Edit Profile Zikatanov, Ludmil T. Compute Distance To: Compute Author ID: zikatanov.ludmil-t Published as: Zikatanov, L.; Zikatanov, L. T.; Zikatanov, Ludmil; Zikatanov, Ludmil T. Homepage: http://www.personal.psu.edu/ltz1/ External Links: MGP · Math-Net.Ru · ORCID · dblp Documents Indexed: 81 Publications since 1992, including 1 Book all top 5 Co-Authors 2 single-authored 23 Xu, Jinchao 15 Hu, Xiaozhe 10 Vassilevski, Panayot Spirov 8 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 Ohm, Peter 2 Antonietti, Paola Francesca 2 Ayuso, Blanca 2 Cho, Durkbin 2 Dobrev, Veselin A. 2 Kim, Hwanho 2 Liu, Chun 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 Chan, Tony Fan-Cheong 1 Chen, Jiabo 1 Deutsch, Frank 1 Falgout, Robert D. 1 Frommer, Andreas 1 Georgiev, Asen 1 Harizanov, Stanislav 1 Holst, Michael J. 1 Hong, Qingguo 1 Huang, Yunqing 1 Hundal, Hein S. 1 Iliev, Oleg P. 1 Kahl, Kartsen 1 Lashuk, Ilya V. 1 Li, Hengguang 1 Li, Yuwen 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, Shuhong 1 Wu, Xiaohui 1 Xu, Wenfang 1 Yu, Guozhu 1 Zhang, Chensong 1 Zhang, Shiquan 1 Zhu, Yunrong all top 5 Serials 8 Numerical Linear Algebra with Applications 6 SIAM Journal on Scientific Computing 4 Computers & Mathematics with Applications 4 Journal of Computational and Applied Mathematics 3 Mathematics of Computation 3 Numerische Mathematik 3 Journal of Computational Mathematics 3 Journal of Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 Linear and Multilinear Algebra 2 Numerical Functional Analysis and Optimization 2 SIAM Journal on Numerical Analysis 2 SIAM Journal on Matrix Analysis and Applications 2 Linear Algebra and its Applications 2 Journal of Numerical Mathematics 2 Multiscale Modeling & Simulation 1 Journal of Computational Physics 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 all top 5 Fields 71 Numerical analysis (65-XX) 37 Partial differential equations (35-XX) 14 Mechanics of deformable solids (74-XX) 13 Fluid mechanics (76-XX) 7 Combinatorics (05-XX) 3 Computer science (68-XX) 3 Optics, electromagnetic theory (78-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-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 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 62 Publications have been cited 901 times in 653 Documents Cited by ▼ Year ▼ The method of alternating projections and the method of subspace corrections in Hilbert space. Zbl 0999.47015Xu, Jinchao; Zikatanov, Ludmil 97 2002 A monotone finite element scheme for convection-diffusion equations. Zbl 0931.65111Xu, Jinchao; Zikatanov, Ludmil 89 1999 Some observations on Babuška and Brezzi theories. Zbl 1028.65115Xu, Jinchao; Zikatanov, Ludmil 77 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 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. 33 2005 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 31 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. 28 2016 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. 28 2006 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. 27 2017 An agglomeration multigrid method for unstructured grids. Zbl 0909.65102Chan, Tony F.; Xu, Jinchao; Zikatanov, Ludmil 23 1998 On an energy minimizing basis for algebraic multigrid methods. Zbl 1077.65130Xu, Jinchao; Zikatanov, Ludmil 22 2004 Interface and mixed boundary value problems on \(n\)-dimensional polyhedral domains. Zbl 1207.35117Bacuta, C.; Mazzucato, A. L.; Nistor, V.; Zikatanov, L. 21 2010 Robust subspace correction methods for nearly singular systems. Zbl 1151.65096Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 19 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 A multigrid method based on graph matching for convection-diffusion equations. Zbl 1071.65167Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil 19 2003 Algebraic multigrid methods. Zbl 1378.65182Xu, Jinchao; Zikatanov, Ludmil 18 2017 Mathematical models for the deformation of electrolyte droplets. Zbl 1147.35343Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil 18 2007 Uniformly convergent iterative methods for discontinuous Galerkin discretizations. Zbl 1203.65242Ayuso de Dios, Blanca; Zikatanov, Ludmil 17 2009 Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Zbl 1296.65153Ayuso De Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil 13 2014 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 On the convergence of iterative methods for semidefinite linear systems. Zbl 1122.65033Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil 13 2006 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 12 2017 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 12 2014 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. 11 2018 A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Zbl 1338.76054Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil 11 2016 Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. Zbl 1284.65052Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil 11 2012 Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids. Zbl 1259.65190Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 11 2012 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 11 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 10 2016 Weak approximation properties of elliptic projections with functional constraints. Zbl 1244.65215Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 8 2011 Two-sided bounds on the convergence rate of two-level methods. Zbl 1212.65503Zikatanov, L. T. 8 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. 7 2020 New estimates for the rate of convergence of the method of subspace corrections. Zbl 1174.65354Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil 7 2008 On multigrid methods for generalized finite element methods. Zbl 1012.65131Xu, Jinchao; Zikatanov, Ludmil T. 7 2002 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. 6 2017 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 Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs. Zbl 1275.65084Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil 6 2013 Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. Zbl 1281.65152Brannick, J.; Chen, Y.; Kraus, J.; Zikatanov, L. 6 2013 Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. Zbl 1205.65321Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L. 6 2010 Robust block preconditioners for Biot’s model. Zbl 1442.65342Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil T. 5 2018 A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians. Zbl 1340.65262Urschel, John C.; Xu, Jinchao; Hu, Xiaozhe; Zikatanov, Ludmil T. 5 2015 Spectral bisection of graphs and connectedness. Zbl 1286.05101Urschel, John C.; Zikatanov, Ludmil T. 5 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 5 2013 A multilevel precondition for generalized finite element method problems on unstructured simplicial meshes. Zbl 1156.65095Cho, D.; Zikatanov, L. 5 2007 Uniformly convergent multigrid methods for convection–diffusion problems without any constraint on coarse grids. Zbl 1039.65090Kim, Hwanho; Xu, Jinchao; Zikatanov, Ludmil 5 2004 Robust solvers for Maxwell’s equations with dissipative boundary conditions. Zbl 1395.65067Adler, J. H.; Hu, X.; Zikatanov, L. T. 4 2017 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. Zbl 1274.65314Brannick, James; Chen, Yao; Zikatanov, Ludmil 4 2012 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 Numerical approximation of asymptotically disappearing solutions of Maxwell’s equations. Zbl 1285.65075Adler, J. H.; Petkov, V.; Zikatanov, L. T. 3 2013 Predictioning of symmetric interior penalty discontinuous Galerkin FEM for elliptic problems. Zbl 1267.65194Dobrev, Veselin A.; Lazarov, Raytcho D.; Zikatanov, Ludmil T. 3 2008 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 the validity of the local Fourier analysis. Zbl 1449.65374Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 2 2019 Circulant block-factorization preconditioning of anisotropic elliptic problems. Zbl 0879.65022Lirkov, I. D.; Margenov, S. D.; Zikatanov, L. T. 2 1997 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 On the maximal error of spectral approximation of graph bisection. Zbl 1352.05120Urschel, John C.; Zikatanov, Ludmil T. 1 2016 A finite element framework for some mimetic finite difference discretizations. Zbl 1443.65285Rodrigo, Carmen; Gaspar, F. J.; Hu, X.; Zikatanov, L. 1 2015 Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. Zbl 1313.65324Yu, Guozhu; Xu, Jinchao; Zikatanov, Ludmil T. 1 2013 Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses. Zbl 1258.65096Boyanova, P.; Georgiev, I.; Margenov, S.; Zikatanov, L. 1 2012 Convergence analysis of iterative methods for semidefinite systems. Zbl 1174.65013Wu, Jinbiao; Lee, Youngju; Xu, Jinchao; Zikatanov, Ludmil 1 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. 7 2020 On the validity of the local Fourier analysis. Zbl 1449.65374Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. 2 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. 11 2018 Robust block preconditioners for Biot’s model. Zbl 1442.65342Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil T. 5 2018 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. 27 2017 Algebraic multigrid methods. Zbl 1378.65182Xu, Jinchao; Zikatanov, Ludmil 18 2017 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 12 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. 6 2017 Robust solvers for Maxwell’s equations with dissipative boundary conditions. Zbl 1395.65067Adler, J. H.; Hu, X.; Zikatanov, L. T. 4 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. 28 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 11 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 10 2016 On the maximal error of spectral approximation of graph bisection. Zbl 1352.05120Urschel, John C.; Zikatanov, Ludmil T. 1 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. 5 2015 A finite element framework for some mimetic finite difference discretizations. Zbl 1443.65285Rodrigo, Carmen; Gaspar, F. J.; Hu, X.; Zikatanov, L. 1 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 13 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 12 2014 Spectral bisection of graphs and connectedness. Zbl 1286.05101Urschel, John C.; Zikatanov, Ludmil T. 5 2014 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 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 Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs. Zbl 1275.65084Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil 6 2013 Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. Zbl 1281.65152Brannick, J.; Chen, Y.; Kraus, J.; Zikatanov, L. 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 5 2013 Numerical approximation of asymptotically disappearing solutions of Maxwell’s equations. Zbl 1285.65075Adler, J. H.; Petkov, V.; Zikatanov, L. T. 3 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. 1 2013 Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. Zbl 1284.65052Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil 11 2012 Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids. Zbl 1259.65190Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 11 2012 An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. Zbl 1274.65314Brannick, James; Chen, Yao; Zikatanov, Ludmil 4 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. 8 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. 21 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. 6 2010 Uniformly convergent iterative methods for discontinuous Galerkin discretizations. Zbl 1203.65242Ayuso de Dios, Blanca; Zikatanov, Ludmil 17 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 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 11 2008 Two-sided bounds on the convergence rate of two-level methods. Zbl 1212.65503Zikatanov, L. T. 8 2008 New estimates for the rate of convergence of the method of subspace corrections. Zbl 1174.65354Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil 7 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 19 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 18 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. 28 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. 33 2005 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 31 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 22 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 77 2003 A multigrid method based on graph matching for convection-diffusion equations. Zbl 1071.65167Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil 19 2003 The method of alternating projections and the method of subspace corrections in Hilbert space. Zbl 0999.47015Xu, Jinchao; Zikatanov, Ludmil 97 2002 On multigrid methods for generalized finite element methods. Zbl 1012.65131Xu, Jinchao; Zikatanov, Ludmil T. 7 2002 A monotone finite element scheme for convection-diffusion equations. Zbl 0931.65111Xu, Jinchao; Zikatanov, Ludmil 89 1999 An agglomeration multigrid method for unstructured grids. Zbl 0909.65102Chan, Tony F.; Xu, Jinchao; Zikatanov, Ludmil 23 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 993 Authors 33 Xu, Jinchao 32 Zikatanov, Ludmil T. 20 Li, Hengguang 18 Hu, Xiaozhe 18 Vassilevski, Panayot Spirov 17 Brenner, Susanne Cecelia 17 Nistor, Victor 14 Bacuta, Constantin 13 Kraus, Johannes K. 13 Zhang, Zhimin 10 Antonietti, Paola Francesca 9 Lee, Youngju 9 Schwab, Christoph 9 Shu, Shi 8 Chen, Long 8 Margenov, Svetozar D. 8 Sacco, Riccardo 8 Scheichl, Robert 8 Zou, Qingsong 7 Burman, Erik 7 Galvis, Juan 7 He, Wenming 7 Liu, Chun 7 Lymbery, Maria 7 Needell, Deanna 7 Rodrigo, Carmen 7 Sung, Li-Yeng 6 Adler, James H. 6 Castelletto, Nicola 6 Cui, Jintao 6 Gaspar, Francisco José 6 Hong, Qingguo 6 Lazarov, Raytcho D. 6 MacLachlan, Scott P. 6 Manteuffel, Thomas A. 6 Veeser, Andreas 6 Wheeler, Mary Fanett 5 Barrenechea, Gabriel R. 5 Ferronato, Massimiliano 5 Korotov, Sergey 5 Kumar, Kundan 5 Langer, Ulrich 5 Nicaise, Serge 5 Nordbotten, Jan Martin 5 Notay, Yvan 5 Rozza, Gianluigi 5 Southworth, Ben S. 5 Sung, Liyeng 5 Wu, Jinbiao 5 Xiao, Yingxiong 5 Zhu, Yunrong 4 Ayuso de Dios, Blanca 4 Chen, Minghua 4 Dryja, Maksymilian 4 Farrell, Patrick Emmet 4 Guermond, Jean-Luc 4 Kahl, Karsten 4 Lee, Chiun-Chang 4 Müller, Fabian Lukas 4 Napov, Artem 4 Neumüller, Martin 4 Nochetto, Ricardo Horacio 4 Olson, Luke N. 4 Peterseim, Daniel 4 Qiao, Yu 4 Sayas, Francisco-Javier 4 Tuminaro, Raymond S. 4 Vejchodský, Tomáš 4 Verani, Marco 4 Verri, Maurizio 4 Wei, Yimin 4 Wu, Shuonan 4 Zhang, Chensong 4 Zhao, Jihong 3 Abdulle, Assyr 3 Almani, Tameem 3 Ammann, Bernd Eberhard 3 Ayuso, Blanca 3 Badea, Catalin 3 Bochev, Pavel B. 3 Brannick, James J. 3 Brezina, Marian 3 Bui-Thanh, Tan 3 Cao, Waixiang 3 Chen, Zhangxin 3 Cho, Durkbin 3 de Falco, Carlo 3 Demkowicz, Leszek F. 3 Deutsch, Frank 3 Dolean, Victorita 3 Efendiev, Yalchin R. 3 Ern, Alexandre 3 Franceschini, Andrea 3 Georgiev, Ivan 3 Graham, Ivan G. 3 Guzmán, Johnny 3 Hannukainen, Antti 3 Hsieh, Chia-Yu 3 Huang, Weizhang 3 Hundal, Hein S. ...and 893 more Authors all top 5 Cited in 119 Serials 49 SIAM Journal on Scientific Computing 41 Journal of Computational and Applied Mathematics 38 Computer Methods in Applied Mechanics and Engineering 37 Numerical Linear Algebra with Applications 36 Numerische Mathematik 35 Computers & Mathematics with Applications 33 Mathematics of Computation 30 Journal of Scientific Computing 27 Journal of Computational Physics 23 SIAM Journal on Numerical Analysis 17 Computational Geosciences 16 Linear Algebra and its Applications 15 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 11 Calcolo 10 Numerical Methods for Partial Differential Equations 9 Applied Mathematics and Computation 9 Computational Methods in Applied Mathematics 8 Applied Numerical Mathematics 7 SIAM Journal on Matrix Analysis and Applications 7 Numerical Algorithms 6 BIT 5 Journal of Mathematical Analysis and Applications 5 Journal of Approximation Theory 5 Mathematics and Computers in Simulation 5 ETNA. Electronic Transactions on Numerical Analysis 5 Advances in Computational Mathematics 5 Computing and Visualization in Science 5 Central European Journal of Mathematics 4 Mathematical Methods in the Applied Sciences 4 Journal of Differential Equations 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Inverse Problems 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Numerical Functional Analysis and Optimization 3 Discrete and Continuous Dynamical Systems 3 Multiscale Modeling & Simulation 3 Acta Numerica 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Science China. Mathematics 2 Journal of Mathematical Physics 2 Integral Equations and Operator Theory 2 International Journal for Numerical Methods in Engineering 2 Journal of Functional Analysis 2 Applied Mathematics Letters 2 Science in China. Series A 2 Applications of Mathematics 2 International Journal of Computer Mathematics 2 SIAM Journal on Mathematical Analysis 2 SIAM Review 2 Bulletin of the American Mathematical Society. New Series 2 Computational and Applied Mathematics 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Foundations of Computational Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Numerical Mathematics 2 Oberwolfach Reports 2 GEM - International Journal on Geomathematics 2 S\(\vec{\text{e}}\)MA Journal 2 East Asian Journal on Applied Mathematics 2 Results in Applied Mathematics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Journal of Engineering Mathematics 1 Letters in Mathematical Physics 1 Linear and Multilinear Algebra 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 Beiträge zur Algebra und Geometrie 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Automatica 1 Computing 1 Czechoslovak Mathematical Journal 1 Journal of Combinatorial Theory. 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 Physica D 1 Journal of Complexity 1 Constructive Approximation 1 Computational Mechanics 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 1 Journal of Mathematical Chemistry 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Abstract and Applied Analysis 1 Mathematical Physics, Analysis and Geometry 1 Taiwanese Journal of Mathematics 1 Fractional Calculus & Applied Analysis 1 Discrete Dynamics in Nature and Society ...and 19 more Serials all top 5 Cited in 44 Fields 558 Numerical analysis (65-XX) 281 Partial differential equations (35-XX) 106 Fluid mechanics (76-XX) 74 Mechanics of deformable solids (74-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 20 Optics, electromagnetic theory (78-XX) 18 Approximations and expansions (41-XX) 18 Functional analysis (46-XX) 18 Operator theory (47-XX) 13 Combinatorics (05-XX) 13 Operations research, mathematical programming (90-XX) 12 Probability theory and stochastic processes (60-XX) 12 Computer science (68-XX) 12 Biology and other natural sciences (92-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Geophysics (86-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Integral equations (45-XX) 6 Potential theory (31-XX) 5 Ordinary differential equations (34-XX) 5 Statistics (62-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Topological groups, Lie groups (22-XX) 3 Dynamical systems and ergodic theory (37-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 Real functions (26-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 2 Classical thermodynamics, heat transfer (80-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