Edit Profile (opens in new tab) Zikatanov, Ludmil T. Compute Distance To: Compute Author ID: zikatanov.ludmil-t Published as: Zikatanov, Ludmil; Zikatanov, Ludmil T.; Zikatanov, L. T.; Zikatanov, L. more...less Homepage: http://www.personal.psu.edu/ltz1/ External Links: MGP · ORCID · Math-Net.Ru · dblp Documents Indexed: 87 Publications since 1992 1 Contribution as Editor Co-Authors: 71 Co-Authors with 86 Joint Publications 2,201 Co-Co-Authors all top 5 Co-Authors 2 single-authored 23 Xu, Jinchao 17 Hu, Xiaozhe 10 Vassilevski, Panayot Spirov 9 Adler, James H. 8 Gaspar, Francisco José 8 Rodrigo, Carmen 6 Brannick, James J. 6 Kraus, Johannes K. 6 Margenov, Svetozar D. 5 Ayuso de Dios, Blanca 5 Bacuta, Constantin 5 Urschel, John C. 4 Lee, Youngju 4 Nistor, Victor 4 Wu, Jinbiao 3 Chen, Yao 3 Georgiev, Ivan 3 Lazarov, Raytcho D. 3 Li, Yuwen 3 Liu, Chun 3 Ohm, Peter 2 Antonietti, Paola Francesca 2 Ayuso, Blanca 2 Cho, Durkbin 2 Deutsch, Frank 2 Dobrev, Veselin A. 2 Hundal, Hein S. 2 Kim, Hwanho 2 MacLachlan, Scott P. 2 Scheichl, Robert 2 Shu, Shi 2 Verani, Marco 2 Xiao, Yingxiong 1 Babuška, Ivo 1 Bank, Randolph E. 1 Batista, Juan 1 Boyanova, Petia 1 Brezzi, Franco 1 Cavanaugh, Casey 1 Chan, Tony Fan-Cheong 1 Falgout, Robert D. 1 Frommer, Andreas 1 Georgiev, Asen 1 Harizanov, Stanislav 1 Holst, Michael J. 1 Hong, Qingguo 1 Huang, Yunqing 1 Iliev, Oleg P. 1 Lashuk, Ilya V. 1 Lee, Sanghyun 1 Li, Hengguang 1 Lin, Junyuan 1 Lirkov, Ivan D. 1 Lymbery, Maria 1 Manteuffel, Thomas A. 1 Marini, Luisa Donatella 1 Mazzucato, Anna L. 1 Minev, Peter Dimitrov 1 Petkov, Vesselin M. 1 Ryham, Rolf J. 1 Sarti, Marco 1 Wang, Chunmei 1 Wu, Kaiyi 1 Wu, Shuhong 1 Wu, Simo 1 Wu, Xiaohui 1 Xu, Wenfang 1 Yu, Guozhu 1 Zhang, Chensong 1 Zhang, Shiquan 1 Zhu, Yunrong all top 5 Serials 8 SIAM Journal on Scientific Computing 8 Numerical Linear Algebra with Applications 4 Computers & Mathematics with Applications 4 Journal of Computational and Applied Mathematics 3 Computer Methods in Applied Mechanics and Engineering 3 Mathematics of Computation 3 Numerische Mathematik 3 SIAM Journal on Numerical Analysis 3 Journal of Computational Mathematics 3 Journal of Scientific Computing 2 Journal of Computational Physics 2 Linear and Multilinear Algebra 2 Numerical Functional Analysis and Optimization 2 SIAM Journal on Matrix Analysis and Applications 2 Linear Algebra and its Applications 2 Journal of Numerical Mathematics 2 Multiscale Modeling & Simulation 1 IMA Journal of Numerical Analysis 1 Computing 1 Mathematics and Computers in Simulation 1 Journal of the American Mathematical Society 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Documenta Mathematica 1 Computing and Visualization in Science 1 Matematicheskoe Modelirovanie 1 Discrete and Continuous Dynamical Systems. Series B 1 Computational Methods in Applied Mathematics 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Numerical Mathematics: Theory, Methods and Applications 1 Springer Proceedings in Mathematics & Statistics 1 Research in the Mathematical Sciences 1 Applied Analysis and Optimization all top 5 Fields 76 Numerical analysis (65-XX) 39 Partial differential equations (35-XX) 15 Mechanics of deformable solids (74-XX) 14 Fluid mechanics (76-XX) 8 Combinatorics (05-XX) 4 Optics, electromagnetic theory (78-XX) 3 Convex and discrete geometry (52-XX) 3 Computer science (68-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 66 Publications have been cited 1,062 times in 752 Documents Cited by ▼ Year ▼ The method of alternating projections and the method of subspace corrections in Hilbert space. Zbl 0999.47015Xu, Jinchao; Zikatanov, Ludmil 108 2002 A monotone finite element scheme for convection-diffusion equations. Zbl 0931.65111Xu, Jinchao; Zikatanov, Ludmil 93 1999 Some observations on Babuška and Brezzi theories. Zbl 1028.65115Xu, Jinchao; Zikatanov, Ludmil 84 2003 Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps. Zbl 1116.65119Băcuţă, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 50 2005 Algebraic multigrid methods. Zbl 1378.65182Xu, Jinchao; Zikatanov, Ludmil 42 2017 A nonconforming finite element method for the Biot’s consolidation model in poroelasticity. Zbl 1381.76175Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 38 2017 Improving the rate of convergence of high-order finite elements on polyhedra. I: A priori estimates. Zbl 1121.35031Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 37 2005 Stability and monotonicity for some discretizations of the Biot’s consolidation model. Zbl 1425.74164Rodrigo, C.; Gaspar, F. J.; Hu, X.; Zikatanov, L. T. 36 2016 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 33 2005 Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Zbl 1224.65263Dobrev, Veselin A.; Lazarov, Raytcho D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 32 2006 An agglomeration multigrid method for unstructured grids. Zbl 0909.65102Chan, Tony F.; Xu, Jinchao; Zikatanov, Ludmil 26 1998 Interface and mixed boundary value problems on \(n\)-dimensional polyhedral domains. Zbl 1207.35117Bacuta, C.; Mazzucato, A. L.; Nistor, V.; Zikatanov, L. 24 2010 Robust subspace correction methods for nearly singular systems. Zbl 1151.65096Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 24 2007 On an energy minimizing basis for algebraic multigrid methods. Zbl 1077.65130Xu, Jinchao; Zikatanov, Ludmil 23 2004 New stabilized discretizations for poroelasticity and the Stokes’ equations. Zbl 1440.76027Rodrigo, C.; Hu, X.; Ohm, P.; Adler, J. H.; Gaspar, F. J.; Zikatanov, L. T. 23 2018 A multigrid method based on graph matching for convection-diffusion equations. Zbl 1071.65167Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil 20 2003 Improving the rate of convergence of high-order finite elements on polyhedra. II: mesh refinements and interpolation. Zbl 1122.65109Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 19 2007 Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil 19 2007 Uniformly convergent iterative methods for discontinuous Galerkin discretizations. Zbl 1203.65242Ayuso de Dios, Blanca; Zikatanov, Ludmil 18 2009 A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Zbl 1338.76054Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil 15 2016 Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Zbl 1296.65153Ayuso De Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil 15 2014 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 14 2017 Uniform convergence of the multigrid \(V\)-cycle on graded meshes for corner singularities. Zbl 1212.65482Brannick, J. J.; Li, Hengguang; Zikatanov, L. T. 13 2008 A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. Zbl 1299.76128Ayuso De Dios, Blanca; Brezzi, Franco; Marini, L. Donatella; Xu, Jinchao; Zikatanov, Ludmil 13 2014 On the convergence of iterative methods for semidefinite linear systems. Zbl 1122.65033Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 13 2006 Two-sided bounds on the convergence rate of two-level methods. Zbl 1212.65503Zikatanov, L. T. 12 2008 Preconditioning heterogeneous \(\boldsymbol{H}(\mathrm{div})\) problems by additive Schur complement approximation and applications. Zbl 1380.65376Kraus, Johannes; Lazarov, Raytcho; Lymbery, Maria; Margenov, Svetozar; Zikatanov, Ludmil 12 2016 A sharp convergence estimate for the method of subspace corrections for singular systems of equations. Zbl 1137.65058Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 12 2008 Robust preconditioners for a new stabilized discretization of the poroelastic equations. Zbl 1448.65145Adler, J. H.; Gaspar, F. J.; Hu, X.; Ohm, P.; Rodrigo, C.; Zikatanov, L. T. 12 2020 Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids. Zbl 1259.65190Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 12 2012 Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. Zbl 1284.65052Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil 12 2012 Weak approximation properties of elliptic projections with functional constraints. Zbl 1244.65215Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 10 2011 Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. Zbl 1281.65152Brannick, J.; Chen, Y.; Kraus, J.; Zikatanov, L. 9 2013 Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs. Zbl 1275.65084Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil 9 2013 Robust block preconditioners for Biot’s model. Zbl 1442.65342Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil T. 9 2018 A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems. Zbl 1381.65091Antonietti, Paola F.; Sarti, Marco; Verani, Marco; Zikatanov, Ludmil T. 8 2017 New estimates for the rate of convergence of the method of subspace corrections. Zbl 1174.65354Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil 8 2008 Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. Zbl 1205.65321Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L. 7 2010 On multigrid methods for generalized finite element methods. Zbl 1012.65131Xu, Jinchao; Zikatanov, Ludmil T. 6 2002 Robust solvers for Maxwell’s equations with dissipative boundary conditions. Zbl 1395.65067Adler, J. H.; Hu, X.; Zikatanov, L. T. 6 2017 A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians. Zbl 1340.65262Urschel, John C.; Xu, Jinchao; Hu, Xiaozhe; Zikatanov, Ludmil T. 6 2015 An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. Zbl 1274.65314Brannick, James; Chen, Yao; Zikatanov, Ludmil 6 2012 A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. Zbl 1311.74108Ayuso De Dios, Blanca; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil 6 2013 Spectral bisection of graphs and connectedness. Zbl 1286.05101Urschel, John C.; Zikatanov, Ludmil T. 6 2014 Combined preconditioning with applications in reservoir simulation. Zbl 1426.76269Hu, Xiaozhe; Wu, Shuhong; Wu, Xiao-Hui; Xu, Jinchao; Zhang, Chen-Song; Zhang, Shiquan; Zikatanov, Ludmil 6 2013 Uniformly convergent multigrid methods for convection–diffusion problems without any constraint on coarse grids. Zbl 1039.65090Kim, Hwanho; Xu, Jinchao; Zikatanov, Ludmil 5 2004 A multilevel precondition for generalized finite element method problems on unstructured simplicial meshes. Zbl 1156.65095Cho, D.; Zikatanov, L. 5 2007 First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L. 4 2011 Multiple vector preserving interpolation mappings in algebraic multigrid. Zbl 1102.65040Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2006 On the validity of the local Fourier analysis. Zbl 1449.65374Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 4 2019 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 Numerical approximation of asymptotically disappearing solutions of Maxwell’s equations. Zbl 1285.65075Adler, J. H.; Petkov, V.; Zikatanov, L. T. 4 2013 On the maximal error of spectral approximation of graph bisection. Zbl 1352.05120Urschel, John C.; Zikatanov, Ludmil T. 3 2016 Partition of unity method on nonmatching grids for the Stokes problem. Zbl 1148.76305Bacuta, C.; Chen, J.; Huang, Y.; Xu, J.; Zikatanov, L. 3 2005 Predictioning of symmetric interior penalty discontinuous Galerkin FEM for elliptic problems. Zbl 1267.65194Dobrev, Veselin A.; Lazarov, Raytcho D.; Zikatanov, Ludmil T. 3 2008 An adaptive multigrid method based on path cover. Zbl 1428.65106Hu, Xiaozhe; Lin, Junyuan; Zikatanov, Ludmil T. 3 2019 Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. Zbl 1313.65324Yu, Guozhu; Xu, Jinchao; Zikatanov, Ludmil T. 2 2013 Circulant block-factorization preconditioning of anisotropic elliptic problems. Zbl 0879.65022Lirkov, I. D.; Margenov, S. D.; Zikatanov, L. T. 2 1997 Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations. Zbl 1467.65114Wang, Chunmei; Zikatanov, Ludmil 2 2021 A finite element framework for some mimetic finite difference discretizations. Zbl 1443.65285Rodrigo, Carmen; Gaspar, F. J.; Hu, X.; Zikatanov, L. 2 2015 Adaptive aggregation on graphs. Zbl 1432.65178Xu, Wenfang; Zikatanov, Ludmil T. 1 2018 Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses. Zbl 1258.65096Boyanova, P.; Georgiev, I.; Margenov, S.; Zikatanov, L. 1 2012 Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation. Zbl 1446.65106Batista, Juan; Hu, Xiaozhe; Zikatanov, Ludmil T. 1 2020 Convergence analysis of iterative methods for semidefinite systems. Zbl 1174.65013Wu, Jinbiao; Lee, Youngju; Xu, Jinchao; Zikatanov, Ludmil 1 2008 New stabilized discretizations for poroelasticity equations. Zbl 1422.65256Gaspar, Francisco J.; Rodrigo, Carmen; Hu, Xiaozhe; Ohm, Peter; Adler, James; Zikatanov, Ludmil 1 2019 On the approximation of Laplacian eigenvalues in graph disaggregation. Zbl 1369.05135Hu, Xiaozhe; Urschel, John C.; Zikatanov, Ludmil T. 1 2017 Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations. Zbl 1467.65114Wang, Chunmei; Zikatanov, Ludmil 2 2021 Robust preconditioners for a new stabilized discretization of the poroelastic equations. Zbl 1448.65145Adler, J. H.; Gaspar, F. J.; Hu, X.; Ohm, P.; Rodrigo, C.; Zikatanov, L. T. 12 2020 Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation. Zbl 1446.65106Batista, Juan; Hu, Xiaozhe; Zikatanov, Ludmil T. 1 2020 On the validity of the local Fourier analysis. Zbl 1449.65374Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 4 2019 An adaptive multigrid method based on path cover. Zbl 1428.65106Hu, Xiaozhe; Lin, Junyuan; Zikatanov, Ludmil T. 3 2019 New stabilized discretizations for poroelasticity equations. Zbl 1422.65256Gaspar, Francisco J.; Rodrigo, Carmen; Hu, Xiaozhe; Ohm, Peter; Adler, James; Zikatanov, Ludmil 1 2019 New stabilized discretizations for poroelasticity and the Stokes’ equations. Zbl 1440.76027Rodrigo, C.; Hu, X.; Ohm, P.; Adler, J. H.; Gaspar, F. J.; Zikatanov, L. T. 23 2018 Robust block preconditioners for Biot’s model. Zbl 1442.65342Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil T. 9 2018 Adaptive aggregation on graphs. Zbl 1432.65178Xu, Wenfang; Zikatanov, Ludmil T. 1 2018 Algebraic multigrid methods. Zbl 1378.65182Xu, Jinchao; Zikatanov, Ludmil 42 2017 A nonconforming finite element method for the Biot’s consolidation model in poroelasticity. Zbl 1381.76175Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 38 2017 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 14 2017 A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems. Zbl 1381.65091Antonietti, Paola F.; Sarti, Marco; Verani, Marco; Zikatanov, Ludmil T. 8 2017 Robust solvers for Maxwell’s equations with dissipative boundary conditions. Zbl 1395.65067Adler, J. H.; Hu, X.; Zikatanov, L. T. 6 2017 On the approximation of Laplacian eigenvalues in graph disaggregation. Zbl 1369.05135Hu, Xiaozhe; Urschel, John C.; Zikatanov, Ludmil T. 1 2017 Stability and monotonicity for some discretizations of the Biot’s consolidation model. Zbl 1425.74164Rodrigo, C.; Gaspar, F. J.; Hu, X.; Zikatanov, L. T. 36 2016 A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Zbl 1338.76054Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil 15 2016 Preconditioning heterogeneous \(\boldsymbol{H}(\mathrm{div})\) problems by additive Schur complement approximation and applications. Zbl 1380.65376Kraus, Johannes; Lazarov, Raytcho; Lymbery, Maria; Margenov, Svetozar; Zikatanov, Ludmil 12 2016 On the maximal error of spectral approximation of graph bisection. Zbl 1352.05120Urschel, John C.; Zikatanov, Ludmil T. 3 2016 A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians. Zbl 1340.65262Urschel, John C.; Xu, Jinchao; Hu, Xiaozhe; Zikatanov, Ludmil T. 6 2015 A finite element framework for some mimetic finite difference discretizations. Zbl 1443.65285Rodrigo, Carmen; Gaspar, F. J.; Hu, X.; Zikatanov, L. 2 2015 Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Zbl 1296.65153Ayuso De Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil 15 2014 A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. Zbl 1299.76128Ayuso De Dios, Blanca; Brezzi, Franco; Marini, L. Donatella; Xu, Jinchao; Zikatanov, Ludmil 13 2014 Spectral bisection of graphs and connectedness. Zbl 1286.05101Urschel, John C.; Zikatanov, Ludmil T. 6 2014 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. Zbl 1281.65152Brannick, J.; Chen, Y.; Kraus, J.; Zikatanov, L. 9 2013 Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs. Zbl 1275.65084Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil 9 2013 A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. Zbl 1311.74108Ayuso De Dios, Blanca; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil 6 2013 Combined preconditioning with applications in reservoir simulation. Zbl 1426.76269Hu, Xiaozhe; Wu, Shuhong; Wu, Xiao-Hui; Xu, Jinchao; Zhang, Chen-Song; Zhang, Shiquan; Zikatanov, Ludmil 6 2013 Numerical approximation of asymptotically disappearing solutions of Maxwell’s equations. Zbl 1285.65075Adler, J. H.; Petkov, V.; Zikatanov, L. T. 4 2013 Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. Zbl 1313.65324Yu, Guozhu; Xu, Jinchao; Zikatanov, Ludmil T. 2 2013 Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids. Zbl 1259.65190Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 12 2012 Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. Zbl 1284.65052Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil 12 2012 An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. Zbl 1274.65314Brannick, James; Chen, Yao; Zikatanov, Ludmil 6 2012 Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses. Zbl 1258.65096Boyanova, P.; Georgiev, I.; Margenov, S.; Zikatanov, L. 1 2012 Weak approximation properties of elliptic projections with functional constraints. Zbl 1244.65215Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 10 2011 First-order system least squares and the energetic variational approach for two-phase flow. Zbl 1408.76528Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L. 4 2011 Interface and mixed boundary value problems on \(n\)-dimensional polyhedral domains. Zbl 1207.35117Bacuta, C.; Mazzucato, A. L.; Nistor, V.; Zikatanov, L. 24 2010 Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. Zbl 1205.65321Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L. 7 2010 Uniformly convergent iterative methods for discontinuous Galerkin discretizations. Zbl 1203.65242Ayuso de Dios, Blanca; Zikatanov, Ludmil 18 2009 Uniform convergence of the multigrid \(V\)-cycle on graded meshes for corner singularities. Zbl 1212.65482Brannick, J. J.; Li, Hengguang; Zikatanov, L. T. 13 2008 Two-sided bounds on the convergence rate of two-level methods. Zbl 1212.65503Zikatanov, L. T. 12 2008 A sharp convergence estimate for the method of subspace corrections for singular systems of equations. Zbl 1137.65058Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 12 2008 New estimates for the rate of convergence of the method of subspace corrections. Zbl 1174.65354Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil 8 2008 Predictioning of symmetric interior penalty discontinuous Galerkin FEM for elliptic problems. Zbl 1267.65194Dobrev, Veselin A.; Lazarov, Raytcho D.; Zikatanov, Ludmil T. 3 2008 Convergence analysis of iterative methods for semidefinite systems. Zbl 1174.65013Wu, Jinbiao; Lee, Youngju; Xu, Jinchao; Zikatanov, Ludmil 1 2008 Robust subspace correction methods for nearly singular systems. Zbl 1151.65096Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 24 2007 Improving the rate of convergence of high-order finite elements on polyhedra. II: mesh refinements and interpolation. Zbl 1122.65109Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 19 2007 Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil 19 2007 A multilevel precondition for generalized finite element method problems on unstructured simplicial meshes. Zbl 1156.65095Cho, D.; Zikatanov, L. 5 2007 Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Zbl 1224.65263Dobrev, Veselin A.; Lazarov, Raytcho D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 32 2006 On the convergence of iterative methods for semidefinite linear systems. Zbl 1122.65033Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 13 2006 Multiple vector preserving interpolation mappings in algebraic multigrid. Zbl 1102.65040Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2006 Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps. Zbl 1116.65119Băcuţă, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 50 2005 Improving the rate of convergence of high-order finite elements on polyhedra. I: A priori estimates. Zbl 1121.35031Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. 37 2005 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 33 2005 Partition of unity method on nonmatching grids for the Stokes problem. Zbl 1148.76305Bacuta, C.; Chen, J.; Huang, Y.; Xu, J.; Zikatanov, L. 3 2005 On an energy minimizing basis for algebraic multigrid methods. Zbl 1077.65130Xu, Jinchao; Zikatanov, Ludmil 23 2004 Uniformly convergent multigrid methods for convection–diffusion problems without any constraint on coarse grids. Zbl 1039.65090Kim, Hwanho; Xu, Jinchao; Zikatanov, Ludmil 5 2004 Some observations on Babuška and Brezzi theories. Zbl 1028.65115Xu, Jinchao; Zikatanov, Ludmil 84 2003 A multigrid method based on graph matching for convection-diffusion equations. Zbl 1071.65167Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil 20 2003 The method of alternating projections and the method of subspace corrections in Hilbert space. Zbl 0999.47015Xu, Jinchao; Zikatanov, Ludmil 108 2002 On multigrid methods for generalized finite element methods. Zbl 1012.65131Xu, Jinchao; Zikatanov, Ludmil T. 6 2002 A monotone finite element scheme for convection-diffusion equations. Zbl 0931.65111Xu, Jinchao; Zikatanov, Ludmil 93 1999 An agglomeration multigrid method for unstructured grids. Zbl 0909.65102Chan, Tony F.; Xu, Jinchao; Zikatanov, Ludmil 26 1998 Circulant block-factorization preconditioning of anisotropic elliptic problems. Zbl 0879.65022Lirkov, I. D.; Margenov, S. D.; Zikatanov, L. T. 2 1997 all cited Publications top 5 cited Publications all top 5 Cited by 1,069 Authors 39 Xu, Jinchao 35 Zikatanov, Ludmil T. 21 Hu, Xiaozhe 21 Li, Hengguang 18 Nistor, Victor 18 Vassilevski, Panayot Spirov 17 Brenner, Susanne Cecelia 14 Bacuta, Constantin 14 Kraus, Johannes K. 13 Shu, Shi 13 Zhang, Zhimin 11 Antonietti, Paola Francesca 11 Castelletto, Nicola 10 Ferronato, Massimiliano 10 Lee, Youngju 9 He, Wenming 9 Hong, Qingguo 9 Scheichl, Robert 9 Schwab, Christoph 8 Chen, Long 8 Lymbery, Maria 8 Margenov, Svetozar D. 8 Rodrigo, Carmen 8 Sacco, Riccardo 8 Zou, Qingsong 7 Adler, James H. 7 Burman, Erik 7 Cui, Jintao 7 Galvis, Juan 7 Gaspar, Francisco José 7 Langer, Ulrich 7 Liu, Chun 7 Needell, Deanna 7 Wheeler, Mary Fanett 7 White, Joshua A. 7 Zhang, Chensong 6 Franceschini, Andrea 6 Frigo, Matteo 6 Lazarov, Raytcho D. 6 MacLachlan, Scott P. 6 Manteuffel, Thomas A. 6 Nicaise, Serge 6 Veeser, Andreas 5 Barrenechea, Gabriel R. 5 Kahl, Karsten 5 Korotov, Sergey 5 Kumar, Kundan 5 Mardal, Kent-Andre 5 Nochetto, Ricardo Horacio 5 Nordbotten, Jan Martin 5 Notay, Yvan 5 Rozza, Gianluigi 5 Southworth, Ben S. 5 Urban, Karsten 5 Wu, Jinbiao 5 Xiao, Yingxiong 5 Xu, Xiaowen 5 Yue, Xiaoqiang 5 Zhu, Yunrong 4 Ayuso de Dios, Blanca 4 Chen, Minghua 4 D’Ambra, Pasqua 4 Dryja, Maksymilian 4 Guermond, Jean-Luc 4 Guzmán, Johnny 4 Hsieh, Chia-Yu 4 Janna, Carlo 4 Kolev, Tzanio V. 4 Lee, Chiun-Chang 4 Li, Yuwen 4 Müller, Fabian Lukas 4 Napov, Artem 4 Neumüller, Martin 4 Olson, Luke N. 4 Peterseim, Daniel 4 Qiao, Yu 4 Radu, Florin Adrian 4 Ruiz-Baier, Ricardo 4 Sayas, Francisco-Javier 4 Tuminaro, Raymond S. 4 Vejchodský, Tomáš 4 Verani, Marco 4 Verri, Maurizio 4 Wang, Chunmei 4 Wei, Yimin 4 Wu, Shuonan 4 Zhao, Jihong 3 Abdulle, Assyr 3 Almani, Tameem 3 Ammann, Bernd Eberhard 3 Ayuso, Blanca 3 Badea, Catalin 3 Bastian, Peter 3 Bochev, Pavel B. 3 Boon, Wietse M. 3 Both, Jakub Wiktor 3 Brannick, James J. 3 Brezina, Marian 3 Bui-Thanh, Tan 3 Cao, Waixiang ...and 969 more Authors all top 5 Cited in 135 Serials 61 SIAM Journal on Scientific Computing 46 Computer Methods in Applied Mechanics and Engineering 43 Journal of Computational and Applied Mathematics 41 Computers & Mathematics with Applications 38 Numerische Mathematik 37 Journal of Computational Physics 37 Numerical Linear Algebra with Applications 36 Mathematics of Computation 35 Journal of Scientific Computing 26 SIAM Journal on Numerical Analysis 18 Computational Geosciences 16 Linear Algebra and its Applications 15 M\(^3\)AS. 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Series A 1 Journal für die Reine und Angewandte Mathematik 1 Meccanica 1 Monatshefte für Mathematik 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Annals of Global Analysis and Geometry 1 Journal of Computational Mathematics 1 Physica D 1 Journal of Complexity 1 Constructive Approximation 1 European Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Computational Mathematics and Mathematical Physics 1 Aequationes Mathematicae 1 Applied Mathematical Modelling 1 Proceedings of the National Academy of Sciences of the United States of America 1 Computational Statistics and Data Analysis 1 Journal of Mathematical Imaging and Vision 1 Cybernetics and Systems Analysis 1 St. Petersburg Mathematical Journal ...and 35 more Serials all top 5 Cited in 45 Fields 644 Numerical analysis (65-XX) 310 Partial differential equations (35-XX) 138 Fluid mechanics (76-XX) 89 Mechanics of deformable solids (74-XX) 25 Optics, electromagnetic theory (78-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 21 Approximations and expansions (41-XX) 21 Functional analysis (46-XX) 18 Operator theory (47-XX) 17 Operations research, mathematical programming (90-XX) 16 Combinatorics (05-XX) 16 Computer science (68-XX) 15 Probability theory and stochastic processes (60-XX) 13 Biology and other natural sciences (92-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Geophysics (86-XX) 8 Integral equations (45-XX) 7 Potential theory (31-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Statistics (62-XX) 6 Ordinary differential equations (34-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 Real functions (26-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Topological groups, Lie groups (22-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Quantum theory (81-XX) 3 Astronomy and astrophysics (85-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 2 \(K\)-theory (19-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year