Pé de la Riva, Álvaro; Rodrigo, Carmen; Gaspar, Francisco J.; Adler, James H.; Hu, Xiaozhe; Zikatanov, Ludmil A local Fourier analysis for additive Schwarz smoothers. (English) Zbl 07813449 Comput. Math. Appl. 158, 13-20 (2024). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{Á. Pé de la Riva} et al., Comput. Math. Appl. 158, 13--20 (2024; Zbl 07813449) Full Text: DOI arXiv
Adler, James H.; Hu, Xiaozhe; Li, Yuwen; Zikatanov, Ludmil T. Parameter-free preconditioning for nearly-incompressible linear elasticity. (English) Zbl 07784346 Comput. Math. Appl. 154, 39-44 (2024). MSC: 65N30 76D05 65F10 35Q30 65N55 PDFBibTeX XMLCite \textit{J. H. Adler} et al., Comput. Math. Appl. 154, 39--44 (2024; Zbl 07784346) Full Text: DOI arXiv
D’Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore; Zikatanov, Ludmil Automatic coarsening in algebraic multigrid utilizing quality measures for matching-based aggregations. (English) Zbl 07731313 Comput. Math. Appl. 144, 290-305 (2023). MSC: 65F10 65N55 65N30 65F08 65F50 PDFBibTeX XMLCite \textit{P. D'Ambra} et al., Comput. Math. Appl. 144, 290--305 (2023; Zbl 07731313) Full Text: DOI arXiv
Budiša, Ana; Hu, Xiaozhe; Kuchta, Miroslav; Mardal, Kent-André; Zikatanov, Ludmil Rational approximation preconditioners for multiphysics problems. (English) Zbl 1521.65014 Georgiev, Ivan (ed.) et al., Numerical methods and applications. 10th international conference, NMA 2022, Borovets, Bulgaria, August 22–26, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13858, 100-113 (2023). MSC: 65D15 65F08 65N30 PDFBibTeX XMLCite \textit{A. Budiša} et al., Lect. Notes Comput. Sci. 13858, 100--113 (2023; Zbl 1521.65014) Full Text: DOI arXiv
Chiri, Maria Teresa; Czuprynski, Kenneth D; Zikatanov, Ludmil T Weakly coupled systems of eikonal equations for autonomous vehicles. arXiv:2310.02966 Preprint, arXiv:2310.02966 [math.OC] (2023). MSC: 65N30 35Q93 65K10 BibTeX Cite \textit{M. T. Chiri} et al., ``Weakly coupled systems of eikonal equations for autonomous vehicles'', Preprint, arXiv:2310.02966 [math.OC] (2023) Full Text: arXiv OA License
Li, Yuwen; Zikatanov, Ludmil T.; Zuo, Cheng A reduced conjugate gradient basis method for fractional diffusion. arXiv:2305.18038 Preprint, arXiv:2305.18038 [math.NA] (2023). MSC: 65N30 65N55 BibTeX Cite \textit{Y. Li} et al., ``A reduced conjugate gradient basis method for fractional diffusion'', Preprint, arXiv:2305.18038 [math.NA] (2023) Full Text: arXiv OA License
Budisa, Ana; Hu, Xiaozhe; Kuchta, Miroslav; Mardal, Kent-Andre; Zikatanov, Ludmil Tomov Algebraic multigrid methods for metric-perturbed coupled problems. arXiv:2305.06073 Preprint, arXiv:2305.06073 [math.NA] (2023). MSC: 65F08 65N55 65S05 BibTeX Cite \textit{A. Budisa} et al., ``Algebraic multigrid methods for metric-perturbed coupled problems'', Preprint, arXiv:2305.06073 [math.NA] (2023) Full Text: arXiv OA License
Li, Yuwen; Zikatanov, Ludmil T. New stabilized \(P_1 \times P_0\) finite element methods for nearly inviscid and incompressible flows. (English) Zbl 1507.76115 Comput. Methods Appl. Mech. Eng. 393, Article ID 114815, 17 p. (2022). MSC: 76M10 76D09 PDFBibTeX XMLCite \textit{Y. Li} and \textit{L. T. Zikatanov}, Comput. Methods Appl. Mech. Eng. 393, Article ID 114815, 17 p. (2022; Zbl 1507.76115) Full Text: DOI arXiv
Li, Yuwen; Zikatanov, Ludmil T. Residual-based a posteriori error estimates of mixed methods for a three-field Biot’s consolidation model. (English) Zbl 1493.65157 IMA J. Numer. Anal. 42, No. 1, 620-648 (2022). MSC: 65M60 65M06 65N30 65M15 76S05 74F10 74L10 35K05 PDFBibTeX XMLCite \textit{Y. Li} and \textit{L. T. Zikatanov}, IMA J. Numer. Anal. 42, No. 1, 620--648 (2022; Zbl 1493.65157) Full Text: DOI arXiv
Yi, Son-Young; Lee, Sanghyun; Zikatanov, Ludmil Locking-free enriched Galerkin method for linear elasticity. (English) Zbl 1483.65195 SIAM J. Numer. Anal. 60, No. 1, 52-75 (2022). MSC: 65N30 65N55 65F08 65F10 35B45 74B10 74S05 35Q74 PDFBibTeX XMLCite \textit{S.-Y. Yi} et al., SIAM J. Numer. Anal. 60, No. 1, 52--75 (2022; Zbl 1483.65195) Full Text: DOI
Budisa, Ana; Hu, Xiaozhe; Kuchta, Miroslav; Mardal, Kent-Andre; Zikatanov, Ludmil HAZniCS – Software Components for Multiphysics Problems. arXiv:2210.13274 Preprint, arXiv:2210.13274 [math.NA] (2022). MSC: 65-04 65N55 65F08 65H10 BibTeX Cite \textit{A. Budisa} et al., ``HAZniCS -- Software Components for Multiphysics Problems'', Preprint, arXiv:2210.13274 [math.NA] (2022) Full Text: arXiv OA License
Wu, Simo; Liu, Chun; Zikatanov, Ludmil Energetic stable discretization for non-isothermal electrokinetics model. (English) Zbl 07508488 J. Comput. Phys. 425, Article ID 109889, 17 p. (2021). MSC: 80-XX 82-XX PDFBibTeX XMLCite \textit{S. Wu} et al., J. Comput. Phys. 425, Article ID 109889, 17 p. (2021; Zbl 07508488) Full Text: DOI arXiv
Hu, Xiaozhe; Wu, Kaiyi; Zikatanov, Ludmil T. A posteriori error estimates for multilevel methods for graph Laplacians. (English) Zbl 1481.65257 SIAM J. Sci. Comput. 43, No. 5, S727-S742 (2021). MSC: 65N55 65K10 65F10 05C50 PDFBibTeX XMLCite \textit{X. Hu} et al., SIAM J. Sci. Comput. 43, No. 5, S727--S742 (2021; Zbl 1481.65257) Full Text: DOI arXiv
Adler, James H.; Cavanaugh, Casey; Hu, Xiaozhe; Zikatanov, Ludmil T. A finite-element framework for a mimetic finite-difference discretization of Maxwell’S equations. (English) Zbl 1470.35348 SIAM J. Sci. Comput. 43, No. 4, A2638-A2659 (2021). MSC: 35Q61 65M60 65M06 65F08 65Z05 78A25 PDFBibTeX XMLCite \textit{J. H. Adler} et al., SIAM J. Sci. Comput. 43, No. 4, A2638--A2659 (2021; Zbl 1470.35348) Full Text: DOI arXiv
Wang, Chunmei; Zikatanov, Ludmil Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations. (English) Zbl 1467.65114 J. Comput. Appl. Math. 394, Article ID 113543, 18 p. (2021). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N15 65N12 74N20 35B45 35J50 35J35 PDFBibTeX XMLCite \textit{C. Wang} and \textit{L. Zikatanov}, J. Comput. Appl. Math. 394, Article ID 113543, 18 p. (2021; Zbl 1467.65114) Full Text: DOI arXiv
Li, Yuwen; Zikatanov, Ludmil A posteriori error estimates of finite element methods by preconditioning. (English) Zbl 1524.65840 Comput. Math. Appl. 91, 192-201 (2021). MSC: 65N30 65N15 35J25 65N50 65F10 65F08 35A15 65M55 PDFBibTeX XMLCite \textit{Y. Li} and \textit{L. Zikatanov}, Comput. Math. Appl. 91, 192--201 (2021; Zbl 1524.65840) Full Text: DOI arXiv
Urschel, John C.; Zikatanov, Ludmil T. Discrete trace theorems and energy minimizing spring embeddings of planar graphs. (English) Zbl 1458.05158 Linear Algebra Appl. 609, 73-107 (2021). MSC: 05C50 05C10 05C40 05C62 05C85 15A18 PDFBibTeX XMLCite \textit{J. C. Urschel} and \textit{L. T. Zikatanov}, Linear Algebra Appl. 609, 73--107 (2021; Zbl 1458.05158) Full Text: DOI arXiv
Batista, Juan; Hu, Xiaozhe; Zikatanov, Ludmil T. Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation. (English) Zbl 1446.65106 Comput. Math. Appl. 80, No. 2, 405-416 (2020). MSC: 65M60 65N30 65M06 65F10 65F08 76S05 35Q35 PDFBibTeX XMLCite \textit{J. Batista} et al., Comput. Math. Appl. 80, No. 2, 405--416 (2020; Zbl 1446.65106) Full Text: DOI
Adler, J. H.; Gaspar, F. J.; Hu, X.; Ohm, P.; Rodrigo, C.; Zikatanov, L. T. Robust preconditioners for a new stabilized discretization of the poroelastic equations. (English) Zbl 1448.65145 SIAM J. Sci. Comput. 42, No. 3, B761-B791 (2020). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M55 65M60 65F22 65F08 74F10 76S05 PDFBibTeX XMLCite \textit{J. H. Adler} et al., SIAM J. Sci. Comput. 42, No. 3, B761--B791 (2020; Zbl 1448.65145) Full Text: DOI arXiv
Li, Yuwen; Zikatanov, Ludmil T. Nodal auxiliary a posteriori error estimates. arXiv:2010.06774 Preprint, arXiv:2010.06774 [math.NA] (2020). MSC: 65N30 65N12 BibTeX Cite \textit{Y. Li} and \textit{L. T. Zikatanov}, ``Nodal auxiliary a posteriori error estimates'', Preprint, arXiv:2010.06774 [math.NA] (2020) Full Text: arXiv OA License
Wu, Shuonan; Zikatanov, Ludmil T. On the unisolvence for the quasi-polynomial spaces of differential forms. arXiv:2003.14278 Preprint, arXiv:2003.14278 [math.NA] (2020). MSC: 65N30 65N12 BibTeX Cite \textit{S. Wu} and \textit{L. T. Zikatanov}, ``On the unisolvence for the quasi-polynomial spaces of differential forms'', Preprint, arXiv:2003.14278 [math.NA] (2020) Full Text: arXiv OA License
Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. On the validity of the local Fourier analysis. (English) Zbl 1449.65374 J. Comput. Math. 37, No. 3, 340-348 (2019). MSC: 65T50 65N55 PDFBibTeX XMLCite \textit{C. Rodrigo} et al., J. Comput. Math. 37, No. 3, 340--348 (2019; Zbl 1449.65374) Full Text: DOI arXiv
Hu, Xiaozhe; Lin, Junyuan; Zikatanov, Ludmil T. An adaptive multigrid method based on path cover. (English) Zbl 1428.65106 SIAM J. Sci. Comput. 41, No. 5, S220-S241 (2019). MSC: 65N55 65F10 65F35 PDFBibTeX XMLCite \textit{X. Hu} et al., SIAM J. Sci. Comput. 41, No. 5, S220--S241 (2019; Zbl 1428.65106) Full Text: DOI arXiv
Hu, Xiaozhe; Xu, Jinchao; Zikatanov, Ludmil T. Randomized and fault-tolerant method of subspace corrections. (English) Zbl 1433.65335 Res. Math. Sci. 6, No. 3, Paper No. 29, 15 p. (2019). MSC: 65N55 65F10 65N30 35J05 65C20 PDFBibTeX XMLCite \textit{X. Hu} et al., Res. Math. Sci. 6, No. 3, Paper No. 29, 15 p. (2019; Zbl 1433.65335) Full Text: DOI arXiv
Gaspar, Francisco J.; Rodrigo, Carmen; Hu, Xiaozhe; Ohm, Peter; Adler, James; Zikatanov, Ludmil New stabilized discretizations for poroelasticity equations. (English) Zbl 1422.65256 Nikolov, Geno (ed.) et al., Numerical methods and applications. 9th international conference, NMA 2018, Borovets, Bulgaria, August 20–24, 2018. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 11189, 3-14 (2019). MSC: 65M60 76S05 76D07 65M06 74F10 76M10 74B10 PDFBibTeX XMLCite \textit{F. J. Gaspar} et al., Lect. Notes Comput. Sci. 11189, 3--14 (2019; Zbl 1422.65256) Full Text: DOI Link
Deutsch, Frank; Hundal, Hein; Zikatanov, Ludmil Some applications of the Hahn-Banach separation theorem. (English) Zbl 1485.46080 Appl. Anal. Optim. 2, No. 2, 199-218 (2018). MSC: 46N10 41A65 52A27 PDFBibTeX XMLCite \textit{F. Deutsch} et al., Appl. Anal. Optim. 2, No. 2, 199--218 (2018; Zbl 1485.46080) Full Text: arXiv Link
Adler, J. H.; Lashuk, I.; MacLachlan, S. P.; Zikatanov, L. T. Discrete energy laws for the first-order system least-squares finite-element approach. (English) Zbl 1476.65233 Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 11th international conference, LSSC 2017, Sozopol, Bulgaria, June 5–9, 2017. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10665, 3-20 (2018). MSC: 65M60 PDFBibTeX XMLCite \textit{J. H. Adler} et al., Lect. Notes Comput. Sci. 10665, 3--20 (2018; Zbl 1476.65233) Full Text: DOI arXiv
Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil T. Robust block preconditioners for Biot’s model. (English) Zbl 1442.65342 Bjørstad, Petter E. (ed.) et al., Domain decomposition methods in science and engineering XXIV. Proceedings of the 24th international conference, Svalbard, Norway, February 6–10, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 125, 3-16 (2018). MSC: 65N30 65M22 76S05 74B10 74F10 65F10 65F08 76M10 74S05 35Q35 35Q74 PDFBibTeX XMLCite \textit{J. H. Adler} et al., Lect. Notes Comput. Sci. Eng. 125, 3--16 (2018; Zbl 1442.65342) Full Text: DOI arXiv Link
Rodrigo, C.; Hu, X.; Ohm, P.; Adler, J. H.; Gaspar, F. J.; Zikatanov, L. T. New stabilized discretizations for poroelasticity and the Stokes’ equations. (English) Zbl 1440.76027 Comput. Methods Appl. Mech. Eng. 341, 467-484 (2018). MSC: 76D07 65M12 76M10 65M60 74F10 76S05 PDFBibTeX XMLCite \textit{C. Rodrigo} et al., Comput. Methods Appl. Mech. Eng. 341, 467--484 (2018; Zbl 1440.76027) Full Text: DOI arXiv Link
Xu, Wenfang; Zikatanov, Ludmil T. Adaptive aggregation on graphs. (English) Zbl 1432.65178 J. Comput. Appl. Math. 340, 718-730 (2018). MSC: 65N55 65N30 35R02 PDFBibTeX XMLCite \textit{W. Xu} and \textit{L. T. Zikatanov}, J. Comput. Appl. Math. 340, 718--730 (2018; Zbl 1432.65178) Full Text: DOI arXiv
Zipp, Katherine Y.; Wu, Yangqingxiang; Wu, Kaiyi; Zikatanov, Ludmil T. Optimal spatial-dynamic management to minimize the damages caused by aquatic invasive species. arXiv:1809.05621 Preprint, arXiv:1809.05621 [q-bio.PE] (2018). BibTeX Cite \textit{K. Y. Zipp} et al., ``Optimal spatial-dynamic management to minimize the damages caused by aquatic invasive species'', Preprint, arXiv:1809.05621 [q-bio.PE] (2018) Full Text: arXiv OA License
Xu, Jinchao; Zikatanov, Ludmil Algebraic multigrid methods. (English) Zbl 1378.65182 Acta Numerica 26, 591-721 (2017). Reviewer: Constantin Popa (Constanţa) MSC: 65N55 65F10 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. Zikatanov}, Acta Numerica 26, 591--721 (2017; Zbl 1378.65182) Full Text: DOI arXiv
Adler, J. H.; Hu, X.; Zikatanov, L. T. Robust solvers for Maxwell’s equations with dissipative boundary conditions. (English) Zbl 1395.65067 SIAM J. Sci. Comput. 39, No. 5, S3-S23 (2017). MSC: 65M60 35Q61 65Z05 65F08 65F10 78M10 78A25 PDFBibTeX XMLCite \textit{J. H. Adler} et al., SIAM J. Sci. Comput. 39, No. 5, S3--S23 (2017; Zbl 1395.65067) Full Text: DOI arXiv
Hu, Xiaozhe; Urschel, John C.; Zikatanov, Ludmil T. On the approximation of Laplacian eigenvalues in graph disaggregation. (English) Zbl 1369.05135 Linear Multilinear Algebra 65, No. 9, 1805-1822 (2017). MSC: 05C50 05C85 65F15 65F08 68R10 PDFBibTeX XMLCite \textit{X. Hu} et al., Linear Multilinear Algebra 65, No. 9, 1805--1822 (2017; Zbl 1369.05135) Full Text: DOI arXiv
Antonietti, Paola F.; Sarti, Marco; Verani, Marco; Zikatanov, Ludmil T. A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1381.65091 J. Sci. Comput. 70, No. 2, 608-630 (2017). Reviewer: Carlos A. De Moura (São Joã del-Rei) MSC: 65N30 65F08 35J25 35J05 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., J. Sci. Comput. 70, No. 2, 608--630 (2017; Zbl 1381.65091) Full Text: DOI arXiv
Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T. A nonconforming finite element method for the Biot’s consolidation model in poroelasticity. (English) Zbl 1381.76175 J. Comput. Appl. Math. 310, 143-154 (2017). MSC: 76M10 65N30 65N12 74F10 76S05 PDFBibTeX XMLCite \textit{X. Hu} et al., J. Comput. Appl. Math. 310, 143--154 (2017; Zbl 1381.76175) Full Text: DOI arXiv
Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. Arbitrary dimension convection-diffusion schemes for space-time discretizations. (English) Zbl 1348.65139 J. Comput. Appl. Math. 310, 19-31 (2017). MSC: 65M60 35K20 PDFBibTeX XMLCite \textit{R. E. Bank} et al., J. Comput. Appl. Math. 310, 19--31 (2017; Zbl 1348.65139) Full Text: DOI arXiv
Xu, Jinchao; Zhang, Hongxuan; Zikatanov, Ludmil A unified approach to the design and analysis of AMG. arXiv:1705.07806 Preprint, arXiv:1705.07806 [math.NA] (2017). BibTeX Cite \textit{J. Xu} et al., ``A unified approach to the design and analysis of AMG'', Preprint, arXiv:1705.07806 [math.NA] (2017) Full Text: arXiv OA License
Xu, Jinchao; Zhang, Hongxuan; Zikatanov, Ludmil On the Weyl’s law for discretized elliptic operators. arXiv:1705.07803 Preprint, arXiv:1705.07803 [math.NA] (2017). BibTeX Cite \textit{J. Xu} et al., ``On the Weyl's law for discretized elliptic operators'', Preprint, arXiv:1705.07803 [math.NA] (2017) Full Text: arXiv OA License
Rodrigo, C.; Gaspar, F. J.; Hu, X.; Zikatanov, L. T. Stability and monotonicity for some discretizations of the Biot’s consolidation model. (English) Zbl 1425.74164 Comput. Methods Appl. Mech. Eng. 298, 183-204 (2016). MSC: 74F10 74S05 65N30 74B05 PDFBibTeX XMLCite \textit{C. Rodrigo} et al., Comput. Methods Appl. Mech. Eng. 298, 183--204 (2016; Zbl 1425.74164) Full Text: DOI arXiv
Urschel, John C.; Zikatanov, Ludmil T. On the maximal error of spectral approximation of graph bisection. (English) Zbl 1352.05120 Linear Multilinear Algebra 64, No. 10, 1972-1979 (2016). MSC: 05C50 05C40 68Q17 PDFBibTeX XMLCite \textit{J. C. Urschel} and \textit{L. T. Zikatanov}, Linear Multilinear Algebra 64, No. 10, 1972--1979 (2016; Zbl 1352.05120) Full Text: DOI arXiv
Kraus, Johannes; Lazarov, Raytcho; Lymbery, Maria; Margenov, Svetozar; Zikatanov, Ludmil Preconditioning heterogeneous \(\boldsymbol{H}(\mathrm{div})\) problems by additive Schur complement approximation and applications. (English) Zbl 1380.65376 SIAM J. Sci. Comput. 38, No. 2, A875-A898 (2016). MSC: 65N30 65F08 65N22 76M10 76S05 65F10 65N20 PDFBibTeX XMLCite \textit{J. Kraus} et al., SIAM J. Sci. Comput. 38, No. 2, A875--A898 (2016; Zbl 1380.65376) Full Text: DOI
Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. (English) Zbl 1338.76054 Numer. Math. 132, No. 1, 23-49 (2016). MSC: 76M10 74S05 65N30 65N55 74B05 76D07 PDFBibTeX XMLCite \textit{Q. Hong} et al., Numer. Math. 132, No. 1, 23--49 (2016; Zbl 1338.76054) Full Text: DOI
Urschel, John C.; Xu, Wenfang; Zikatanov, Ludmil T. Constructing Frequency Domains on Graphs in Near-Linear Time. arXiv:1609.04115 Preprint, arXiv:1609.04115 [math.NA] (2016). MSC: 05C50 05C85 15A18 94A12 BibTeX Cite \textit{J. C. Urschel} et al., ``Constructing Frequency Domains on Graphs in Near-Linear Time'', Preprint, arXiv:1609.04115 [math.NA] (2016) Full Text: arXiv OA License
Antonietti, Paola F.; Verani, Marco; Zikatanov, Ludmil A two-level method for mimetic finite difference discretizations of elliptic problems. (English) Zbl 1443.65279 Comput. Math. Appl. 70, No. 11, 2674-2687 (2015). MSC: 65N06 65N55 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Comput. Math. Appl. 70, No. 11, 2674--2687 (2015; Zbl 1443.65279) Full Text: DOI arXiv
Rodrigo, Carmen; Gaspar, F. J.; Hu, X.; Zikatanov, L. A finite element framework for some mimetic finite difference discretizations. (English) Zbl 1443.65285 Comput. Math. Appl. 70, No. 11, 2661-2673 (2015). MSC: 65N06 PDFBibTeX XMLCite \textit{C. Rodrigo} et al., Comput. Math. Appl. 70, No. 11, 2661--2673 (2015; Zbl 1443.65285) Full Text: DOI arXiv
Harizanov, Stanislav; Margenov, Svetozar; Zikatanov, Ludmil Fast constrained image segmentation using optimal spanning trees. (English) Zbl 1440.68317 Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 10th international conference, LSSC 2015, Sozopol, Bulgaria, June 8–12, 2015. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 9374, 15-29 (2015). MSC: 68U10 PDFBibTeX XMLCite \textit{S. Harizanov} et al., Lect. Notes Comput. Sci. 9374, 15--29 (2015; Zbl 1440.68317) Full Text: DOI
Urschel, John C.; Xu, Jinchao; Hu, Xiaozhe; Zikatanov, Ludmil T. A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians. (English) Zbl 1340.65262 J. Comput. Math. 33, No. 2, 209-226 (2015). MSC: 65N25 05C50 65N55 PDFBibTeX XMLCite \textit{J. C. Urschel} et al., J. Comput. Math. 33, No. 2, 209--226 (2015; Zbl 1340.65262) Full Text: DOI arXiv
de Dios, Blanca Ayuso; Zikatanov, Ludmil Space decompositions and solvers for discontinuous Galerkin methods. (English) Zbl 1382.65423 Erhel, Jocelyne (ed.) et al., Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Cham: Springer (ISBN 978-3-319-05788-0/hbk; 978-3-319-35548-1/pbk; 978-3-319-05789-7/ebook). Lecture Notes in Computational Science and Engineering 98, 3-15 (2014). MSC: 65N30 65N55 35J05 PDFBibTeX XMLCite \textit{B. A. de Dios} and \textit{L. Zikatanov}, Lect. Notes Comput. Sci. Eng. 98, 3--15 (2014; Zbl 1382.65423) Full Text: DOI arXiv
Vassilevski, Panayot S.; Zikatanov, Ludmil T. Commuting projections on graphs. (English) Zbl 1340.65062 Numer. Linear Algebra Appl. 21, No. 3, 297-315 (2014). MSC: 65F15 05C50 PDFBibTeX XMLCite \textit{P. S. Vassilevski} and \textit{L. T. Zikatanov}, Numer. Linear Algebra Appl. 21, No. 3, 297--315 (2014; Zbl 1340.65062) Full Text: DOI Link
Ayuso De Dios, Blanca; Brezzi, Franco; Marini, L. Donatella; Xu, Jinchao; Zikatanov, Ludmil A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. (English) Zbl 1299.76128 J. Sci. Comput. 58, No. 3, 517-547 (2014). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{B. Ayuso De Dios} et al., J. Sci. Comput. 58, No. 3, 517--547 (2014; Zbl 1299.76128) Full Text: DOI arXiv
Urschel, John C.; Zikatanov, Ludmil T. Spectral bisection of graphs and connectedness. (English) Zbl 1286.05101 Linear Algebra Appl. 449, 1-16 (2014). MSC: 05C50 PDFBibTeX XMLCite \textit{J. C. Urschel} and \textit{L. T. Zikatanov}, Linear Algebra Appl. 449, 1--16 (2014; Zbl 1286.05101) Full Text: DOI
Ayuso De Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. (English) Zbl 1296.65153 Math. Comput. 83, No. 287, 1083-1120 (2014). Reviewer: Pavel Burda (Praha) MSC: 65N30 65N55 65F08 35J25 35R05 PDFBibTeX XMLCite \textit{B. Ayuso De Dios} et al., Math. Comput. 83, No. 287, 1083--1120 (2014; Zbl 1296.65153) Full Text: DOI arXiv
Kraus, Johannes; Lazarov, Raytcho; Lymbery, Maria; Margenov, Svetozar; Zikatanov, Ludmil Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media. arXiv:1406.4455 Preprint, arXiv:1406.4455 [math.NA] (2014). MSC: 65F10 65N20 65N30 BibTeX Cite \textit{J. Kraus} et al., ``Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media'', Preprint, arXiv:1406.4455 [math.NA] (2014) Full Text: arXiv OA License
Yu, Guozhu; Xu, Jinchao; Zikatanov, Ludmil T. Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. (English) Zbl 1313.65324 Numer. Linear Algebra Appl. 20, No. 5, 832-851 (2013). Reviewer: Svetozar D. Margenov (Sofia) MSC: 65N55 65N30 35J05 65N50 65N12 PDFBibTeX XMLCite \textit{G. Yu} et al., Numer. Linear Algebra Appl. 20, No. 5, 832--851 (2013; Zbl 1313.65324) Full Text: DOI arXiv
Hu, Xiaozhe; Wu, Shuhong; Wu, Xiao-Hui; Xu, Jinchao; Zhang, Chen-Song; Zhang, Shiquan; Zikatanov, Ludmil Combined preconditioning with applications in reservoir simulation. (English) Zbl 1426.76269 Multiscale Model. Simul. 11, No. 2, 507-521 (2013). MSC: 76M10 76S05 65F10 PDFBibTeX XMLCite \textit{X. Hu} et al., Multiscale Model. Simul. 11, No. 2, 507--521 (2013; Zbl 1426.76269) Full Text: DOI arXiv
Ayuso De Dios, Blanca; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. (English) Zbl 1311.74108 ESAIM, Math. Model. Numer. Anal. 47, No. 5, 1315-1333 (2013). MSC: 74S05 74B05 65F10 65N22 65N30 PDFBibTeX XMLCite \textit{B. Ayuso De Dios} et al., ESAIM, Math. Model. Numer. Anal. 47, No. 5, 1315--1333 (2013; Zbl 1311.74108) Full Text: DOI arXiv
Deutsch, Frank; Hundal, Hein; Zikatanov, Ludmil Visible points in convex sets and best approximation. (English) Zbl 1298.52009 Bailey, David H. (ed.) et al., Computational and analytical mathematics. In Honor of Jonathan Borwein’s 60th birthday. Selected papers based on the presentations at the workshop, also known as JonFest, Simon Fraser University, BC, Canada, May 16–20, 2011. New York, NY: Springer (ISBN 978-1-4614-7620-7/hbk; 978-1-4614-7621-4/ebook). Springer Proceedings in Mathematics & Statistics 50, 349-364 (2013). Reviewer: Alexey Alimov (Moskva) MSC: 52A30 52A27 52A05 PDFBibTeX XMLCite \textit{F. Deutsch} et al., Springer Proc. Math. Stat. 50, 349--364 (2013; Zbl 1298.52009) Full Text: DOI arXiv
Adler, J. H.; Petkov, V.; Zikatanov, L. T. Numerical approximation of asymptotically disappearing solutions of Maxwell’s equations. (English) Zbl 1285.65075 SIAM J. Sci. Comput. 35, No. 5, S386-S401 (2013). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 65N30 35Q61 78M10 78M20 78A46 65N06 78A25 PDFBibTeX XMLCite \textit{J. H. Adler} et al., SIAM J. Sci. Comput. 35, No. 5, S386--S401 (2013; Zbl 1285.65075) Full Text: DOI arXiv
Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs. (English) Zbl 1275.65084 Iliev, Oleg P. (ed.) et al., Numerical solution of partial differential equations: Theory, algorithms, and their applications. Papers based on the international symposium, Sozopol, Bulgaria, June 7–8, 2013. In Honor of Professor Raytcho Lazarov’s 40 years of research in computational methods and applied mathematics and on the occasion of his 70th birthday. New York, NY: Springer (ISBN 978-1-4614-7171-4/hbk; 978-1-4614-7172-1/ebook). Springer Proceedings in Mathematics & Statistics 45, 81-102 (2013). MSC: 65N55 35J05 65Y05 65F50 65F10 PDFBibTeX XMLCite \textit{J. Brannick} et al., Springer Proc. Math. Stat. 45, 81--102 (2013; Zbl 1275.65084) Full Text: DOI arXiv
Brannick, J.; Chen, Y.; Kraus, J.; Zikatanov, L. Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. (English) Zbl 1281.65152 SIAM J. Numer. Anal. 51, No. 3, 1805-1827 (2013). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65N55 65N30 65N15 65F08 05C85 35J05 65N06 PDFBibTeX XMLCite \textit{J. Brannick} et al., SIAM J. Numer. Anal. 51, No. 3, 1805--1827 (2013; Zbl 1281.65152) Full Text: DOI arXiv
Iliev, Oleg P. (ed.); Margenov, Svetozar D. (ed.); Minev, Peter D. (ed.); Vassilevski, Panayot S. (ed.); Zikatanov, Ludmil T. (ed.) Numerical solution of partial differential equations: Theory, algorithms, and their applications. Papers based on the international symposium, Sozopol, Bulgaria, June 7–8, 2013. In Honor of Professor Raytcho Lazarov’s 40 years of research in computational methods and applied mathematics and on the occasion of his 70th birthday. (English) Zbl 1269.65002 Springer Proceedings in Mathematics & Statistics 45. New York, NY: Springer (ISBN 978-1-4614-7171-4/hbk; 978-1-4614-7172-1/ebook). xii, 327 p. (2013). MSC: 65-06 65F10 65Mxx 65Nxx 65Z05 00B15 00B25 00B30 PDFBibTeX XMLCite \textit{O. P. Iliev} (ed.) et al., Numerical solution of partial differential equations: Theory, algorithms, and their applications. Papers based on the international symposium, Sozopol, Bulgaria, June 7--8, 2013. In Honor of Professor Raytcho Lazarov's 40 years of research in computational methods and applied mathematics and on the occasion of his 70th birthday. New York, NY: Springer (2013; Zbl 1269.65002) Full Text: DOI
Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmil Polynomial of best uniform approximation to \(1/x\) and smoothing in two-level methods. (English) Zbl 1284.65052 Comput. Methods Appl. Math. 12, No. 4, 448-468 (2012). MSC: 65F10 65N20 65N30 PDFBibTeX XMLCite \textit{J. Kraus} et al., Comput. Methods Appl. Math. 12, No. 4, 448--468 (2012; Zbl 1284.65052) Full Text: DOI arXiv Link
Brannick, James; Chen, Yao; Zikatanov, Ludmil An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching. (English) Zbl 1274.65314 Numer. Linear Algebra Appl. 19, No. 2, 279-295 (2012). MSC: 65N55 65F10 65N22 35J05 PDFBibTeX XMLCite \textit{J. Brannick} et al., Numer. Linear Algebra Appl. 19, No. 2, 279--295 (2012; Zbl 1274.65314) Full Text: DOI
Boyanova, P.; Georgiev, I.; Margenov, S.; Zikatanov, L. Multilevel preconditioning of graph-Laplacians: Polynomial approximation of the pivot blocks inverses. (English) Zbl 1258.65096 Math. Comput. Simul. 82, No. 10, 1964-1971 (2012). Reviewer: Ludwig Kohaupt (Berlin) MSC: 65N30 65F08 65N55 35J25 35Q30 PDFBibTeX XMLCite \textit{P. Boyanova} et al., Math. Comput. Simul. 82, No. 10, 1964--1971 (2012; Zbl 1258.65096) Full Text: DOI
Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids. (English) Zbl 1259.65190 SIAM J. Numer. Anal. 50, No. 3, 1675-1694 (2012). Reviewer: Angela Handlovičová (Bratislava) MSC: 65N55 65N30 35J25 35R05 65N12 PDFBibTeX XMLCite \textit{R. Scheichl} et al., SIAM J. Numer. Anal. 50, No. 3, 1675--1694 (2012; Zbl 1259.65190) Full Text: DOI Link
Lazarov, Raytcho D.; Zikatanov, Ludmil T. An exponential fitting scheme for general convection-diffusion equations on tetrahedral meshes. arXiv:1211.0869 Preprint, arXiv:1211.0869 [math.NA] (2012). MSC: 65N30 65N15 BibTeX Cite \textit{R. D. Lazarov} and \textit{L. T. Zikatanov}, ``An exponential fitting scheme for general convection-diffusion equations on tetrahedral meshes'', Preprint, arXiv:1211.0869 [math.NA] (2012) Full Text: arXiv OA License
Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T. Weak approximation properties of elliptic projections with functional constraints. (English) Zbl 1244.65215 Multiscale Model. Simul. 9, No. 4, 1677-1699 (2011). MSC: 65N55 65F10 35J25 PDFBibTeX XMLCite \textit{R. Scheichl} et al., Multiscale Model. Simul. 9, No. 4, 1677--1699 (2011; Zbl 1244.65215) Full Text: DOI Link
Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L. First-order system least squares and the energetic variational approach for two-phase flow. (English) Zbl 1408.76528 J. Comput. Phys. 230, No. 17, 6647-6663 (2011). MSC: 76T20 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{J. H. Adler} et al., J. Comput. Phys. 230, No. 17, 6647--6663 (2011; Zbl 1408.76528) Full Text: DOI arXiv
Ayuso, Blanca; Zikatanov, Ludmil T. A simple uniformly convergent iterative method for the non-symmetric incomplete interior penalty discontinuous Galerkin discretization. (English) Zbl 1217.65208 Huang, Yunqing (ed.) et al., Domain decomposition methods in science and engineering XIX. Selected papers based on the presentations at the 19th international conference on domain decoposition (DD19), Zhanjiajie, China, August 17–22, 2009. Berlin: Springer (ISBN 978-3-642-11303-1/hbk; 978-3-642-11304-8/ebook). Lecture Notes in Computational Science and Engineering 78, 335-342 (2011). MSC: 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{B. Ayuso} and \textit{L. T. Zikatanov}, Lect. Notes Comput. Sci. Eng. 78, 335--342 (2011; Zbl 1217.65208) Full Text: DOI
Ayuso, B.; Georgiev, I.; Kraus, J.; Zikatanov, L. A simple preconditioner for the SIPG discretization of linear elasticity equations. (English) Zbl 1317.65083 Dimov, Ivan (ed.) et al., Numerical methods and applications. 7th international conference, NMA 2010, Borovets, Bulgaria, August 20–24, 2010. Revised papers. Berlin: Springer (ISBN 978-3-642-18465-9/pbk). Lecture Notes in Computer Science 6046, 353-360 (2011). MSC: 65F08 65N30 74B05 PDFBibTeX XMLCite \textit{B. Ayuso} et al., Lect. Notes Comput. Sci. 6046, 353--360 (2011; Zbl 1317.65083) Full Text: DOI
de Dios, Blanca Ayuso; Lombardi, Ariel; Pietra, Paola; Zikatanov, Ludmil A Block Solver for the Exponentially Fitted IIPG-0 method. arXiv:1107.2831 Preprint, arXiv:1107.2831 [math.NA] (2011). MSC: 65F10 65N20 65N30 BibTeX Cite \textit{B. A. de Dios} et al., ``A Block Solver for the Exponentially Fitted IIPG-0 method'', Preprint, arXiv:1107.2831 [math.NA] (2011) Full Text: arXiv OA License
De Dios, Blanca Ayuso; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. arXiv:1107.2160 Preprint, arXiv:1107.2160 [math.NA] (2011). MSC: 65M55 65N55 65F08 BibTeX Cite \textit{B. A. De Dios} et al., ``Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients'', Preprint, arXiv:1107.2160 [math.NA] (2011) Full Text: arXiv OA License
Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L. Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. (English) Zbl 1205.65321 ETNA, Electron. Trans. Numer. Anal. 37, 276-295 (2010). MSC: 65N55 65N22 65F10 PDFBibTeX XMLCite \textit{J. Brannick} et al., ETNA, Electron. Trans. Numer. Anal. 37, 276--295 (2010; Zbl 1205.65321) Full Text: EuDML EMIS
Bacuta, C.; Mazzucato, A. L.; Nistor, V.; Zikatanov, L. Interface and mixed boundary value problems on \(n\)-dimensional polyhedral domains. (English) Zbl 1207.35117 Doc. Math. 15, 687-745 (2010). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35J25 58J32 52B70 51B25 35B65 PDFBibTeX XMLCite \textit{C. Bacuta} et al., Doc. Math. 15, 687--745 (2010; Zbl 1207.35117) Full Text: EuDML EMIS
Ayuso de Dios, Blanca; Zikatanov, Ludmil Uniformly convergent iterative methods for discontinuous Galerkin discretizations. (English) Zbl 1203.65242 J. Sci. Comput. 40, No. 1-3, 4-36 (2009). MSC: 65N30 65F08 65F10 65N22 PDFBibTeX XMLCite \textit{B. Ayuso de Dios} and \textit{L. Zikatanov}, J. Sci. Comput. 40, No. 1--3, 4--36 (2009; Zbl 1203.65242) Full Text: DOI arXiv
Zikatanov, L. T. Two-sided bounds on the convergence rate of two-level methods. (English) Zbl 1212.65503 Numer. Linear Algebra Appl. 15, No. 5, 439-454 (2008). MSC: 65N55 65F10 65N12 65N15 PDFBibTeX XMLCite \textit{L. T. Zikatanov}, Numer. Linear Algebra Appl. 15, No. 5, 439--454 (2008; Zbl 1212.65503) Full Text: DOI
Brannick, J. J.; Li, Hengguang; Zikatanov, L. T. Uniform convergence of the multigrid \(V\)-cycle on graded meshes for corner singularities. (English) Zbl 1212.65482 Numer. Linear Algebra Appl. 15, No. 2-3, 291-306 (2008). MSC: 65N55 65N30 35J05 65F10 65N12 PDFBibTeX XMLCite \textit{J. J. Brannick} et al., Numer. Linear Algebra Appl. 15, No. 2--3, 291--306 (2008; Zbl 1212.65482) Full Text: DOI
Shu, Shi; Babuška, Ivo; Xiao, Yingxiong; Xu, Jinchao; Zikatanov, Ludmil Multilevel preconditioning methods for discrete models of lattice block materials. (English) Zbl 1404.74046 SIAM J. Sci. Comput. 31, No. 1, 687-707 (2008). MSC: 74G15 65F10 74K99 PDFBibTeX XMLCite \textit{S. Shu} et al., SIAM J. Sci. Comput. 31, No. 1, 687--707 (2008; Zbl 1404.74046) Full Text: DOI
Wu, Jinbiao; Lee, Youngju; Xu, Jinchao; Zikatanov, Ludmil Convergence analysis of iterative methods for semidefinite systems. (English) Zbl 1174.65013 J. Comput. Math. 26, No. 6, 797-815 (2008). MSC: 65F10 65N55 PDFBibTeX XMLCite \textit{J. Wu} et al., J. Comput. Math. 26, No. 6, 797--815 (2008; Zbl 1174.65013)
Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil New estimates for the rate of convergence of the method of subspace corrections. (English) Zbl 1174.65354 Numer. Math., Theory Methods Appl. 1, No. 1, 44-56 (2008). MSC: 65F10 65F35 65Y05 PDFBibTeX XMLCite \textit{D. Cho} et al., Numer. Math., Theory Methods Appl. 1, No. 1, 44--56 (2008; Zbl 1174.65354)
Dobrev, Veselin A.; Lazarov, Raytcho D.; Zikatanov, Ludmil T. Predictioning of symmetric interior penalty discontinuous Galerkin FEM for elliptic problems. (English) Zbl 1267.65194 Langer, Ulrich (ed.) et al., Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Berlin: Springer (ISBN 978-3-540-75198-4/pbk). Lecture Notes in Computational Science and Engineering 60, 33-44 (2008). MSC: 65N55 PDFBibTeX XMLCite \textit{V. A. Dobrev} et al., Lect. Notes Comput. Sci. Eng. 60, 33--44 (2008; Zbl 1267.65194)
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil A sharp convergence estimate for the method of subspace corrections for singular systems of equations. (English) Zbl 1137.65058 Math. Comput. 77, No. 262, 831-850 (2008). Reviewer: Erwin Schechter (Moers) MSC: 65N12 65J10 65N55 65N30 35J05 74B05 74S05 47A50 PDFBibTeX XMLCite \textit{Y.-J. Lee} et al., Math. Comput. 77, No. 262, 831--850 (2008; Zbl 1137.65058) Full Text: DOI
Cho, D.; Zikatanov, L. A multilevel precondition for generalized finite element method problems on unstructured simplicial meshes. (English) Zbl 1156.65095 J. Numer. Math. 15, No. 3, 163-180 (2007). Reviewer: Constantin Popa (Constanţa) MSC: 65N30 65N55 65F35 35J25 65F10 PDFBibTeX XMLCite \textit{D. Cho} and \textit{L. Zikatanov}, J. Numer. Math. 15, No. 3, 163--180 (2007; Zbl 1156.65095)
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil Robust subspace correction methods for nearly singular systems. (English) Zbl 1151.65096 Math. Models Methods Appl. Sci. 17, No. 11, 1937-1963 (2007). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N55 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{Y.-J. Lee} et al., Math. Models Methods Appl. Sci. 17, No. 11, 1937--1963 (2007; Zbl 1151.65096) Full Text: DOI
Ryham, Rolf; Liu, Chun; Zikatanov, Ludmil Mathematical models for the deformation of electrolyte droplets. (English) Zbl 1147.35343 Discrete Contin. Dyn. Syst., Ser. B 8, No. 3, 649-661 (2007). MSC: 35Q35 35Q30 76W05 76M10 76M30 PDFBibTeX XMLCite \textit{R. Ryham} et al., Discrete Contin. Dyn. Syst., Ser. B 8, No. 3, 649--661 (2007; Zbl 1147.35343) Full Text: DOI
Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. Improving the rate of convergence of high-order finite elements on polyhedra. II: mesh refinements and interpolation. (English) Zbl 1122.65109 Numer. Funct. Anal. Optimization 28, No. 7-8, 775-824 (2007). MSC: 65N30 35J05 35A35 65N15 65N50 PDFBibTeX XMLCite \textit{C. Bacuta} et al., Numer. Funct. Anal. Optim. 28, No. 7--8, 775--824 (2007; Zbl 1122.65109) Full Text: DOI Link
Dobrev, Veselin A.; Lazarov, Raytcho D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. (English) Zbl 1224.65263 Numer. Linear Algebra Appl. 13, No. 9, 753-770 (2006). Reviewer: Vít Dolejší (Praha) MSC: 65N30 65N22 65F10 65F08 35J25 PDFBibTeX XMLCite \textit{V. A. Dobrev} et al., Numer. Linear Algebra Appl. 13, No. 9, 753--770 (2006; Zbl 1224.65263) Full Text: DOI
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil On the convergence of iterative methods for semidefinite linear systems. (English) Zbl 1122.65033 SIAM J. Matrix Anal. Appl. 28, No. 3, 634-641 (2006). Reviewer: Dietrich Braess (Bochum) MSC: 65F10 65N22 PDFBibTeX XMLCite \textit{Y.-J. Lee} et al., SIAM J. Matrix Anal. Appl. 28, No. 3, 634--641 (2006; Zbl 1122.65033) Full Text: DOI
Vassilevski, Panayot S.; Zikatanov, Ludmil T. Multiple vector preserving interpolation mappings in algebraic multigrid. (English) Zbl 1102.65040 SIAM J. Matrix Anal. Appl. 27, No. 4, 1040-1055 (2006). MSC: 65F10 65N30 35J25 65N55 65F50 PDFBibTeX XMLCite \textit{P. S. Vassilevski} and \textit{L. T. Zikatanov}, SIAM J. Matrix Anal. Appl. 27, No. 4, 1040--1055 (2006; Zbl 1102.65040) Full Text: DOI Link
Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T. On two-grid convergence estimates. (English) Zbl 1164.65343 Numer. Linear Algebra Appl. 12, No. 5-6, 471-494 (2005). Reviewer: Jan Chleboun (Praha) MSC: 65F10 65F35 PDFBibTeX XMLCite \textit{R. D. Falgout} et al., Numer. Linear Algebra Appl. 12, No. 5--6, 471--494 (2005; Zbl 1164.65343) Full Text: DOI
Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil T. Improving the rate of convergence of high-order finite elements on polyhedra. I: A priori estimates. (English) Zbl 1121.35031 Numer. Funct. Anal. Optimization 26, No. 6, 613-639 (2005). Reviewer: Nicolae Pop (Baia Mare) MSC: 35J05 65N15 65N30 35A35 35B35 35J55 PDFBibTeX XMLCite \textit{C. Bacuta} et al., Numer. Funct. Anal. Optim. 26, No. 6, 613--639 (2005; Zbl 1121.35031) Full Text: DOI
Bacuta, C.; Chen, J.; Huang, Y.; Xu, J.; Zikatanov, L. Partition of unity method on nonmatching grids for the Stokes problem. (English) Zbl 1148.76305 J. Numer. Math. 13, No. 3, 157-169 (2005). MSC: 76D07 65N30 65N12 76M10 PDFBibTeX XMLCite \textit{C. Bacuta} et al., J. Numer. Math. 13, No. 3, 157--169 (2005; Zbl 1148.76305) Full Text: DOI
Băcuţă, Constantin; Nistor, Victor; Zikatanov, Ludmil T. Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps. (English) Zbl 1116.65119 Numer. Math. 100, No. 2, 165-184 (2005). Reviewer: Nedyu Popivanov (Sofia) MSC: 65N30 35J05 65N12 PDFBibTeX XMLCite \textit{C. Băcuţă} et al., Numer. Math. 100, No. 2, 165--184 (2005; Zbl 1116.65119) Full Text: DOI
Xu, Jinchao; Zikatanov, Ludmil On an energy minimizing basis for algebraic multigrid methods. (English) Zbl 1077.65130 Comput. Vis. Sci. 7, No. 3-4, 121-127 (2004). Reviewer: Jan Mandel (Denver) MSC: 65N55 65F10 35J25 65N30 65N12 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. Zikatanov}, Comput. Vis. Sci. 7, No. 3--4, 121--127 (2004; Zbl 1077.65130) Full Text: DOI
Kim, Hwanho; Xu, Jinchao; Zikatanov, Ludmil Uniformly convergent multigrid methods for convection–diffusion problems without any constraint on coarse grids. (English) Zbl 1039.65090 Adv. Comput. Math. 20, No. 4, 385-399 (2004). MSC: 65N55 65N15 35J25 65F10 65F35 65N12 65N30 PDFBibTeX XMLCite \textit{H. Kim} et al., Adv. Comput. Math. 20, No. 4, 385--399 (2004; Zbl 1039.65090) Full Text: DOI
Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil Regularity and well posedness for the Laplace operator on polyhedral domains. arXiv:math/0410207 Preprint, arXiv:math/0410207 [math.AP] (2004). BibTeX Cite \textit{C. Bacuta} et al., ``Regularity and well posedness for the Laplace operator on polyhedral domains'', Preprint, arXiv:math/0410207 [math.AP] (2004) Full Text: arXiv
Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil A multigrid method based on graph matching for convection-diffusion equations. (English) Zbl 1071.65167 Numer. Linear Algebra Appl. 10, No. 1-2, 181-195 (2003). Reviewer: Josef Dalík (Brno) MSC: 65N55 65N12 PDFBibTeX XMLCite \textit{H. Kim} et al., Numer. Linear Algebra Appl. 10, No. 1--2, 181--195 (2003; Zbl 1071.65167) Full Text: DOI
Xu, Jinchao; Zikatanov, Ludmil Some observations on Babuška and Brezzi theories. (English) Zbl 1028.65115 Numer. Math. 94, No. 1, 195-202 (2003). Reviewer: Dietrich Braess (Bochum) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. Zikatanov}, Numer. Math. 94, No. 1, 195--202 (2003; Zbl 1028.65115) Full Text: DOI
Shu, Shi; Xu, Jinchao; Xiao, Yingxiong; Zikatanov, Ludmil Algebraic multigrid method on lattice block materials. (English) Zbl 1060.74068 Chan, Tony F. (ed.) et al., Recent progress in computational and applied PDEs. Conference proceedings for the international conference held in Zhangjiajie, China, July 1–7, 2001. New York, NY: Kluwer Academic / Plenum Publishers (ISBN 0-306-47420-4/hbk). 289-307 (2002). MSC: 74S30 74K10 74S05 65F10 PDFBibTeX XMLCite \textit{S. Shu} et al., in: Recent progress in computational and applied PDEs. Conference proceedings for the international conference held in Zhangjiajie, China, July 1--7, 2001. New York, NY: Kluwer Academic / Plenum Publishers. 289--307 (2002; Zbl 1060.74068)