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ORCIDLudmil T. Zikatanov
Ludmil Tomov Zikatanov
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- affiliation: Penn State, University Park, USA
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Journal Articles
- 2025
[j58]Yuwen Li
, Ludmil T. Zikatanov, Cheng Zuo:
Reduced Krylov Basis Methods for Parametric Partial Differential Equations. SIAM J. Numer. Anal. 63(2): 976-999 (2025)- [j57]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. SIAM J. Sci. Comput. 47(3): 1809- (2025) - 2024
- [j56]James H. Adler, Xiaozhe Hu, Yuwen Li, Ludmil T. Zikatanov:
Parameter-free preconditioning for nearly-incompressible linear elasticity. Comput. Math. Appl. 154: 39-44 (2024) - [j55]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: 13-20 (2024) - [j54]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): 1461- (2024) - [j53]Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo:
A Reduced Conjugate Gradient Basis Method for Fractional Diffusion. SIAM J. Sci. Comput. 46(5): S68-S87 (2024) - 2023
- [j52]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: 290-305 (2023) - [j51]Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov:
HAZniCS - Software Components for Multiphysics Problems. ACM Trans. Math. Softw. 49(4): 36:1-36:23 (2023) - 2022
- [j50]Son-Young Yi, Sanghyun Lee, Ludmil T. Zikatanov:
Locking-Free Enriched Galerkin Method for Linear Elasticity. SIAM J. Numer. Anal. 60(1): 52-75 (2022) - 2021
- [j49]Yuwen Li, Ludmil T. Zikatanov:
A posteriori error estimates of finite element methods by preconditioning. Comput. Math. Appl. 91: 192-201 (2021) - [j48]Chunmei Wang, Ludmil T. Zikatanov:
Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations. J. Comput. Appl. Math. 394: 113543 (2021) - [j47]Simo Wu, Chun Liu, Ludmil T. Zikatanov:
Energetic stable discretization for non-isothermal electrokinetics model. J. Comput. Phys. 425: 109889 (2021) - [j46]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): A2638-A2659 (2021) - [j45]Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov:
A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians. SIAM J. Sci. Comput. 43(5): S727-S742 (2021) - 2020
- [j44]Juan Batista, Xiaozhe Hu, Ludmil T. Zikatanov:
Auxiliary space preconditioning for mixed finite element discretizations of Richards' equation. Comput. Math. Appl. 80(2): 405-416 (2020) - [j43]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): B761-B791 (2020) - 2019
- [j42]Xiaozhe Hu, Junyuan Lin, Ludmil T. Zikatanov:
An Adaptive Multigrid Method Based on Path Cover. SIAM J. Sci. Comput. 41(5): S220-S241 (2019) - 2018
- [j41]Wenfang Xu, Ludmil T. Zikatanov:
Adaptive aggregation on graphs. J. Comput. Appl. Math. 340: 718-730 (2018) - 2017
- [j40]Jinchao Xu, Ludmil T. Zikatanov:
Algebraic multigrid methods. Acta Numer. 26: 591-721 (2017) - [j39]Randolph E. Bank, Panayot S. Vassilevski, Ludmil T. Zikatanov:
Arbitrary dimension convection-diffusion schemes for space-time discretizations. J. Comput. Appl. Math. 310: 19-31 (2017) - [j38]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: 143-154 (2017) - [j37]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): 608-630 (2017) - [j36]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) - 2016
- [j35]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): 23-49 (2016) - [j34]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) - 2015
- [j33]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): 2661-2673 (2015) - [j32]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): 2674-2687 (2015) - 2014
- [j31]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): 517-547 (2014) - [j30]Blanca Ayuso de Dios, Michael J. Holst, Yunrong Zhu, Ludmil T. Zikatanov:
Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Math. Comput. 83(287): 1083-1120 (2014) - [j29]Panayot S. Vassilevski, Ludmil T. Zikatanov:
Commuting projections on graphs. Numer. Linear Algebra Appl. 21(3): 297-315 (2014) - 2013
- [j28]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): 507-521 (2013) - [j27]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): 832-851 (2013) - [j26]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): 1805-1827 (2013) - [j25]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) - 2012
- [j24]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): 448-468 (2012) - [j23]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): 1964-1971 (2012) - [j22]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): 279-295 (2012) - [j21]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): 1675-1694 (2012) - 2011
- [j20]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): 6647-6663 (2011) - [j19]Robert Scheichl, Panayot S. Vassilevski, Ludmil T. Zikatanov:
Weak Approximation Properties of Elliptic Projections with Functional Constraints. Multiscale Model. Simul. 9(4): 1677-1699 (2011) - 2009
- [j18]Blanca Ayuso de Dios, Ludmil T. Zikatanov:
Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations. J. Sci. Comput. 40(1-3): 4-36 (2009) - 2008
- [j17]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): 831-850 (2008) - [j16]James J. Brannick, Hengguang Li, Ludmil T. Zikatanov:
Uniform convergence of the multigrid V-cycle on graded meshes for corner singularities. Numer. Linear Algebra Appl. 15(2-3): 291-306 (2008) - [j15]Panayot S. Vassilevski, Ludmil T. Zikatanov:
Advanced multigrid methods for systems of PDEs. Numer. Linear Algebra Appl. 15(5): 393 (2008) - [j14]Ludmil T. Zikatanov:
Two-sided bounds on the convergence rate of two-level methods. Numer. Linear Algebra Appl. 15(5): 439-454 (2008) - [j13]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): 687-707 (2008) - 2007
- [j12]Durkbin Cho, Ludmil T. Zikatanov:
A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes. J. Num. Math. 15(3): 163-180 (2007) - 2006
- [j11]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): 753-770 (2006) - [j10]Panayot S. Vassilevski, Ludmil T. Zikatanov:
Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid. SIAM J. Matrix Anal. Appl. 27(4): 1040-1055 (2006) - [j9]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): 634-641 (2006) - 2005
- [j8]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): 157-169 (2005) - [j7]Robert D. Falgout, Panayot S. Vassilevski, Ludmil T. Zikatanov:
On two-grid convergence estimates. Numer. Linear Algebra Appl. 12(5-6): 471-494 (2005) - [j6]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): 165-184 (2005) - 2004
- [j5]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): 385-399 (2004) - 2003
- [j4]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): 181-195 (2003) - [j3]Jinchao Xu, Ludmil T. Zikatanov:
Some observations on Babu\vs}ka and Brezzi theories. Numerische Mathematik 94(1): 195-202 (2003) - 1999
- [j2]Jinchao Xu, Ludmil T. Zikatanov:
A monotone finite element scheme for convection-diffusion equations. Math. Comput. 68(228): 1429-1446 (1999) - 1997
- [j1]Ivan Lirkov, Svetozar Margenov, Ludmil T. Zikatanov:
Circulant Block-Factorization Preconditioning of Anisotropic Elliptic Problems. Computing 58(3): 245-258 (1997)
Conference and Workshop Papers
- 2024
- [c7]Maria Teresa Chiri, Kenneth D. Czuprynski, Ludmil T. Zikatanov:
Weakly Coupled Systems of Eikonal Equations in Path-Planning Problems. ACC 2024: 5036-5041 - 2022
- [c6]Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov:
Rational Approximation Preconditioners for Multiphysics Problems. NMA 2022: 100-113 - 2018
- [c5]Francisco José Gaspar, Carmen Rodrigo, Xiaozhe Hu, Peter Ohm, James H. Adler, Ludmil T. Zikatanov:
New Stabilized Discretizations for Poroelasticity Equations. NMA 2018: 3-14 - 2017
- [c4]Yangqingxiang Wu, Ludmil T. Zikatanov:
Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator. HPCSE 2017: 34-46 - [c3]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: 3-20 - 2015
- [c2]Stanislav Harizanov, Svetozar Margenov, Ludmil T. Zikatanov:
Fast Constrained Image Segmentation Using Optimal Spanning Trees. LSSC 2015: 15-29 - 2010
- [c1]Blanca Ayuso de Dios, Ivan Georgiev, Johannes Kraus, Ludmil T. Zikatanov:
A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations. NMA 2010: 353-360
Parts in Books or Collections
- 2013
- [p4]James J. Brannick, Yao Chen, Johannes Kraus, Ludmil T. Zikatanov:
An Algebraic Multigrid Method Based on Matching in Graphs. Domain Decomposition Methods in Science and Engineering XX 2013: 143-150 - [p3]Erwin Karer, Johannes K. Kraus, Ludmil T. Zikatanov:
A Subspace Correction Method for Nearly Singular Linear Elasticity Problems. Domain Decomposition Methods in Science and Engineering XX 2013: 159-166 - [p2]Blanca Ayuso de Dios, Michael J. Holst, Yunrong Zhu, Ludmil T. Zikatanov:
Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. Domain Decomposition Methods in Science and Engineering XX 2013: 183-190 - [p1]Blanca Ayuso de Dios, Ariel L. Lombardi, Paola Pietra, Ludmil T. Zikatanov:
A Block Solver for the Exponentially Fitted IIPG-0 Method. Domain Decomposition Methods in Science and Engineering XX 2013: 239-246
Informal and Other Publications
- 2024
- [i18]Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo:
Reduced Krylov Basis Methods for Parametric Partial Differential Equations. CoRR abs/2405.07139 (2024) - [i17]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 abs/2407.19599 (2024) - 2023
- [i16]James H. Adler, Xiaozhe Hu, Yuwen Li, Ludmil T. Zikatanov:
Parameter-free preconditioning for nearly-incompressible linear elasticity. CoRR abs/2304.00103 (2023) - [i15]Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil Tomov Zikatanov:
Algebraic multigrid methods for metric-perturbed coupled problems. CoRR abs/2305.06073 (2023) - [i14]Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo:
A reduced conjugate gradient basis method for fractional diffusion. CoRR abs/2305.18038 (2023) - [i13]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. CoRR abs/2310.09381 (2023) - 2022
- [i12]Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov:
Rational approximation preconditioners for multiphysics problems. CoRR abs/2209.11659 (2022) - [i11]Ana Budisa, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov:
HAZniCS - Software Components for Multiphysics Problems. CoRR abs/2210.13274 (2022) - 2021
- [i10]Yuwen Li, Ludmil T. Zikatanov:
New stabilized P1×P0 finite element methods for nearly inviscid and incompressible flows. CoRR abs/2109.04013 (2021) - [i9]Yuwen Li, Zhengqi Liu, Ludmil T. Zikatanov:
Neural networks with trainable matrix activation functions. CoRR abs/2109.09948 (2021) - [i8]Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James H. Adler, Ludmil T. Zikatanov:
An Enriched Galerkin Method for the Stokes Equations. CoRR abs/2110.05310 (2021) - 2020
- [i7]Yuwen Li, Ludmil T. Zikatanov:
A posteriori error estimates of finite element methods by preconditioning. CoRR abs/2002.06697 (2020) - [i6]Shuonan Wu, Ludmil T. Zikatanov:
On the unisolvence for the quasi-polynomial spaces of differential forms. CoRR abs/2003.14278 (2020) - [i5]Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov:
A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians. CoRR abs/2007.00189 (2020) - [i4]Yuwen Li, Ludmil T. Zikatanov:
Nodal auxiliary a posteriori error estimates. CoRR abs/2010.06774 (2020) - [i3]Yuwen Li, Ludmil T. Zikatanov:
Fast auxiliary space preconditioners on surfaces. CoRR abs/2011.13502 (2020) - [i2]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 abs/2012.03148 (2020) - 2019
- [i1]Yuwen Li, Ludmil T. Zikatanov:
Residual-based a posteriori error estimates of mixed methods in Biot's consolidation model. CoRR abs/1911.08692 (2019)
Coauthor Index
J. H. Adler
aka: James H. Adler
aka: James H. Adler
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