Edit Profile (opens in new tab) Vassilevski, Panayot Spirov Compute Distance To: Compute Author ID: vassilevski.panayot-s Published as: Vassilevski, Panayot S.; Vassilevski, P. S.; Vassilevski, Panayot; Vassilevski, P.; Vasilevski, P.; Vassilevski, Panayot. S.; Vasilevski, Panayot; Vassilevskij, P. S.; Vasilevski, P. S. more...less Homepage: http://people.llnl.gov/vassilevski1 External Links: MGP · Google Scholar · dblp Documents Indexed: 181 Publications since 1983, including 2 Books 6 Contributions as Editor Co-Authors: 112 Co-Authors with 157 Joint Publications 2,595 Co-Co-Authors all top 5 Co-Authors 30 single-authored 24 Lazarov, Raytcho D. 15 Ewing, Richard Edward 11 Axelsson, Axel Owe Holger 10 Margenov, Svetozar D. 10 Pasciak, Joseph E. 10 Villa, Umberto E. 10 Zikatanov, Ludmil T. 8 Kolev, Tzanio V. 8 Lee, Chak Shing 7 Iliev, Oleg P. 5 Dobrev, Veselin A. 5 Petrova, Svetozara I. 4 Chou, So-Hsiang 4 Kalchev, Delyan Z. 4 Osborn, Sarah V. 4 Wang, Junping 3 Barker, Andrew T. 3 Brezina, Marian 3 D’Ambra, Pasqua 3 Efendiev, Yalchin R. 3 Eijkhout, Victor L. 3 Fairbanks, Hillary R. 3 Falgout, Robert D. 3 Hu, Xiaozhe 3 Lashuk, Ilya V. 3 Neumüller, Martin 3 Rusten, Torgeir 3 Tobiska, Lutz 3 Winther, Ragnar 2 Adler, James H. 2 Carey, Graham Francis 2 Castelletto, Nicola 2 Chan, Tony Fan-Cheong 2 Griebel, Michael 2 Hamon, François P. 2 Henson, Van Emden 2 Jones, Jim E. 2 Kwak, Do Young 2 la Cour Christensen, Max 2 Makarov, Mikhail M. 2 Manteuffel, Thomas A. 2 McCormick, Steve Fahrney 2 Mishev, Ilya D. 2 Pehlivanov, A. I. 2 Ponce, Colin 2 Ruge, J. 2 Scheichl, Robert 2 Sendov, Blagovest Khristov 2 White, Joshua A. 2 Woodward, Carol S. 2 Xu, Jinchao 1 Aposporidis, Alexis 1 Ayuso de Dios, Blanca 1 Bacuta, Constantin 1 Bank, Randolph E. 1 Bindel, David S. 1 Bramble, James H. 1 Brown, Peter N. 1 Cai, Difeng 1 Cai, Xiao-Chuan 1 Cai, Zhiqiang 1 Chartier, Timothy P. 1 Chow, Edmond G. W. 1 Dimov, Ivan Todor 1 Djidjev, Hristo Nicolov 1 Engsig-Karup, Allan P. 1 Etova, Maya H. 1 Filippone, Salvatore 1 Galvis, Juan 1 Gelever, Stephan V. 1 Georgiev, Asen 1 Gu, Ming 1 Haug, Einar 1 Iontcheva, Ana H. 1 John, Volker 1 Ketelsen, Christian 1 Kim, Chisup 1 Kostova, Tanya V. 1 Kraus, Johannes K. 1 Krause, Rolf H. 1 Kuhlemann, Verena 1 Li, Xiaoye Sherry 1 Lirkov, Ivan D. 1 Marcinkowski, Leszek 1 Markov, Svetoslav Marinovich 1 Matthies, Gunar 1 Meier Yang, Ulrike 1 Minev, Peter Dimitrov 1 Mitkova, T. I. 1 Neytcheva, Maya G. 1 Notay, Yvan 1 Oeltz, Daniel 1 Polman, Ben 1 Proskurowski, Wlodek 1 Proskurowski, Włodzimierz 1 Quiring, Benjamin 1 Russell, Thomas F. 1 Sanders, Geoffrey D. 1 Schafelner, Andreas 1 Schöberl, Joachim ...and 12 more Co-Authors all top 5 Serials 34 SIAM Journal on Scientific Computing 28 Numerical Linear Algebra with Applications 13 Doklady Bolgarskoĭ Akademii Nauk 11 SIAM Journal on Numerical Analysis 6 Mathematics of Computation 5 Numerische Mathematik 5 SIAM Journal on Matrix Analysis and Applications 5 Computational Methods in Applied Mathematics 4 Computing 3 Numerical Methods for Partial Differential Equations 3 East-West Journal of Numerical Mathematics 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 BIT 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Scientific and Statistical Computing 2 Mathematica Balkanica. New Series 2 International Journal of Computer Mathematics 2 SIAM Review 2 ETNA. Electronic Transactions on Numerical Analysis 1 Journal of Computational Physics 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Differentsial’nye Uravneniya 1 Differential Equations 1 Moscow University Computational Mathematics and Cybernetics 1 Journal of Computational Mathematics 1 Parallel Computing 1 Applied Numerical Mathematics 1 Communications in Applied Numerical Methods 1 Applications of Mathematics 1 Computing and Visualization in Science 1 Multiscale Modeling & Simulation 1 Oberwolfach Reports 1 Advances in Adaptive Data Analysis 1 Springer Proceedings in Mathematics & Statistics 1 Godishnik na Sofiskiya Universitet. Fakultet po Matematika i Mekhanika all top 5 Fields 180 Numerical analysis (65-XX) 109 Partial differential equations (35-XX) 15 Fluid mechanics (76-XX) 7 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 4 Mechanics of deformable solids (74-XX) 3 Combinatorics (05-XX) 3 Operator theory (47-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 145 Publications have been cited 1,764 times in 1,052 Documents Cited by ▼ Year ▼ Multilevel block factorization preconditioners. Matrix-based analysis and algorithms for solving finite element equations. Zbl 1170.65001Vassilevski, Panayot S. 99 2008 Finite volume methods for convection-diffusion problems. Zbl 0847.65075Lazarov, R. D.; Mishev, Ilya D.; Vassilevski, P. S. 97 1996 Algebraic multilevel preconditioning methods. I. Zbl 0661.65110Axelsson, O.; Vassilevski, P. S. 86 1989 Algebraic multilevel preconditioning methods. II. Zbl 0715.65091Axelsson, O.; Vassilevski, P. S. 82 1990 The role of the strengthened Cauchy-Buniakowskii-Schwarz inequality in multilevel methods. Zbl 0737.65026Eijkhout, Victor; Vassilevski, Panayot 47 1991 AMGe based on element agglomeration. Zbl 0992.65140Jones, Jim E.; Vassilevski, Panayot S. 44 2001 Local refinement techniques for elliptic problems on cell-centered grids. I: Error analysis. Zbl 0724.65093Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S. 40 1991 On generalizing the algebraic multigrid framework. Zbl 1077.65129Falgout, Robert D.; Vassilevski, Panayot S. 38 2004 Spectral AMGe (\(\rho\)AMGe). Zbl 1057.65096Chartier, T.; Falgout, R. D.; Henson, V. E.; Jones, J.; Manteuffel, T.; McCormick, S.; Ruge, J.; Vassilevski, P. S. 37 2003 Multiplier spaces for the mortar finite element method in three dimensions. Zbl 1006.65129Kim, Chisup; Lazarov, Raytcho D.; Pasciak, Joseph E.; Vassilevski, Panayot S. 35 2001 Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo 34 2010 Computational scales of Sobolev norms with application to preconditioning. Zbl 0941.65052Bramble, James H.; Pasciak, Joseph E.; Vassilevski, Panayot S. 33 2000 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 33 2005 Mixed covolume methods for elliptic problems on triangular grids. Zbl 0914.65107Chou, So-Hsiang; Kwak, Do Y.; Vassilevski, Panayot S. 32 1998 Parallel auxiliary space AMG for \(\boldsymbol{H}\) (curl) problems. Zbl 1212.65128Kolev, Tzanio V.; Vassilevski, Panayot S. 32 2009 A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning. Zbl 0748.65028Axelsson, O.; Vassilevski, P. S. 32 1991 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 Least-squares mixed finite element methods for non-selfadjoint elliptic problems. I: Error estimates. Zbl 0878.65096Pehlivanov, A. I.; Carey, G. F.; Vassilevski, P. S. 30 1996 A general mixed covolume framework for constructing conservative schemes for elliptic problems. Zbl 0924.65099Chou, So-Hsiang; Vassilevski, Panayot S. 26 1999 Recursive Krylov-based multigrid cycles. Zbl 1212.65132Notay, Y.; Vassilevski, P. S. 26 2008 Finite difference schemes on triangular cell-centered grids with local refinement. Zbl 0813.65115Vassilevski, P. S.; Petrova, S. I.; Lazarov, R. D. 26 1992 Multilevel iterative methods for mixed finite element discretizations of elliptic problems. Zbl 0797.65086Vassilevski, Panayot S.; Wang, Junping 24 1992 Interior penalty preconditioners for mixed finite element approximations of elliptic problems. Zbl 0857.65117Rusten, Torgeir; Vassilevski, Panayot S.; Winther, Ragnar 22 1996 Preconditioning mixed finite element saddle-point elliptic problems. Zbl 0848.65079Vassilevski, Panayot S.; Lazarov, Raytcho D. 20 1996 Element-free AMGe: General algorithms for computing interpolation weights in AMG. Zbl 0992.65141Henson, Van Emden; Vassilevski, Panayot S. 19 2001 A mixed formulation for the Brinkman problem. Zbl 1457.65219Vassilevski, Panayot S.; Villa, Umberto 18 2014 Parallel auxiliary space AMG solver for \(H(\operatorname{div})\) problems. Zbl 1332.65042Kolev, Tzanio V.; Vassilevski, Panayot S. 18 2012 Variable-step multilevel preconditioning methods. I: Self-adjoint and positive definite elliptic problems. Zbl 0804.65104Axelsson, O.; Vassilevski, P. S. 18 1994 Exact de Rham sequences of spaces defined on macro-elements in two and three spatial dimensions. Zbl 1195.78061Pasciak, Joseph E.; Vassilevski, Panayot S. 17 2008 An improved convergence analysis of smoothed aggregation algebraic multigrid. Zbl 1274.65315Brezina, Marian; Vaněk, Petr; Vassilevski, Panayot S. 16 2012 Hybrid \(V\)-cycle algebraic multilevel preconditioners. Zbl 0765.65044Vassilevski, P. S. 16 1992 Least-squares mixed finite element methods for non-selfadjoint elliptic problems. II: Performance of block-ILU factorization methods. Zbl 0840.65109Carey, G. F.; Pehlivanov, A. I.; Vassilevski, P. S. 16 1995 An application of the abstract multilevel theory to nonconforming finite element methods. Zbl 0828.65125Vassilevski, Panayot S.; Wang, Junping 15 1995 Spectral element agglomerate algebraic multigrid methods for elliptic problems with high-contrast coefficients. Zbl 1217.65222Efendiev, Yalchin; Galvis, Juan; Vassilevski, Panayot S. 15 2011 Local refinement via domain decomposition techniques for mixed finite element methods with rectangular Raviart-Thomas elements. Zbl 0705.65080Ewing, R. E.; Lazarov, R. D.; Russell, T. F.; Vassilevski, P. S. 14 1990 The construction of the coarse de Rham complexes with improved approximation properties. Zbl 1284.65156Lashuk, Ilya V.; Vassilevski, Panayot S. 14 2014 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 14 2017 Coarse spaces by algebraic multigrid: multigrid convergence and upscaling error estimates. Zbl 1229.65226Vassilevski, Panayot S. 14 2011 A survey of multilevel preconditioned iterative methods. Zbl 0694.65009Axelsson, O.; Vassilevski, P. S. 13 1989 Mixed upwinding covolume methods on rectangular grids for convection-diffusion problems. Zbl 0947.65120Chou, So-Hsiang; Kwak, Do Y.; Vassilevski, Panayot S. 13 1999 Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. Zbl 1284.65052Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil 12 2012 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 On some versions of the element agglomeration AMGe method. Zbl 1212.65494Lashuk, I.; Vassilevski, P. S. 12 2008 Sparse matrix element topology with application to AMG(e) and preconditioning. Zbl 1071.65538Vassilevski, Panayot S. 12 2002 Finite difference schemes on grids with local refinement in time and space for parabolic problems. I: Derivation, stability, and error analysis. Zbl 0721.65047Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S. 11 1990 A block-diagonal algebraic multigrid preconditioner for the Brinkman problem. Zbl 1282.65133Vassilevski, Panayot S.; Villa, Umberto 11 2013 A multilevel, hierarchical sampling technique for spatially correlated random fields. Zbl 1422.65406Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto 11 2017 Local refinement techniques for elliptic problems on cell-centered grids. III: Algebraic multilevel BEPS preconditioners. Zbl 0726.65137Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S. 10 1991 Stabilizing the hierarchical basis by approximate wavelets. II: Implementation and numerical results. Zbl 0924.65108Vassilevski, Panayot S.; Wang, Junping 10 1999 Weak approximation properties of elliptic projections with functional constraints. Zbl 1244.65215Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 10 2011 Adaptive AMG with coarsening based on compatible weighted matching. Zbl 1376.65038D’Ambra, Pasqua; Vassilevski, Panayot S. 10 2013 Incomplete block-matrix factorization iterative methods for convection- diffusion problems. Zbl 0687.65029Axelsson, O.; Eijkhout, V.; Polman, B.; Vassilevski, P. 9 1989 Space-time approximation with sparse grids. Zbl 1114.35082Griebel, Michael; Oeltz, Daniel; Vassilevski, Panayot 9 2006 On two ways of stabilizing the hierarchical basis multilevel methods. Zbl 0880.65085Vassilevski, Panayot S. 9 1997 Stabilizing the hierarchical basis by approximate wavelets. I: Theory. Zbl 0889.65126Vassilevskij, P. S.; Wang, J. 9 1997 Algebraic hybridization and static condensation with application to scalable \(H\)(div) preconditioning. Zbl 1420.65029Dobrev, V.; Kolev, T.; Lee, C. S.; Tomov, V.; Vassilevski, P. S. 9 2019 Element agglomeration coarse Raviart-Thomas spaces with improved approximation properties. Zbl 1274.65302Lashuk, I. V.; Vassilevski, P. S. 9 2012 Local refinement techniques for elliptic problems on cell-centered grids. II: Optimal order two-grid iterative methods. Zbl 0840.65124Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S. 9 1994 Circulant block-factorization preconditioners for elliptic problems. Zbl 0810.65039Lirkov, I. D.; Margenov, S. D.; Vassilevski, P. S. 9 1994 Reducing communication in algebraic multigrid using additive variants. Zbl 1340.65304Vassilevski, Panayot S.; Yang, Ulrike Meier 8 2014 Streamline diffusion least-squares mixed finite element methods for convection-diffusion problems. Zbl 0895.65049Lazarov, R. D.; Tobiska, L.; Vassilevski, P. S. 8 1997 Upscaling of mixed finite element discretization problems by the spectral AMGe method. Zbl 1348.65165Kalchev, D. Z.; Lee, C. S.; Villa, U.; Efendiev, Y.; Vassilevski, P. S. 8 2016 Direction-preserving and Schur-monotonic semiseparable approximations of symmetric positive definite matrices. Zbl 1209.65033Gu, Ming; Li, Xiaoye S.; Vassilevski, Panayot S. 8 2010 Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes. Zbl 06945785Osborn, Sarah; Zulian, Patrick; Benson, Thomas; Villa, Umberto; Krause, Rolf; Vassilevski, Panayot S. 8 2018 Fast algorithm for solving a linear algebraic problem with separable variables. Zbl 0575.65022Vassilevski, P. S. 7 1984 Smoothed aggregation spectral element agglomeration AMG: SA-\(\rho \)AMGe. Zbl 1310.65151Brezina, Marian; Vassilevski, Panayot S. 7 2012 Comparative convergence analysis of nonlinear AMLI-cycle multigrid. Zbl 1276.65089Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao 7 2013 Monotone multigrid methods based on element agglomeration coarsening away from the contact boundary for the Signorini’s problem. Zbl 1164.74554Iontcheva, Ana H.; Vassilevski, Panayot S. 7 2004 A framework for block ILU factorizations using block-size reduction. Zbl 0819.65018Chan, Tony F.; Vassilevski, Panayot S. 7 1995 Domain decomposition type iterative techniques for parabolic problems on locally refined grids. Zbl 0794.65076Ewing, Richard E.; Lazarov, Raytcho D.; Pasciak, Joseph E.; Vassilevski, Panayot S. 7 1993 Asymptotic work estimates for AMLI methods. Zbl 0729.65082Axelsson, O.; Vassilevski, P. S. 6 1991 On some ways of approximating inverses of banded matrices in connection with deriving preconditioners based on incomplete block factorizations. Zbl 0691.65017Vassilevski, P. S. 6 1990 Positive definiteness aspects of vectorizable preconditioners. Zbl 0692.65024Eijkhout, V.; Vassilevski, P. 6 1989 On mesh-independent convergence of an inexact Newton–multigrid algorithm. Zbl 1049.65115Brown, Peter N.; Vassilevski, Panayot S.; Woodward, Carol S. 6 2003 Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on nonmatching grids. Zbl 1095.65103Lazarov, R. D.; Pasciak, J. E.; Schöberl, J.; Vassilevski, P. S. 6 2003 Balancing domain decomposition by constraints algorithms for curl-conforming spaces of arbitrary order. Zbl 1442.65435Zampini, Stefano; Vassilevski, Panayot; Dobrev, Veselin; Kolev, Tzanio 6 2018 AMG by element agglomeration and constrained energy minimization interpolation. Zbl 1174.65546Kolev, Tzanio V.; Vassilevski, Panayot S. 6 2006 A two-grid SA-AMG convergence bound that improves when increasing the polynomial degree. Zbl 1413.65062Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao 6 2016 Interior penalty discontinuous approximations of elliptic problems. Zbl 0995.65114Lazarov, R.; Tomov, S.; Vassilevski, P. 6 2001 Algebraic two-level preconditioning of non-conforming FEM systems. Zbl 0912.65103Margenov, Svetozar D.; Vassilevski, Panayot S. 5 1998 A new approach for solving Stokes systems arising from a distributive relaxation method. Zbl 1221.65301Bacuta, Constantin; Vassilevski, Panayot S.; Zhang, Shangyou 5 2011 General constrained energy minimization interpolation mappings for AMG. Zbl 1209.65133Vassilevski, Panayot S. 5 2010 Multilevel block factorizations in generalized hierarchical bases. Zbl 1071.65061Chow, Edmond; Vassilevski, Panayot S. 5 2003 Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties. Zbl 1432.76160la Cour Christensen, Max; Vassilevski, Panayot S.; Villa, Umberto 5 2018 BootCMatch: a software package for bootstrap AMG based on graph weighted matching. Zbl 1484.65059D’Ambra, Pasqua; Filippone, Salvatore; Vassilevski, Panayot S. 5 2018 Space-time discretizations using constrained first-order system least squares (CFOSLS). Zbl 1416.65362Voronin, Kirill; Lee, Chak Shing; Neumüller, Martin; Sepulveda, Paulina; Vassilevski, Panayot S. 5 2018 Performance of certain iterative methods in solving implicit difference schemes for 2-D Navier-Stokes equations. Zbl 0764.76047Iliev, O. P.; Makarov, M. M.; Vassilevski, P. S. 5 1992 Parallel solver for \(\boldsymbol{H}(\operatorname{div})\) problems using hybridization and AMG. Zbl 1367.65172Lee, Chak S.; Vassilevski, Panayot S. 5 2017 Multiple vector preserving interpolation mappings in algebraic multigrid. Zbl 1102.65040Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2006 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 An upwinding cell-centered method with piecewise constant velocity over covolumes. Zbl 0939.65115Chou, So-Hsiang; Vassilevski, Panayot S. 4 1999 Auxiliary space AMG for \(H\)(curl) problems. Zbl 1142.78009Kolev, Tzanio V.; Vassilevski, Panayot. S. 4 2008 \({\mathbf H}\)(curl) auxiliary mesh preconditioning. Zbl 1212.65490Kolev, T. V.; Pasciak, J. E.; Vassilevski, P. S. 4 2008 Finite difference schemes on grids with local refinement in time and in space for parabolic problems. Optimal order two-grid iterative methods. Zbl 0829.65112Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S. 4 1991 Construction of variable-step preconditioners for inner-outer iteration methods. Zbl 0785.65018Axelsson, O.; Vassilevski, P. S. 4 1992 Mini-workshop: Numerical upscaling for media with deterministic and stochastic heterogeneity. Abstracts from the workshop held February 10–16, 2013. Zbl 1349.00152 4 2013 Space-time CFOSLS methods with AMGe upscaling. Zbl 1367.65145Neumüller, Martin; Vassilevski, Panayot S.; Villa, Umberto E. 4 2017 Preconditioning capacitance matrix problems in domain imbedding. Zbl 0806.65118Proskurowski, Wlodek; Vassilevski, Panayot S. 4 1994 Algebraic multilevel preconditioning of anisotropic elliptic problems. Zbl 0813.65066Margenov, Svetozar D.; Vassilevski, Panayot S. 4 1994 Error analysis for constrained first-order system least-squares finite-element methods. Zbl 1310.76086Adler, J. H.; Vassilevski, P. S. 3 2014 Multilevel graph embedding. Zbl 07361105Quiring, Benjamin; Vassilevski, Panayot S. 1 2021 Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems. Zbl 07337917Lee, Chak Shing; Hamon, François; Castelletto, Nicola; Vassilevski, Panayot S.; White, Joshua A. 2 2020 Eigenvalue problems for exponential-type kernels. Zbl 1437.65230Cai, Difeng; Vassilevski, Panayot S. 1 2020 Auxiliary space preconditioning of finite element equations using a nonconforming interior penalty reformulation and static condensation. Zbl 1448.65235Kalchev, Delyan Z.; Vassilevski, Panayot S. 1 2020 Algebraic hybridization and static condensation with application to scalable \(H\)(div) preconditioning. Zbl 1420.65029Dobrev, V.; Kolev, T.; Lee, C. S.; Tomov, V.; Vassilevski, P. S. 9 2019 Improving solve time of aggregation-based adaptive AMG. Zbl 1463.65401D’Ambra, Pasqua; Vassilevski, Panayot S. 2 2019 Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes. Zbl 06945785Osborn, Sarah; Zulian, Patrick; Benson, Thomas; Villa, Umberto; Krause, Rolf; Vassilevski, Panayot S. 8 2018 Balancing domain decomposition by constraints algorithms for curl-conforming spaces of arbitrary order. Zbl 1442.65435Zampini, Stefano; Vassilevski, Panayot; Dobrev, Veselin; Kolev, Tzanio 6 2018 Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties. Zbl 1432.76160la Cour Christensen, Max; Vassilevski, Panayot S.; Villa, Umberto 5 2018 BootCMatch: a software package for bootstrap AMG based on graph weighted matching. Zbl 1484.65059D’Ambra, Pasqua; Filippone, Salvatore; Vassilevski, Panayot S. 5 2018 Space-time discretizations using constrained first-order system least squares (CFOSLS). Zbl 1416.65362Voronin, Kirill; Lee, Chak Shing; Neumüller, Martin; Sepulveda, Paulina; Vassilevski, Panayot S. 5 2018 The auxiliary space preconditioner for the de Rham complex. Zbl 1402.65017Gopalakrishnan, J.; Neumüller, M.; Vassilevski, P. S. 2 2018 Arbitrary dimension convection-diffusion schemes for space-time discretizations. Zbl 1348.65139Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 14 2017 A multilevel, hierarchical sampling technique for spatially correlated random fields. Zbl 1422.65406Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto 11 2017 Parallel solver for \(\boldsymbol{H}(\operatorname{div})\) problems using hybridization and AMG. Zbl 1367.65172Lee, Chak S.; Vassilevski, Panayot S. 5 2017 Space-time CFOSLS methods with AMGe upscaling. Zbl 1367.65145Neumüller, Martin; Vassilevski, Panayot S.; Villa, Umberto E. 4 2017 Spectral upscaling for graph Laplacian problems with application to reservoir simulation. Zbl 1422.65435Barker, Andrew T.; Lee, Chak S.; Vassilevski, Panayot S. 3 2017 Numerical multilevel upscaling for incompressible flow in reservoir simulation: an element-based algebraic multigrid (amge) approach. Zbl 1360.65247la Cour Christensen, Max; Villa, Umberto; Engsig-Karup, Allan P.; Vassilevski, Panayot S. 3 2017 Solving graph Laplacian systems through recursive partitioning and two-grid preconditioning. Zbl 1371.65030Ponce, Colin; Vassilevski, Panayot S. 2 2017 Upscaling of mixed finite element discretization problems by the spectral AMGe method. Zbl 1348.65165Kalchev, D. Z.; Lee, C. S.; Villa, U.; Efendiev, Y.; Vassilevski, P. S. 8 2016 A two-grid SA-AMG convergence bound that improves when increasing the polynomial degree. Zbl 1413.65062Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao 6 2016 A mixed formulation for the Brinkman problem. Zbl 1457.65219Vassilevski, Panayot S.; Villa, Umberto 18 2014 The construction of the coarse de Rham complexes with improved approximation properties. Zbl 1284.65156Lashuk, Ilya V.; Vassilevski, Panayot S. 14 2014 Reducing communication in algebraic multigrid using additive variants. Zbl 1340.65304Vassilevski, Panayot S.; Yang, Ulrike Meier 8 2014 Commuting projections on graphs. Zbl 1340.65062Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2014 Error analysis for constrained first-order system least-squares finite-element methods. Zbl 1310.76086Adler, J. H.; Vassilevski, P. S. 3 2014 A combined preconditioning strategy for nonsymmetric systems. Zbl 1308.65043Ayuso de Dios, B.; Barker, A. T.; Vassilevski, P. S. 3 2014 Multigrid preconditioning of the non-regularized augmented Bingham fluid problem. Zbl 1367.76033Aposporidis, Alexis; Vassilevski, Panayot S.; Veneziani, Alessandro 1 2014 A block-diagonal algebraic multigrid preconditioner for the Brinkman problem. Zbl 1282.65133Vassilevski, Panayot S.; Villa, Umberto 11 2013 Adaptive AMG with coarsening based on compatible weighted matching. Zbl 1376.65038D’Ambra, Pasqua; Vassilevski, Panayot S. 10 2013 Comparative convergence analysis of nonlinear AMLI-cycle multigrid. Zbl 1276.65089Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao 7 2013 Mini-workshop: Numerical upscaling for media with deterministic and stochastic heterogeneity. Abstracts from the workshop held February 10–16, 2013. Zbl 1349.00152 4 2013 Improving the communication pattern in matrix-vector operations for large scale-free graphs by disaggregation. Zbl 1280.05124Kuhlemann, Verena; Vassilevski, Panayot S. 3 2013 Two-level adaptive algebraic multigrid for a sequence of problems with slowly varying random coefficients. Zbl 1285.65083Kalchev, D.; Ketelsen, C.; Vassilevski, P. S. 2 2013 Improving conservation for first-order system least-squares finite-element methods. Zbl 1275.65077Adler, J. H.; Vassilevski, P. S. 2 2013 Parallel auxiliary space AMG solver for \(H(\operatorname{div})\) problems. Zbl 1332.65042Kolev, Tzanio V.; Vassilevski, Panayot S. 18 2012 An improved convergence analysis of smoothed aggregation algebraic multigrid. Zbl 1274.65315Brezina, Marian; Vaněk, Petr; Vassilevski, Panayot S. 16 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 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 Element agglomeration coarse Raviart-Thomas spaces with improved approximation properties. Zbl 1274.65302Lashuk, I. V.; Vassilevski, P. S. 9 2012 Smoothed aggregation spectral element agglomeration AMG: SA-\(\rho \)AMGe. Zbl 1310.65151Brezina, Marian; Vassilevski, Panayot S. 7 2012 Regular decompositions for \(H(\mathrm{div})\) spaces. Zbl 1284.65051Kolev, Tzanio; Vassilevski, Panayot 2 2012 Spectral element agglomerate algebraic multigrid methods for elliptic problems with high-contrast coefficients. Zbl 1217.65222Efendiev, Yalchin; Galvis, Juan; Vassilevski, Panayot S. 15 2011 Coarse spaces by algebraic multigrid: multigrid convergence and upscaling error estimates. Zbl 1229.65226Vassilevski, Panayot S. 14 2011 Weak approximation properties of elliptic projections with functional constraints. Zbl 1244.65215Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 10 2011 A new approach for solving Stokes systems arising from a distributive relaxation method. Zbl 1221.65301Bacuta, Constantin; Vassilevski, Panayot S.; Zhang, Shangyou 5 2011 Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo 34 2010 Direction-preserving and Schur-monotonic semiseparable approximations of symmetric positive definite matrices. Zbl 1209.65033Gu, Ming; Li, Xiaoye S.; Vassilevski, Panayot S. 8 2010 General constrained energy minimization interpolation mappings for AMG. Zbl 1209.65133Vassilevski, Panayot S. 5 2010 Parallel auxiliary space AMG for \(\boldsymbol{H}\) (curl) problems. Zbl 1212.65128Kolev, Tzanio V.; Vassilevski, Panayot S. 32 2009 Multilevel block factorization preconditioners. Matrix-based analysis and algorithms for solving finite element equations. Zbl 1170.65001Vassilevski, Panayot S. 99 2008 Recursive Krylov-based multigrid cycles. Zbl 1212.65132Notay, Y.; Vassilevski, P. S. 26 2008 Exact de Rham sequences of spaces defined on macro-elements in two and three spatial dimensions. Zbl 1195.78061Pasciak, Joseph E.; Vassilevski, Panayot S. 17 2008 On some versions of the element agglomeration AMGe method. Zbl 1212.65494Lashuk, I.; Vassilevski, P. S. 12 2008 Auxiliary space AMG for \(H\)(curl) problems. Zbl 1142.78009Kolev, Tzanio V.; Vassilevski, Panayot. S. 4 2008 \({\mathbf H}\)(curl) auxiliary mesh preconditioning. Zbl 1212.65490Kolev, T. V.; Pasciak, J. E.; Vassilevski, P. S. 4 2008 A generalized eigensolver based on smoothed aggregation (GES-SA) for initializing smoothed aggregation (SA) multigrid. Zbl 1212.65149Brezina, M.; Manteuffel, T.; McCormick, S.; Ruge, J.; Sanders, G.; Vassilevski, P. 1 2008 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 Space-time approximation with sparse grids. Zbl 1114.35082Griebel, Michael; Oeltz, Daniel; Vassilevski, Panayot 9 2006 AMG by element agglomeration and constrained energy minimization interpolation. Zbl 1174.65546Kolev, Tzanio V.; Vassilevski, Panayot S. 6 2006 Multiple vector preserving interpolation mappings in algebraic multigrid. Zbl 1102.65040Vassilevski, Panayot S.; Zikatanov, Ludmil T. 4 2006 Mesh-independent convergence of the modified inexact Newton method for a second order non-linear problem. Zbl 1193.65200Kim, T.; Pasciak, J. E.; Vassilevski, P. S. 2 2006 On two-grid convergence estimates. Zbl 1164.65343Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. 33 2005 An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. Zbl 1099.65031Cai, Xiao-Chuan; Marcinkowski, Leszek; Vassilevski, Panayot S. 3 2005 On generalizing the algebraic multigrid framework. Zbl 1077.65129Falgout, Robert D.; Vassilevski, Panayot S. 38 2004 Monotone multigrid methods based on element agglomeration coarsening away from the contact boundary for the Signorini’s problem. Zbl 1164.74554Iontcheva, Ana H.; Vassilevski, Panayot S. 7 2004 Spectral AMGe (\(\rho\)AMGe). Zbl 1057.65096Chartier, T.; Falgout, R. D.; Henson, V. E.; Jones, J.; Manteuffel, T.; McCormick, S.; Ruge, J.; Vassilevski, P. S. 37 2003 On mesh-independent convergence of an inexact Newton–multigrid algorithm. Zbl 1049.65115Brown, Peter N.; Vassilevski, Panayot S.; Woodward, Carol S. 6 2003 Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on nonmatching grids. Zbl 1095.65103Lazarov, R. D.; Pasciak, J. E.; Schöberl, J.; Vassilevski, P. S. 6 2003 Multilevel block factorizations in generalized hierarchical bases. Zbl 1071.65061Chow, Edmond; Vassilevski, Panayot S. 5 2003 On the occasion of the 60th birthday of Raytcho Lazarov. Zbl 1071.01524Vassilevski, Panayot S. 3 2003 Sparse matrix element topology with application to AMG(e) and preconditioning. Zbl 1071.65538Vassilevski, Panayot S. 12 2002 Numerical methods for convection-diffusion problems on general grids. Zbl 1029.65129Lazarov, Raytcho D.; Vassilevski, Panayot S. 3 2002 AMGe based on element agglomeration. Zbl 0992.65140Jones, Jim E.; Vassilevski, Panayot S. 44 2001 Multiplier spaces for the mortar finite element method in three dimensions. Zbl 1006.65129Kim, Chisup; Lazarov, Raytcho D.; Pasciak, Joseph E.; Vassilevski, Panayot S. 35 2001 Element-free AMGe: General algorithms for computing interpolation weights in AMG. Zbl 0992.65141Henson, Van Emden; Vassilevski, Panayot S. 19 2001 Interior penalty discontinuous approximations of elliptic problems. Zbl 0995.65114Lazarov, R.; Tomov, S.; Vassilevski, P. 6 2001 Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems. Zbl 1051.65107Lazarov, Raytcho D.; Pasciak, Joseph E.; Vassilevski, Panayot S. 3 2001 Computational scales of Sobolev norms with application to preconditioning. Zbl 0941.65052Bramble, James H.; Pasciak, Joseph E.; Vassilevski, Panayot S. 33 2000 A survey of a class of algebraic multilevel iteration methods for positive definite symmetric matrices. Zbl 0968.65015Axelsson, Owe; Vassilevski, Panayot S. 2 2000 A comparison of three solvers for the incompressible Navier-Stokes equations. Zbl 0985.76053John, V.; Matthies, G.; Mitkova, T. I.; Tobiska, L.; Vassilevski, P. S. 1 2000 A general mixed covolume framework for constructing conservative schemes for elliptic problems. Zbl 0924.65099Chou, So-Hsiang; Vassilevski, Panayot S. 26 1999 Mixed upwinding covolume methods on rectangular grids for convection-diffusion problems. Zbl 0947.65120Chou, So-Hsiang; Kwak, Do Y.; Vassilevski, Panayot S. 13 1999 Stabilizing the hierarchical basis by approximate wavelets. II: Implementation and numerical results. Zbl 0924.65108Vassilevski, Panayot S.; Wang, Junping 10 1999 An upwinding cell-centered method with piecewise constant velocity over covolumes. Zbl 0939.65115Chou, So-Hsiang; Vassilevski, Panayot S. 4 1999 Coupling mixed and finite volume discretizations of convection-diffusion-reaction equations on non-matching grids. Zbl 1052.65554Lazarov, Raytcho D.; Pasciak, Joseph E.; Vassilevski, Panayot S. 2 1999 Recent advances in numerical methods and applications. Proceedings of the 4th international conference, NMA ’98, Sofia, Bulgaria, August 19–23, 1998. Zbl 0964.00049 1 1999 Mixed covolume methods for elliptic problems on triangular grids. Zbl 0914.65107Chou, So-Hsiang; Kwak, Do Y.; Vassilevski, Panayot S. 32 1998 Algebraic two-level preconditioning of non-conforming FEM systems. Zbl 0912.65103Margenov, Svetozar D.; Vassilevski, Panayot S. 5 1998 Domain embedding preconditioners for mixed systems. Zbl 0969.65105Rusten, Torgeir; Vassilevski, Panayot S.; Winther, Ragnar 3 1998 Preconditioning of indefinite and almost singular finite element elliptic equations. Zbl 0955.65083Neytcheva, Maya G.; Vassilevski, Panayot S. 1 1998 A block-factorization (algebraic) formulation of multigrid and Schwarz methods. Zbl 0915.65120Vassilevski, P. S. 1 1998 On two ways of stabilizing the hierarchical basis multilevel methods. Zbl 0880.65085Vassilevski, Panayot S. 9 1997 Stabilizing the hierarchical basis by approximate wavelets. I: Theory. Zbl 0889.65126Vassilevskij, P. S.; Wang, J. 9 1997 Streamline diffusion least-squares mixed finite element methods for convection-diffusion problems. Zbl 0895.65049Lazarov, R. D.; Tobiska, L.; Vassilevski, P. S. 8 1997 A comparison of multilevel methods for total variation regularization. Zbl 0888.65135Vassilevski, P. S.; Wade, J. G. 2 1997 Finite volume methods for convection-diffusion problems. Zbl 0847.65075Lazarov, R. D.; Mishev, Ilya D.; Vassilevski, P. S. 97 1996 Least-squares mixed finite element methods for non-selfadjoint elliptic problems. I: Error estimates. Zbl 0878.65096Pehlivanov, A. I.; Carey, G. F.; Vassilevski, P. S. 30 1996 Interior penalty preconditioners for mixed finite element approximations of elliptic problems. Zbl 0857.65117Rusten, Torgeir; Vassilevski, Panayot S.; Winther, Ragnar 22 1996 Preconditioning mixed finite element saddle-point elliptic problems. Zbl 0848.65079Vassilevski, Panayot S.; Lazarov, Raytcho D. 20 1996 ...and 45 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,379 Authors 52 Vassilevski, Panayot Spirov 42 Axelsson, Axel Owe Holger 24 Yuan, Yirang 20 Zikatanov, Ludmil T. 18 Kraus, Johannes K. 18 Lazarov, Raytcho D. 18 Margenov, Svetozar D. 16 Ewing, Richard Edward 15 Li, Changfeng 14 Lamichhane, Bishnu Prasad 14 Neytcheva, Maya G. 13 Xu, Jinchao 12 Chung, Tsz Shun Eric 12 Hu, Xiaozhe 12 Notay, Yvan 12 Wohlmuth, Barbara I. 11 Efendiev, Yalchin R. 10 Scheichl, Robert 10 Shu, Shi 10 Zampini, Stefano 9 Bai, Zhongzhi 9 Galvis, Juan 9 Kolev, Tzanio V. 9 Langer, Ulrich 9 Mardal, Kent-Andre 9 Pasciak, Joseph E. 9 Serra-Capizzano, Stefano 9 Zou, Qingsong 8 Antonietti, Paola Francesca 8 Bacuta, Constantin 8 Bramble, James H. 8 Gatica, Gabriel N. 8 Lymbery, Maria 8 Manteuffel, Thomas A. 8 Napov, Artem 8 Xiao, Yingxiong 7 Castelletto, Nicola 7 Chen, Zhangxin 7 Franceschini, Andrea 7 Iliev, Oleg P. 7 Lee, Chak Shing 7 Ruiz-Baier, Ricardo 7 Saad, Yousef 7 Villa, Umberto E. 7 Winther, Ragnar 7 Xu, Xuejun 7 Zhang, Zhimin 6 Blaheta, Radim 6 Chainais-Hillairet, Claire 6 Ferronato, Massimiliano 6 Ku, Jaeun 6 Kuchta, Miroslav 6 Liang, Dong 6 Liu, Jinn-Liang 6 Marcinkowski, Leszek 6 Nataf, Frédéric 6 Neumüller, Martin 6 Rahman, Talal 6 Schroder, Jacob B. 6 Southworth, Ben S. 6 Yang, Danping 6 Yang, Qing 6 Ye, Xiu 5 Brenner, Susanne Cecelia 5 Cai, Zhiqiang 5 di Serafino, Daniela 5 Dobrev, Veselin A. 5 Dostál, Zdeněk 5 Gaspar, Francisco José 5 Georgiev, Ivan 5 Grigori, Laura 5 Janna, Carlo 5 Karátson, János 5 Kozubek, Tomas 5 Leung, Wingtat 5 Li, Likang 5 Li, Yonghai 5 Mora, David 5 Olson, Luke N. 5 Oyarzúa, Ricardo 5 Sarkis, Marcus V. 5 Sun, Tongjun 5 Szyld, Daniel B. 5 Wang, Junping 5 Widlund, Olof B. 5 Zhang, Chensong 5 Zhou, Aihui 4 Anaya, Verónica 4 Barker, Andrew T. 4 Bertoluzza, Silvia 4 Bespalov, Alexei 4 Bessemoulin-Chatard, Marianne 4 Brzobohatý, Tomáš 4 Bustinza, Rommel A. 4 Carey, Graham Francis 4 Chen, Long 4 Chou, So-Hsiang 4 D’Ambra, Pasqua 4 Fang, Zhichao 4 Gratton, Serge ...and 1,279 more Authors all top 5 Cited in 128 Serials 83 Journal of Computational and Applied Mathematics 78 Computer Methods in Applied Mechanics and Engineering 73 SIAM Journal on Scientific Computing 70 Numerical Linear Algebra with Applications 53 Journal of Computational Physics 48 Mathematics of Computation 47 Numerische Mathematik 41 Computers & Mathematics with Applications 29 Applied Numerical Mathematics 26 Journal of Scientific Computing 25 Applied Mathematics and Computation 22 Computing 20 SIAM Journal on Numerical Analysis 18 International Journal of Computer Mathematics 17 Numerical Methods for Partial Differential Equations 15 International Journal for Numerical Methods in Engineering 14 Linear Algebra and its Applications 13 BIT 12 Mathematics and Computers in Simulation 11 Calcolo 11 Computational Geosciences 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Communications in Numerical Methods in Engineering 10 Advances in Computational Mathematics 9 Numerical Algorithms 9 Computational Methods in Applied Mathematics 8 Computers and Fluids 8 SIAM Journal on Matrix Analysis and Applications 8 M\(^3\)AS. 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