Liu, Lulu; Hwang, Feng-Nan; Luo, Li; Cai, Xiao-Chuan; Keyes, David E. A nonlinear elimination preconditioned inexact Newton algorithm. (English) Zbl 1492.65144 SIAM J. Sci. Comput. 44, No. 3, A1579-A1605 (2022). MSC: 65H20 65N06 65N22 65Y05 76H05 PDFBibTeX XMLCite \textit{L. Liu} et al., SIAM J. Sci. Comput. 44, No. 3, A1579--A1605 (2022; Zbl 1492.65144) Full Text: DOI
Luo, Li; Cai, Xiao-Chuan; Keyes, David E. Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. (English) Zbl 1490.65203 SIAM J. Sci. Comput. 43, No. 5, S317-S344 (2021). MSC: 65M60 65M22 65Y05 76S05 76T06 PDFBibTeX XMLCite \textit{L. Luo} et al., SIAM J. Sci. Comput. 43, No. 5, S317--S344 (2021; Zbl 1490.65203) Full Text: DOI
Luo, Li; Cai, Xiao-Chuan; Keyes, David E. Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. (English) Zbl 1469.76063 SIAM J. Sci. Comput. 43, No. 3, S317-S344 (2021). Reviewer: J. Manimaran (Ponda) MSC: 76M10 76S05 76T30 65Y05 PDFBibTeX XMLCite \textit{L. Luo} et al., SIAM J. Sci. Comput. 43, No. 3, S317--S344 (2021; Zbl 1469.76063) Full Text: DOI
Luo, Li; Chen, Rongliang; Cai, Xiao-Chuan; Keyes, David E. A nonlinear elimination preconditioned inexact Newton algorithm for steady state incompressible flow problems on 3D unstructured meshes. (English) Zbl 1502.65248 Haynes, Ronald (ed.) et al., Domain decomposition methods in science and engineering XXV. Selected papers based on the presentations at the 25th international conference on domain decomposition methods, Memorial University of Newfoundland, in St. John’s, Newfoundland and Labrador, Canada, July 23–27, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 138, 441-449 (2020). MSC: 65N55 65N22 65N30 65H10 65F08 65F10 65N12 65Y05 76D05 35Q30 PDFBibTeX XMLCite \textit{L. Luo} et al., Lect. Notes Comput. Sci. Eng. 138, 441--449 (2020; Zbl 1502.65248) Full Text: DOI
Luo, Li; Cai, Xiao-Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. (English) Zbl 1456.76104 SIAM J. Sci. Comput. 42, No. 6, B1404-B1428 (2020). MSC: 76M99 76D05 65N12 65N55 65Y05 PDFBibTeX XMLCite \textit{L. Luo} et al., SIAM J. Sci. Comput. 42, No. 6, B1404--B1428 (2020; Zbl 1456.76104) Full Text: DOI
Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E. Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. (English) Zbl 1435.76038 J. Comput. Phys. 409, Article ID 109312, 19 p. (2020). MSC: 76M10 76S05 76T06 65Y05 PDFBibTeX XMLCite \textit{L. Luo} et al., J. Comput. Phys. 409, Article ID 109312, 19 p. (2020; Zbl 1435.76038) Full Text: DOI
Lee, Chang-Ock (ed.); Cai, Xiao-Chuan (ed.); Keyes, David E. (ed.); Kim, Hyea Hyun (ed.); Klawonn, Axel (ed.); Park, Eun-Jae (ed.); Widlund, Olof B. (ed.) Domain decomposition methods in science and engineering XXIII. Proceedings of the 23rd international conference, Jeju Island, South Korea, July 6–10, 2015. (English) Zbl 1371.65003 Lecture Notes in Computational Science and Engineering 116. Cham: Springer (ISBN 978-3-319-52388-0/hbk; 978-3-319-52389-7/ebook). xviii, 415 p. (2017). MSC: 65-06 65M55 65N55 00B25 PDFBibTeX XMLCite \textit{C.-O. Lee} (ed.) et al., Domain decomposition methods in science and engineering XXIII. Proceedings of the 23rd international conference, Jeju Island, South Korea, July 6--10, 2015. Cham: Springer (2017; Zbl 1371.65003) Full Text: DOI
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David A parallel domain decomposition-based implicit method for the Cahn-Hilliard-cook phase-field equation in 3D. (English) Zbl 1351.76199 J. Comput. Phys. 285, 55-70 (2015). MSC: 76M20 65M06 65M22 76D27 82C26 PDFBibTeX XMLCite \textit{X. Zheng} et al., J. Comput. Phys. 285, 55--70 (2015; Zbl 1351.76199) Full Text: DOI
Yang, Chao; Cai, Xiao-Chuan; Keyes, David E.; Pernice, Michael NKS method for the implicit solution of a coupled Allen-Cahn/Cahn-Hilliard system. (English) Zbl 1465.35343 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. Lect. Notes Comput. Sci. Eng. 98, 819-827 (2014). MSC: 35Q35 65M06 PDFBibTeX XMLCite \textit{C. Yang} et al., Lect. Notes Comput. Sci. Eng. 98, 819--827 (2014; Zbl 1465.35343) Full Text: DOI
Tuminaro, Ray (ed.); Benzi, Michele (ed.); Cai, Xiao-Chuan (ed.); Duff, Iain (ed.); Elman, Howard (ed.); Freund, Roland (ed.); Jordan, Kirk (ed.); Kelley, Tim (ed.); Keyes, David (ed.); Kilmer, Misha (ed.); Leyffer, Sven (ed.); Manteuffel, Tom (ed.); McCormick, Steve (ed.); Silvester, David (ed.); Walker, Homer (ed.); Woodward, Carol (ed.); Yavneh, Irad (ed.) Special section: 2010 Copper Mountain conference. (English) Zbl 1231.00050 SIAM J. Sci. Comput. 33, No. 5, 2685 (2011). MSC: 00B25 65-06 PDFBibTeX XMLCite \textit{R. Tuminaro} (ed.) et al., SIAM J. Sci. Comput. 33, No. 5, 2685 (2011; Zbl 1231.00050) Full Text: DOI Link
Ovtchinnikov, S.; Dobrian, F.; Cai, X.-C.; Keyes, D. E. Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. (English) Zbl 1343.76049 J. Comput. Phys. 225, No. 2, 1919-1936 (2007). MSC: 76M25 76W05 76X05 PDFBibTeX XMLCite \textit{S. Ovtchinnikov} et al., J. Comput. Phys. 225, No. 2, 1919--1936 (2007; Zbl 1343.76049) Full Text: DOI
Cai, Xiao-Chuan; Keyes, David E.; Young, David P. A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. (English) Zbl 1201.76107 Debit, N. (ed.) et al., Domain decomposition methods in science and engineering. Papers of the thirteenth international conference on domain decomposition methods, Lyon, France, October 9–12, 2000. Barcelona: International Center for Numerical Methods in Engineering (CIMNE) (ISBN 84-95999-07-2/hbk). Theory Eng. Appl. Comput. Methods, 345-352 (2002). MSC: 76L05 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., in: Domain decomposition methods in science and engineering. XIII. Papers of the thirteenth international conference on domain decomposition methods, Lyon, France, October 9--12, 2000. Barcelona: International Center for Numerical Methods in Engineering (CIMNE). 345--352 (2002; Zbl 1201.76107)
Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. (English) Zbl 1025.76040 Int. J. Numer. Methods Fluids 40, No. 12, 1463-1470 (2002). MSC: 76M99 76D05 65N55 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., Int. J. Numer. Methods Fluids 40, No. 12, 1463--1470 (2002; Zbl 1025.76040) Full Text: DOI
Cai, Xiao-Chuan; Keyes, David E. Nonlinearly preconditioned inexact Newton algorithms. (English) Zbl 1015.65058 SIAM J. Sci. Comput. 24, No. 1, 183-200 (2002). Reviewer: Willi Schönauer (Karlsruhe) MSC: 65N06 65H10 65N55 76D05 65N12 65Y05 PDFBibTeX XMLCite \textit{X.-C. Cai} and \textit{D. E. Keyes}, SIAM J. Sci. Comput. 24, No. 1, 183--200 (2002; Zbl 1015.65058) Full Text: DOI
Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E. Additive Schwarz methods for hyperbolic equations. (English) Zbl 0909.65062 Mandel, Jan (ed.) et al., Domain decomposition methods 10. The 10th international conference, Boulder, CO, USA, August 10–14, 1997. Providence, RI: AMS, American Mathematical Society. Contemp. Math. 218, 468-476 (1998). MSC: 65M55 65M60 65M12 65Y05 35L45 65F10 65F35 PDFBibTeX XMLCite \textit{Y. Wu} et al., Contemp. Math. 218, 468--476 (1998; Zbl 0909.65062)
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. (English) Zbl 0917.76035 SIAM J. Sci. Comput. 19, No. 1, 246-265 (1998). Reviewer: S.Nocilla (Torino) MSC: 76M10 76H05 76G25 65N55 65Y05 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., SIAM J. Sci. Comput. 19, No. 1, 246--265 (1998; Zbl 0917.76035) Full Text: DOI
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. (English) Zbl 0838.65025 Numer. Linear Algebra Appl. 1, No. 5, 477-504 (1994). MSC: 65F10 65F35 65N06 65N55 35J25 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., Numer. Linear Algebra Appl. 1, No. 5, 477--504 (1994; Zbl 0838.65025) Full Text: DOI
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. Parallel implicit methods for aerodynamics. (English) Zbl 0818.76065 Keyes, David E. (ed.) et al., Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 180, 465-470 (1994). MSC: 76M25 76N10 65Y05 65N55 PDFBibTeX XMLCite \textit{X. C. Cai} et al., Contemp. Math. 180, 465--470 (1994; Zbl 0818.76065)
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. Newton-Krylov-Schwarz methods in CFD. (English) Zbl 0876.76059 Hebeker, Friedrich-Karl (ed.) et al., Numerical methods for the Navier-Stokes equations. Proceedings of the international workshop held, Heidelberg, Germany, October 25-28, 1993. Braunschweig: Vieweg. Notes Numer. Fluid Mech. 47, 17-30 (1994). MSC: 76M25 76N10 76R99 PDFBibTeX XMLCite \textit{X. C. Cai} et al., Notes Numer. Fluid Mech. 47, 17--30 (1994; Zbl 0876.76059)
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. (English) Zbl 0770.65079 Domain decomposition methods for partial differential equations, Proc. 5th Int. SIAM Symp., Norfolk/VA (USA) 1991, 224-235 (1992). MSC: 65N55 65F10 35J25 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., in: Fifth international SIAM symposium on domain decomposition methods for partial differential equations, held in Norfolk, Virginia, USA, May 6-8, 1991. Philadelphia, PA: SIAM. 224--235 (1992; Zbl 0770.65079)
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. Convergence rate estimate for a domain decomposition method. (English) Zbl 0727.65105 Numer. Math. 61, No. 2, 153-170 (1991). Reviewer: X.-C.Cai (Lexington, KY) MSC: 65N55 65N30 65F10 35J25 PDFBibTeX XMLCite \textit{X.-C. Cai} et al., Numer. Math. 61, No. 2, 153--170 (1991; Zbl 0727.65105) Full Text: DOI EuDML