Borthagaray, Juan Pablo; Nochetto, Ricardo H.; Wu, Shuonan; Xu, Jinchao Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains. (English) Zbl 1521.65123 Math. Comput. 92, No. 344, 2439-2473 (2023). MSC: 65N30 35R11 65F08 65N55 PDFBibTeX XMLCite \textit{J. P. Borthagaray} et al., Math. Comput. 92, No. 344, 2439--2473 (2023; Zbl 1521.65123) Full Text: DOI arXiv
Chen, Yuyan; Dong, Bin; Xu, Jinchao Meta-mgnet: meta multigrid networks for solving parameterized partial differential equations. (English) Zbl 07518081 J. Comput. Phys. 455, Article ID 110996, 26 p. (2022). MSC: 65Nxx 68Txx 76Mxx PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Phys. 455, Article ID 110996, 26 p. (2022; Zbl 07518081) Full Text: DOI arXiv
Hong, Qingguo; Li, Yuwen; Xu, Jinchao An extended Galerkin analysis in finite element exterior calculus. (English) Zbl 1492.65311 Math. Comput. 91, No. 335, 1077-1106 (2022). Reviewer: Zhiming Chen (Beijing) MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{Q. Hong} et al., Math. Comput. 91, No. 335, 1077--1106 (2022; Zbl 1492.65311) Full Text: DOI arXiv
Hu, Kaibo; Lee, Young-Ju; Xu, Jinchao Helicity-conservative finite element discretization for incompressible MHD systems. (English) Zbl 07513848 J. Comput. Phys. 436, Article ID 110284, 17 p. (2021). MSC: 65Nxx 76Mxx 76Wxx PDFBibTeX XMLCite \textit{K. Hu} et al., J. Comput. Phys. 436, Article ID 110284, 17 p. (2021; Zbl 07513848) Full Text: DOI arXiv
Hong, Qingguo; Hu, Jun; Ma, Limin; Xu, Jinchao New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor. (English) Zbl 1480.65336 Numer. Math. 149, No. 3, 645-678 (2021). MSC: 65N30 65N12 74B10 74S05 35Q74 PDFBibTeX XMLCite \textit{Q. Hong} et al., Numer. Math. 149, No. 3, 645--678 (2021; Zbl 1480.65336) Full Text: DOI arXiv
Chen, Shuangshuang; Hong, Qingguo; Xu, Jinchao; Yang, Kai Robust block preconditioners for poroelasticity. (English) Zbl 1506.74104 Comput. Methods Appl. Mech. Eng. 369, Article ID 113229, 20 p. (2020). MSC: 74F10 74S10 65F08 PDFBibTeX XMLCite \textit{S. Chen} et al., Comput. Methods Appl. Mech. Eng. 369, Article ID 113229, 20 p. (2020; Zbl 1506.74104) Full Text: DOI arXiv
Xiao, Yuanming; Xu, Jinchao; Wang, Fei High-order extended finite element methods for solving interface problems. (English) Zbl 1442.74243 Comput. Methods Appl. Mech. Eng. 364, Article ID 112964, 21 p. (2020). MSC: 74S05 65N30 74A50 PDFBibTeX XMLCite \textit{Y. Xiao} et al., Comput. Methods Appl. Mech. Eng. 364, Article ID 112964, 21 p. (2020; Zbl 1442.74243) Full Text: DOI arXiv
Xu, Jinchao; Li, Yukun; Wu, Shuonan; Bousquet, Arthur On the stability and accuracy of partially and fully implicit schemes for phase field modeling. (English) Zbl 1440.80003 Comput. Methods Appl. Mech. Eng. 345, 826-853 (2019). MSC: 80M10 65M60 80A22 PDFBibTeX XMLCite \textit{J. Xu} et al., Comput. Methods Appl. Mech. Eng. 345, 826--853 (2019; Zbl 1440.80003) 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
He, Juncai; Xu, Jinchao MgNet: a unified framework of multigrid and convolutional neural network. (English) Zbl 1476.65026 Sci. China, Math. 62, No. 7, 1331-1354 (2019). MSC: 65D19 65N55 68T07 68T30 PDFBibTeX XMLCite \textit{J. He} and \textit{J. Xu}, Sci. China, Math. 62, No. 7, 1331--1354 (2019; Zbl 1476.65026) Full Text: DOI arXiv
Hong, Qingguo; Wang, Fei; Wu, Shuonan; Xu, Jinchao A unified study of continuous and discontinuous Galerkin methods. (English) Zbl 1412.65214 Sci. China, Math. 62, No. 1, 1-32 (2019). MSC: 65N30 65N12 65N15 35J15 35J30 PDFBibTeX XMLCite \textit{Q. Hong} et al., Sci. China, Math. 62, No. 1, 1--32 (2019; Zbl 1412.65214) Full Text: DOI arXiv
Gong, Shihua; Wu, Shuonan; Xu, Jinchao New hybridized mixed methods for linear elasticity and optimal multilevel solvers. (English) Zbl 1412.65211 Numer. Math. 141, No. 2, 569-604 (2019). Reviewer: Jichun Li (Las Vegas) MSC: 65N30 65N55 74B10 PDFBibTeX XMLCite \textit{S. Gong} et al., Numer. Math. 141, No. 2, 569--604 (2019; Zbl 1412.65211) Full Text: DOI arXiv
Bousquet, Arthur; Hu, Xiaozhe; Metti, Maximilian S.; Xu, Jinchao Newton solvers for drift-diffusion and electrokinetic equations. (English) Zbl 1448.65151 SIAM J. Sci. Comput. 40, No. 3, B982-B1006 (2018). MSC: 65M60 65M15 65M12 65M50 65M20 35K61 35Q60 78M10 PDFBibTeX XMLCite \textit{A. Bousquet} et al., SIAM J. Sci. Comput. 40, No. 3, B982--B1006 (2018; Zbl 1448.65151) Full Text: DOI
Wu, Shuonan; Gong, Shihua; Xu, Jinchao Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor. (English) Zbl 1457.65222 Math. Models Methods Appl. Sci. 27, No. 14, 2711-2743 (2017). MSC: 65N30 65N15 74B10 35Q74 PDFBibTeX XMLCite \textit{S. Wu} et al., Math. Models Methods Appl. Sci. 27, No. 14, 2711--2743 (2017; Zbl 1457.65222) Full Text: DOI arXiv
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
Cui, Tao; Xu, Jinchao; Zhang, Chen-Song An error-resilient redundant subspace correction method. (English) Zbl 1364.65275 Comput. Vis. Sci. 18, No. 2-3, 65-77 (2017). MSC: 65N55 65N30 PDFBibTeX XMLCite \textit{T. Cui} et al., Comput. Vis. Sci. 18, No. 2--3, 65--77 (2017; Zbl 1364.65275) Full Text: DOI arXiv
Hu, Kaibo; Ma, Yicong; Xu, Jinchao Stable finite element methods preserving \(\nabla \cdot \boldsymbol{B}=0\) exactly for MHD models. (English) Zbl 1381.76174 Numer. Math. 135, No. 2, 371-396 (2017). MSC: 76M10 65M60 76W05 PDFBibTeX XMLCite \textit{K. Hu} et al., Numer. Math. 135, No. 2, 371--396 (2017; Zbl 1381.76174) Full Text: DOI arXiv
Li, Zheng; Wu, Shuhong; Xu, Jinchao; Zhang, Chensong Toward cost-effective reservoir simulation solvers on GPUs. (English) Zbl 1488.65264 Adv. Appl. Math. Mech. 8, No. 6, 971-991 (2016). MSC: 65M06 65K10 76S05 76T10 76M20 PDFBibTeX XMLCite \textit{Z. Li} et al., Adv. Appl. Math. Mech. 8, No. 6, 971--991 (2016; Zbl 1488.65264) Full Text: DOI
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao A two-grid SA-AMG convergence bound that improves when increasing the polynomial degree. (English) Zbl 1413.65062 Numer. Linear Algebra Appl. 23, No. 4, 746-771 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65M55 PDFBibTeX XMLCite \textit{X. Hu} et al., Numer. Linear Algebra Appl. 23, No. 4, 746--771 (2016; Zbl 1413.65062) Full Text: DOI
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun Energetically stable discretizations for charge transport and electrokinetic models. (English) Zbl 1351.78040 J. Comput. Phys. 306, 1-18 (2016). MSC: 78M10 65M60 65M20 78A48 PDFBibTeX XMLCite \textit{M. S. Metti} et al., J. Comput. Phys. 306, 1--18 (2016; Zbl 1351.78040) Full Text: DOI arXiv
Grasedyck, Lars; Wang, Lu; Xu, Jinchao A nearly optimal multigrid method for general unstructured grids. (English) Zbl 1356.65241 Numer. Math. 134, No. 3, 637-666 (2016). Reviewer: Marius Ghergu (Dublin) MSC: 65N55 65N30 65F08 35J25 65N50 65N12 PDFBibTeX XMLCite \textit{L. Grasedyck} et al., Numer. Math. 134, No. 3, 637--666 (2016; Zbl 1356.65241) Full Text: DOI arXiv
Xu, Jinchao; Zhang, Shuo Optimal finite element methods for interface problems. (English) Zbl 1339.65224 Dickopf, Thomas (ed.) et al., Domain decomposition methods in science and engineering XXII. Proceedings of the 22nd international conference on domain decomposition methods, Lugano, Switzerland, September 16–20, 2013. Cham: Springer (ISBN 978-3-319-18826-3/hbk; 978-3-319-18827-0/ebook). Lecture Notes in Computational Science and Engineering 104, 77-91 (2016). MSC: 65N30 PDFBibTeX XMLCite \textit{J. Xu} and \textit{S. Zhang}, Lect. Notes Comput. Sci. Eng. 104, 77--91 (2016; Zbl 1339.65224) Full Text: DOI
Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong Multilevel preconditioners for reaction-diffusion problems with discontinuous coefficients. (English) Zbl 1353.65131 J. Sci. Comput. 67, No. 1, 324-350 (2016). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65N55 65F08 65N30 35J25 35R05 65N12 PDFBibTeX XMLCite \textit{T. V. Kolev} et al., J. Sci. Comput. 67, No. 1, 324--350 (2016; Zbl 1353.65131) Full Text: DOI arXiv
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
Xu, Jinchao; Yang, Kai Well-posedness and robust preconditioners for discretized fluid-structure interaction systems. (English) Zbl 1423.74936 Comput. Methods Appl. Mech. Eng. 292, 69-91 (2015). MSC: 74S05 74F10 65F08 65M22 65M60 PDFBibTeX XMLCite \textit{J. Xu} and \textit{K. Yang}, Comput. Methods Appl. Mech. Eng. 292, 69--91 (2015; Zbl 1423.74936) Full Text: DOI arXiv
Trask, Nathaniel; Maxey, Martin; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Yang, Kai; Xu, Jinchao A scalable consistent second-order SPH solver for unsteady low Reynolds number flows. (English) Zbl 1423.76372 Comput. Methods Appl. Mech. Eng. 289, 155-178 (2015). MSC: 76M28 65M75 65M70 76D05 PDFBibTeX XMLCite \textit{N. Trask} et al., Comput. Methods Appl. Mech. Eng. 289, 155--178 (2015; Zbl 1423.76372) Full Text: DOI
Hu, Xiaozhe; Xu, Jinchao; Zhang, Chensong Application of auxiliary space preconditioning in field-scale reservoir simulation. (English) Zbl 1305.86001 Sci. China, Math. 56, No. 12, 2737-2751 (2013). MSC: 86-08 86A20 65N22 65F08 65N55 PDFBibTeX XMLCite \textit{X. Hu} et al., Sci. China, Math. 56, No. 12, 2737--2751 (2013; Zbl 1305.86001) Full Text: DOI
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
Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao Optimal multilevel methods for graded bisection grids. (English) Zbl 1235.65144 Numer. Math. 120, No. 1, 1-34 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65N55 65N22 65F10 65N30 PDFBibTeX XMLCite \textit{L. Chen} et al., Numer. Math. 120, No. 1, 1--34 (2012; Zbl 1235.65144) Full Text: DOI
Lee, Young-Ju; Xu, Jinchao; Zhang, Chen-Song Global existence, uniqueness and optimal solvers of discretized viscoelastic flow models. (English) Zbl 1225.76198 Math. Models Methods Appl. Sci. 21, No. 8, 1713-1732 (2011). MSC: 76M10 76A05 PDFBibTeX XMLCite \textit{Y.-J. Lee} et al., Math. Models Methods Appl. Sci. 21, No. 8, 1713--1732 (2011; Zbl 1225.76198) Full Text: DOI
Xu, Jinchao; Zhu, Yunrong Robust preconditioner for H(curl) interface problems. (English) Zbl 1217.78062 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, 173-180 (2011). MSC: 78M10 65N30 65F10 65F08 PDFBibTeX XMLCite \textit{J. Xu} and \textit{Y. Zhu}, Lect. Notes Comput. Sci. Eng. 78, 173--180 (2011; Zbl 1217.78062) Full Text: DOI
Sun, Pengtao; Chen, Long; Xu, Jinchao Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. (English) Zbl 1203.65261 J. Sci. Comput. 43, No. 1, 24-43 (2010). MSC: 65N30 PDFBibTeX XMLCite \textit{P. Sun} et al., J. Sci. Comput. 43, No. 1, 24--43 (2010; Zbl 1203.65261) Full Text: DOI
Cai, Mingchao; Mu, Mo; Xu, Jinchao Preconditioning techniques for a mixed Stokes/Darcy model in porous medium applications. (English) Zbl 1172.76023 J. Comput. Appl. Math. 233, No. 2, 346-355 (2009). MSC: 76M10 76S05 76D07 PDFBibTeX XMLCite \textit{M. Cai} et al., J. Comput. Appl. Math. 233, No. 2, 346--355 (2009; Zbl 1172.76023) Full Text: DOI
Xu, Jinchao; Zou, Qingsong Analysis of linear and quadratic simplicial finite volume methods for elliptic equations. (English) Zbl 1169.65110 Numer. Math. 111, No. 3, 469-492 (2009). Reviewer: Abdallah Bradji (Tebessa) MSC: 65N30 65N12 35J05 35J25 65N15 PDFBibTeX XMLCite \textit{J. Xu} and \textit{Q. Zou}, Numer. Math. 111, No. 3, 469--492 (2009; Zbl 1169.65110) Full Text: DOI
Xu, Jinchao; Zhu, Yunrong Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. (English) Zbl 1151.65097 Math. Models Methods Appl. Sci. 18, No. 1, 77-105 (2008). Reviewer: Dietrich Braess (Bochum) MSC: 65N55 65N30 65N12 65F10 65F35 35J25 35R05 PDFBibTeX XMLCite \textit{J. Xu} and \textit{Y. Zhu}, Math. Models Methods Appl. Sci. 18, No. 1, 77--105 (2008; Zbl 1151.65097) Full Text: DOI
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
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
Shu, S.; Sun, D.; Xu, J. An algebraic multigrid method for higher-order finite element discretizations. (English) Zbl 1127.65092 Computing 77, No. 4, 347-377 (2006). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N55 65N30 35J25 PDFBibTeX XMLCite \textit{S. Shu} et al., Computing 77, No. 4, 347--377 (2006; Zbl 1127.65092) Full Text: DOI
Shu, Shi; Xu, Jinchao; Yang, Ying; Yu, Haiyuan An algebraic multigrid method for finite element systems on criss-cross grids. (English) Zbl 1103.65128 Adv. Comput. Math. 25, No. 1-3, 287-304 (2006). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N55 65F10 65N30 PDFBibTeX XMLCite \textit{S. Shu} et al., Adv. Comput. Math. 25, No. 1--3, 287--304 (2006; Zbl 1103.65128) 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 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 The method of subspace corrections. (English) Zbl 0983.65133 J. Comput. Appl. Math. 128, No. 1-2, 335-362 (2001). Reviewer: M.Plum (Karlsruhe) MSC: 65N55 65H10 35J65 65N30 65N12 PDFBibTeX XMLCite \textit{J. Xu}, J. Comput. Appl. Math. 128, No. 1--2, 335--362 (2001; Zbl 0983.65133) Full Text: DOI