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
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
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
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
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
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
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
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
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
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
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. 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
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
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)
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)
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
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
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)
Xu, Jinchao; Zikatanov, Ludmil T. On multigrid methods for generalized finite element methods. (English) Zbl 1012.65131 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations. International workshop, Univ. Bonn, Germany, September 11-14, 2001. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 26, 401-418 (2002). MSC: 65N55 65N30 65F10 65N12 35J05 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. T. Zikatanov}, Lect. Notes Comput. Sci. Eng. 26, 401--418 (2002; Zbl 1012.65131)
Xu, Jinchao; Zikatanov, Ludmil The method of alternating projections and the method of subspace corrections in Hilbert space. (English) Zbl 0999.47015 J. Am. Math. Soc. 15, No. 3, 573-597 (2002). Reviewer: F.H.Vasilescu (Villeneuve d’Ascq) MSC: 47A58 47N10 47N40 49M20 65F10 65J05 65N22 65N55 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. Zikatanov}, J. Am. Math. Soc. 15, No. 3, 573--597 (2002; Zbl 0999.47015) Full Text: DOI
Lirkov, I. D.; Margenov, S. D.; Zikatanov, L. T. Circulant block-factorization preconditioning of anisotropic elliptic problems. (English) Zbl 0879.65022 Computing 58, No. 3, 245-258 (1997). Reviewer: V.V.Kobkov (Novosibirsk) MSC: 65F10 65N06 65N30 65F35 35J25 PDFBibTeX XMLCite \textit{I. D. Lirkov} et al., Computing 58, No. 3, 245--258 (1997; Zbl 0879.65022) Full Text: DOI