Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov
A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians. SIAM J. Sci. Comput. 43 (5) (2021)
Chunmei Wang, Ludmil T. Zikatanov
Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations. J. Comput. Appl. Math. 394 (2021)
Yuwen Li, Ludmil T. Zikatanov
finite element methods for nearly inviscid and incompressible flows. CoRR (2021)
Yuwen Li, Zhengqi Liu, Ludmil T. Zikatanov
Neural networks with trainable matrix activation functions. CoRR (2021)
James H. Adler, Casey Cavanaugh, Xiaozhe Hu, Ludmil T. Zikatanov
A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations. SIAM J. Sci. Comput. 43 (4) (2021)
Yuwen Li, Ludmil T. Zikatanov
Fast auxiliary space preconditioners on surfaces. CoRR (2020)
Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov
A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians. CoRR (2020)
J. H. Adler, Francisco José Gaspar, Xiaozhe Hu, Peter Ohm, Carmen Rodrigo, Ludmil T. Zikatanov
Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations. SIAM J. Sci. Comput. 42 (3) (2020)
Shuonan Wu, Ludmil T. Zikatanov
On the unisolvence for the quasi-polynomial spaces of differential forms. CoRR (2020)
Yuwen Li, Ludmil T. Zikatanov
A posteriori error estimates of finite element methods by preconditioning. CoRR (2020)
James H. Adler, Casey Cavanaugh, Xiaozhe Hu, Ludmil T. Zikatanov
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations. CoRR (2020)
Juan Batista, Xiaozhe Hu, Ludmil T. Zikatanov
Auxiliary space preconditioning for mixed finite element discretizations of Richards' equation. Comput. Math. Appl. 80 (2) (2020)
Yuwen Li, Ludmil T. Zikatanov
Nodal auxiliary a posteriori error estimates. CoRR (2020)
Xiaozhe Hu, Junyuan Lin, Ludmil T. Zikatanov
An Adaptive Multigrid Method Based on Path Cover. SIAM J. Sci. Comput. 41 (5) (2019)
Yuwen Li, Ludmil T. Zikatanov
Residual-based a posteriori error estimates of mixed methods in Biot's consolidation model. CoRR (2019)
Francisco José Gaspar, Carmen Rodrigo, Xiaozhe Hu, Peter Ohm, James H. Adler, Ludmil T. Zikatanov
New Stabilized Discretizations for Poroelasticity Equations. NMA (2018)
Wenfang Xu, Ludmil T. Zikatanov
Adaptive aggregation on graphs. J. Comput. Appl. Math. 340 (2018)
Jinchao Xu, Ludmil T. Zikatanov
Algebraic multigrid methods. Acta Numer. 26 (2017)
J. H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov
Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions. SIAM J. Sci. Comput. 39 (5) (2017)
Paola F. Antonietti, Marco Sarti, Marco Verani, Ludmil T. Zikatanov
A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems. J. Sci. Comput. 70 (2) (2017)
Xiaozhe Hu, Carmen Rodrigo, Francisco José Gaspar, Ludmil T. Zikatanov
A nonconforming finite element method for the Biot's consolidation model in poroelasticity. J. Comput. Appl. Math. 310 (2017)
Yangqingxiang Wu, Ludmil T. Zikatanov
Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator. HPCSE (2017)
James H. Adler, Ilya Lashuk, Scott P. MacLachlan, Ludmil T. Zikatanov
Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach. LSSC (2017)
Randolph E. Bank, Panayot S. Vassilevski, Ludmil T. Zikatanov
Arbitrary dimension convection-diffusion schemes for space-time discretizations. J. Comput. Appl. Math. 310 (2017)
Qingguo Hong, Johannes Kraus, Jinchao Xu, Ludmil T. Zikatanov
A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Numerische Mathematik 132 (1) (2016)
Johannes K. Kraus, Raytcho D. Lazarov, Maria Lymbery, Svetozar Margenov, Ludmil T. Zikatanov
Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications. SIAM J. Sci. Comput. 38 (2) (2016)
Carmen Rodrigo, Francisco José Gaspar, Xiaozhe Hu, Ludmil T. Zikatanov
A finite element framework for some mimetic finite difference discretizations. Comput. Math. Appl. 70 (11) (2015)
Paola F. Antonietti, Marco Verani, Ludmil T. Zikatanov
A two-level method for mimetic finite difference discretizations of elliptic problems. Comput. Math. Appl. 70 (11) (2015)
Stanislav Harizanov, Svetozar Margenov, Ludmil T. Zikatanov
Fast Constrained Image Segmentation Using Optimal Spanning Trees. LSSC (2015)
Panayot S. Vassilevski, Ludmil T. Zikatanov
Commuting projections on graphs. Numer. Linear Algebra Appl. 21 (3) (2014)
Blanca Ayuso de Dios, Franco Brezzi, L. Donatella Marini, Jinchao Xu, Ludmil T. Zikatanov
A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem. J. Sci. Comput. 58 (3) (2014)
Blanca Ayuso de Dios, Michael Holst, Yunrong Zhu, Ludmil T. Zikatanov
Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Math. Comput. 83 (287) (2014)
Xiaozhe Hu, Shuhong Wu, Xiao-hui Wu, Jinchao Xu, Chen-Song Zhang, Shiquan Zhang, Ludmil T. Zikatanov
Combined Preconditioning with Applications in Reservoir Simulation. Multiscale Model. Simul. 11 (2) (2013)
J. H. Adler, V. Petkov, Ludmil T. Zikatanov
Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations. SIAM J. Sci. Comput. 35 (5) (2013)
Guozhu Yu, Jinchao Xu, Ludmil T. Zikatanov
Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. Numer. Linear Algebra Appl. 20 (5) (2013)
James J. Brannick, Yao Chen, Johannes Kraus, Ludmil T. Zikatanov
Algebraic Multilevel Preconditioners for the Graph Laplacian Based on Matching in Graphs. SIAM J. Numer. Anal. 51 (3) (2013)
Robert Scheichl, Panayot S. Vassilevski, Ludmil T. Zikatanov
Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids. SIAM J. Numer. Anal. 50 (3) (2012)
Petia T. Boyanova, Ivan Georgiev, Svetozar Margenov, Ludmil T. Zikatanov
Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses. Math. Comput. Simul. 82 (10) (2012)
James J. Brannick, Yao Chen, Ludmil T. Zikatanov
An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. Numer. Linear Algebra Appl. 19 (2) (2012)
Johannes Kraus, Panayot S. Vassilevski, Ludmil T. Zikatanov
Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-level Methods. Comput. Methods Appl. Math. 12 (4) (2012)
Robert Scheichl, Panayot S. Vassilevski, Ludmil T. Zikatanov
Weak Approximation Properties of Elliptic Projections with Functional Constraints. Multiscale Model. Simul. 9 (4) (2011)
J. H. Adler, James J. Brannick, Chun Liu, Thomas A. Manteuffel, Ludmil T. Zikatanov
First-order system least squares and the energetic variational approach for two-phase flow. J. Comput. Phys. 230 (17) (2011)
Blanca Ayuso de Dios, Ivan Georgiev, Johannes Kraus, Ludmil T. Zikatanov
A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations. NMA (2010)
Blanca Ayuso de Dios, Ludmil T. Zikatanov
Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations. J. Sci. Comput. 40 (1-3) (2009)
Shi Shu, Ivo Babuska, Yingxiong Xiao, Jinchao Xu, Ludmil T. Zikatanov
Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials. SIAM J. Sci. Comput. 31 (1) (2008)
Ludmil T. Zikatanov
Two-sided bounds on the convergence rate of two-level methods. Numer. Linear Algebra Appl. 15 (5) (2008)
Panayot S. Vassilevski, Ludmil T. Zikatanov
Advanced multigrid methods for systems of PDEs. Numer. Linear Algebra Appl. 15 (5) (2008)
James J. Brannick, Hengguang Li, Ludmil T. Zikatanov
-cycle on graded meshes for corner singularities. Numer. Linear Algebra Appl. 15 (2-3) (2008)
Young-Ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil T. Zikatanov
A sharp convergence estimate for the method of subspace corrections for singular systems of equations. Math. Comput. 77 (262) (2008)
Durkbin Cho, Ludmil T. Zikatanov
A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes. J. Num. Math. 15 (3) (2007)
Young-Ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil T. Zikatanov
On the Convergence of Iterative Methods for Semidefinite Linear Systems. SIAM J. Matrix Anal. Appl. 28 (3) (2006)
Panayot S. Vassilevski, Ludmil T. Zikatanov
Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid. SIAM J. Matrix Anal. Appl. 27 (4) (2006)
Veselin Dobrev, Raytcho D. Lazarov, Panayot S. Vassilevski, Ludmil T. Zikatanov
Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Numer. Linear Algebra Appl. 13 (9) (2006)
Robert D. Falgout, Panayot S. Vassilevski, Ludmil T. Zikatanov
On two-grid convergence estimates. Numer. Linear Algebra Appl. 12 (5-6) (2005)
Constantin Bacuta, Victor Nistor, Ludmil T. Zikatanov
Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps. Numerische Mathematik 100 (2) (2005)
Constantin Bacuta, Jinru Chen, Yunqing Huang, Jinchao Xu, Ludmil T. Zikatanov
Partition of unity method on nonmatching grids for the Stokes problem. J. Num. Math. 13 (3) (2005)
Hwanho Kim, Jinchao Xu, Ludmil T. Zikatanov
Uniformly Convergent Multigrid Methods for Convection-Diffusion Problems without Any Constraint on Coarse Grids. Adv. Comput. Math. 20 (4) (2004)
Jinchao Xu, Ludmil T. Zikatanov
Some observations on Babu\vs}ka and Brezzi theories. Numerische Mathematik 94 (1) (2003)
Hwanho Kim, Jinchao Xu, Ludmil T. Zikatanov
A multigrid method based on graph matching for convection-diffusion equations. Numer. Linear Algebra Appl. 10 (1-2) (2003)
Jinchao Xu, Ludmil T. Zikatanov
A monotone finite element scheme for convection-diffusion equations. Math. Comput. 68 (228) (1999)
Ivan Lirkov, Svetozar Margenov, Ludmil T. Zikatanov
Circulant Block-Factorization Preconditioning of Anisotropic Elliptic Problems. Computing 58 (3) (1997)