Liu, Lulu; Gao, Weiguo; Yu, Han; Keyes, David E. Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems. (English) Zbl 07807975 J. Comput. Phys. 496, Article ID 112548, 22 p. (2024). MSC: 65Nxx 65Fxx 65Hxx PDFBibTeX XMLCite \textit{L. Liu} et al., J. Comput. Phys. 496, Article ID 112548, 22 p. (2024; Zbl 07807975) Full Text: DOI
Yang, Haijian; Li, Rui; Yang, Chao Nonlinearly constrained pressure residual (NCPR) algorithms for fractured reservoir simulation. (English) Zbl 07805920 SIAM J. Sci. Comput. 46, No. 1, A561-A586 (2024). MSC: 76S05 65H10 65Y05 65F08 65N22 PDFBibTeX XMLCite \textit{H. Yang} et al., SIAM J. Sci. Comput. 46, No. 1, A561--A586 (2024; Zbl 07805920) Full Text: DOI
Shao, Baiqiang; Yang, Haijian; Zhao, Hong-Jie Scalable fully implicit methods for subsurface flows in porous media with fractional derivative. (English) Zbl 07674293 Comput. Math. Appl. 134, 55-65 (2023). MSC: 65M55 35R11 65H05 65K10 PDFBibTeX XMLCite \textit{B. Shao} et al., Comput. Math. Appl. 134, 55--65 (2023; Zbl 07674293) Full Text: DOI
Huynh, Ngoc Mai Monica Newton-Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model. (English) Zbl 1502.65101 Numer. Math. 152, No. 4, 841-879 (2022). MSC: 65M55 65M06 65H10 65F08 65F10 65Y05 65M12 92C30 92C37 92C50 PDFBibTeX XMLCite \textit{N. M. M. Huynh}, Numer. Math. 152, No. 4, 841--879 (2022; Zbl 1502.65101) Full Text: DOI arXiv
Huynh, Ngoc Mai Monica; Pavarino, Luca F.; Scacchi, Simone Scalable and robust dual-primal Newton-Krylov deluxe solvers for cardiac electrophysiology with biophysical ionic models. (English) Zbl 1507.65276 Vietnam J. Math. 50, No. 4, 1029-1052 (2022). Reviewer: Michael Jung (Dresden) MSC: 65N55 65M55 65M60 65M06 65N30 65H10 65F08 65F10 65Y05 92C30 35Q92 PDFBibTeX XMLCite \textit{N. M. M. Huynh} et al., Vietnam J. Math. 50, No. 4, 1029--1052 (2022; Zbl 1507.65276) Full Text: DOI
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
Dedner, Andreas; Klöfkorn, Robert Extendible and efficient Python framework for solving evolution equations with stabilized discontinuous Galerkin methods. (English) Zbl 1499.65490 Commun. Appl. Math. Comput. 4, No. 2, 657-696 (2022). MSC: 65M60 65N30 65M08 35Q31 35Q90 65D32 65M20 65L06 65H10 76N06 35Q35 PDFBibTeX XMLCite \textit{A. Dedner} and \textit{R. Klöfkorn}, Commun. Appl. Math. Comput. 4, No. 2, 657--696 (2022; Zbl 1499.65490) Full Text: DOI arXiv
Liu, Lulu; Keyes, David E. Approximate error bounds on solutions of nonlinearly preconditioned PDEs. (English) Zbl 1469.49028 SIAM J. Sci. Comput. 43, No. 4, A2526-A2554 (2021). MSC: 49M15 65H10 65H20 65N15 65N22 PDFBibTeX XMLCite \textit{L. Liu} and \textit{D. E. Keyes}, SIAM J. Sci. Comput. 43, No. 4, A2526--A2554 (2021; Zbl 1469.49028) Full Text: DOI
Farrell, Patrick E.; Croci, Matteo; Surowiec, Thomas M. Deflation for semismooth equations. (English) Zbl 1467.65067 Optim. Methods Softw. 35, No. 6, 1248-1271 (2020). MSC: 65K15 65P30 65H10 35M86 90C33 PDFBibTeX XMLCite \textit{P. E. Farrell} et al., Optim. Methods Softw. 35, No. 6, 1248--1271 (2020; Zbl 1467.65067) Full Text: DOI arXiv
Luo, Li; Shiu, Wen-Shin; Chen, Rongliang; Cai, Xiao-Chuan A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis. (English) Zbl 1453.65109 J. Comput. Phys. 399, Article ID 108926, 20 p. (2019). MSC: 65H10 76Z05 92C35 76M10 65M60 PDFBibTeX XMLCite \textit{L. Luo} et al., J. Comput. Phys. 399, Article ID 108926, 20 p. (2019; Zbl 1453.65109) Full Text: DOI Link
Yildirim, Anil; Kenway, Gaetan K. W.; Mader, Charles A.; Martins, Joaquim R. R. A. A Jacobian-free approximate Newton-Krylov startup strategy for RANS simulations. (English) Zbl 1453.76117 J. Comput. Phys. 397, Article ID 108741, 27 p. (2019). MSC: 76M12 76M20 76F55 65H10 PDFBibTeX XMLCite \textit{A. Yildirim} et al., J. Comput. Phys. 397, Article ID 108741, 27 p. (2019; Zbl 1453.76117) Full Text: DOI
Gong, Shihua; Cai, Xiao-Chuan A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity. (English) Zbl 1436.65065 SIAM J. Sci. Comput. 41, No. 5, S390-S408 (2019). MSC: 65H20 74S05 65Z05 PDFBibTeX XMLCite \textit{S. Gong} and \textit{X.-C. Cai}, SIAM J. Sci. Comput. 41, No. 5, S390--S408 (2019; Zbl 1436.65065) Full Text: DOI
Farrell, Patrick E.; Mitchell, Lawrence; Wechsung, Florian An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at High Reynolds number. (English) Zbl 1448.65261 SIAM J. Sci. Comput. 41, No. 5, A3073-A3096 (2019). Reviewer: Vit Dolejsi (Praha) MSC: 65N55 65N30 65F08 65F10 65H10 76D05 PDFBibTeX XMLCite \textit{P. E. Farrell} et al., SIAM J. Sci. Comput. 41, No. 5, A3073--A3096 (2019; Zbl 1448.65261) Full Text: DOI arXiv
Kelley, C. T. Numerical methods for nonlinear equations. (English) Zbl 1429.65108 Acta Numerica 27, 207-287 (2018). MSC: 65H10 PDFBibTeX XMLCite \textit{C. T. Kelley}, Acta Numerica 27, 207--287 (2018; Zbl 1429.65108) Full Text: DOI
Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver Nonlinear BDDC methods with approximate solvers. (English) Zbl 1410.65473 ETNA, Electron. Trans. Numer. Anal. 49, 244-273 (2018). MSC: 65N55 65F08 65Y05 74C05 65H10 65N30 PDFBibTeX XMLCite \textit{A. Klawonn} et al., ETNA, Electron. Trans. Numer. Anal. 49, 244--273 (2018; Zbl 1410.65473) Full Text: DOI Link
Kong, Fande; Wang, Yaqi; Schunert, Sebastian; Peterson, John W.; Permann, Cody J.; Andrš, David; Martineau, Richard C. A fully coupled two-level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations. (English) Zbl 1513.65367 Numer. Linear Algebra Appl. 25, No. 3, e2162, 23 p. (2018). MSC: 65M60 65M06 65N30 65N55 65N50 65H10 65N25 65F08 65F10 82D75 65Y05 35Q82 PDFBibTeX XMLCite \textit{F. Kong} et al., Numer. Linear Algebra Appl. 25, No. 3, e2162, 23 p. (2018; Zbl 1513.65367) Full Text: DOI Link
Yang, Haijian; Hwang, Feng-Nan An adaptive nonlinear elimination preconditioned inexact Newton algorithm for highly local nonlinear multicomponent PDE systems. (English) Zbl 1397.65245 Appl. Numer. Math. 133, 100-115 (2018). MSC: 65N22 65H10 76D05 65F08 65F10 76H05 PDFBibTeX XMLCite \textit{H. Yang} and \textit{F.-N. Hwang}, Appl. Numer. Math. 133, 100--115 (2018; Zbl 1397.65245) Full Text: DOI
Zhao, Tao A convergence analysis of the inexact simplified Jacobi-Davidson algorithm for polynomial eigenvalue problems. (English) Zbl 1415.65120 J. Sci. Comput. 75, No. 3, 1207-1228 (2018). MSC: 65H17 65F15 15A22 PDFBibTeX XMLCite \textit{T. Zhao}, J. Sci. Comput. 75, No. 3, 1207--1228 (2018; Zbl 1415.65120) Full Text: DOI
Liu, Lulu; Keyes, David E.; Krause, Rolf A note on adaptive nonlinear preconditioning techniques. (English) Zbl 1446.65027 SIAM J. Sci. Comput. 40, No. 2, A1171-A1186 (2018). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{L. Liu} et al., SIAM J. Sci. Comput. 40, No. 2, A1171--A1186 (2018; Zbl 1446.65027) Full Text: DOI
Mezzadri, Francesco; Galligani, Emanuele An inexact Newton method for solving complementarity problems in hydrodynamic lubrication. (English) Zbl 1384.76045 Calcolo 55, No. 1, Paper No. 1, 28 p. (2018). MSC: 76M25 76D08 65H10 65K05 90C51 76B10 PDFBibTeX XMLCite \textit{F. Mezzadri} and \textit{E. Galligani}, Calcolo 55, No. 1, Paper No. 1, 28 p. (2018; Zbl 1384.76045) Full Text: DOI
Güttel, Stefan; Tisseur, Françoise The nonlinear eigenvalue problem. (English) Zbl 1377.65061 Acta Numerica 26, 1-94 (2017). MSC: 65H17 65D05 65-02 PDFBibTeX XMLCite \textit{S. Güttel} and \textit{F. Tisseur}, Acta Numerica 26, 1--94 (2017; Zbl 1377.65061) Full Text: DOI
Kahle, Christian An \(L^\infty\) bound for the Cahn-Hilliard equation with relaxed non-smooth free energy. (English) Zbl 1368.35220 Int. J. Numer. Anal. Model. 14, No. 2, 243-254 (2017). MSC: 35Q35 35B45 65M15 65H10 65F05 PDFBibTeX XMLCite \textit{C. Kahle}, Int. J. Numer. Anal. Model. 14, No. 2, 243--254 (2017; Zbl 1368.35220) Full Text: arXiv Link
Zhao, Tao; Hwang, Feng-Nan; Cai, Xiao-Chuan Parallel two-level domain decomposition based Jacobi-Davidson algorithms for pyramidal quantum dot simulation. (English) Zbl 1378.65110 Comput. Phys. Commun. 204, 74-81 (2016). MSC: 65H17 81V65 65N08 PDFBibTeX XMLCite \textit{T. Zhao} et al., Comput. Phys. Commun. 204, 74--81 (2016; Zbl 1378.65110) Full Text: DOI
Hwang, Feng-Nan; Su, Yi-Cheng; Cai, Xiao-Chuan A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation. (English) Zbl 1390.76271 Comput. Fluids 110, 96-107 (2015). MSC: 76H05 76M20 65H10 65N06 65N22 PDFBibTeX XMLCite \textit{F.-N. Hwang} et al., Comput. Fluids 110, 96--107 (2015; Zbl 1390.76271) Full Text: DOI
Farrell, P. E.; Birkisson, Á.; Funke, S. W. Deflation techniques for finding distinct solutions of nonlinear partial differential equations. (English) Zbl 1327.65237 SIAM J. Sci. Comput. 37, No. 4, A2026-A2045 (2015). MSC: 65N30 65N35 65H99 35B32 PDFBibTeX XMLCite \textit{P. E. Farrell} et al., SIAM J. Sci. Comput. 37, No. 4, A2026--A2045 (2015; Zbl 1327.65237) Full Text: DOI arXiv
Liu, Lulu; Keyes, David E. Field-split preconditioned inexact Newton algorithms. (English) Zbl 1328.65122 SIAM J. Sci. Comput. 37, No. 3, A1388-A1409 (2015). MSC: 65H10 65H20 65N22 65N55 PDFBibTeX XMLCite \textit{L. Liu} and \textit{D. E. Keyes}, SIAM J. Sci. Comput. 37, No. 3, A1388--A1409 (2015; Zbl 1328.65122) Full Text: DOI Link
Berenguer, L.; Tromeur-Dervout, D. Developments on the Broyden procedure to solve nonlinear problems arising in CFD. (English) Zbl 1390.65042 Comput. Fluids 88, 891-896 (2013). MSC: 65H10 65Y05 PDFBibTeX XMLCite \textit{L. Berenguer} and \textit{D. Tromeur-Dervout}, Comput. Fluids 88, 891--896 (2013; Zbl 1390.65042) Full Text: DOI
Hwang, Feng-Nan; Cai, Xiao-Chuan; Cheng, Yu-Lun; Tsao, Chia-Wen A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D. (English) Zbl 1273.76008 Int. J. Comput. Math. 90, No. 3, 615-629 (2013). MSC: 76-04 76M10 76D05 65H10 65N30 65N55 PDFBibTeX XMLCite \textit{F.-N. Hwang} et al., Int. J. Comput. Math. 90, No. 3, 615--629 (2013; Zbl 1273.76008) Full Text: DOI
Hwang, Feng-Nan; Cai, Shang-Rong; Shao, Yun-Long; Wu, Jong-Shinn Parallel Newton-Krylov-Schwarz algorithms for the three-dimensional Poisson-Boltzmann equation in numerical simulation of colloidal particle interactions. (English) Zbl 1219.82024 Comput. Phys. Commun. 181, No. 9, 1529-1537 (2010). MSC: 82-08 82C22 76P05 65N08 65H10 65F08 65F10 65Y10 35J61 35Q20 PDFBibTeX XMLCite \textit{F.-N. Hwang} et al., Comput. Phys. Commun. 181, No. 9, 1529--1537 (2010; Zbl 1219.82024) Full Text: DOI
Munteanu, M.; Pavarino, L. F.; Scacchi, S. A scalable Newton-Krylov-Schwarz method for the bidomain reaction-diffusion system. (English) Zbl 1205.65261 SIAM J. Sci. Comput. 31, No. 5, 3861-3883 (2009). Reviewer: Michael Jung (Dresden) MSC: 65M55 65M60 35K57 65H10 65F08 65Y05 35K65 PDFBibTeX XMLCite \textit{M. Munteanu} et al., SIAM J. Sci. Comput. 31, No. 5, 3861--3883 (2009; Zbl 1205.65261) Full Text: DOI
Munteanu, Marilena; Pavarino, Luca F. Decoupled Schwarz algorithms for implicit discretizations of nonlinear monodomain and bidomain systems. (English) Zbl 1178.65116 Math. Models Methods Appl. Sci. 19, No. 7, 1065-1097 (2009). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M55 35K57 35Q92 92C50 65M06 65M60 65H10 65M12 65F08 PDFBibTeX XMLCite \textit{M. Munteanu} and \textit{L. F. Pavarino}, Math. Models Methods Appl. Sci. 19, No. 7, 1065--1097 (2009; Zbl 1178.65116) Full Text: DOI
Fang, Liang; He, Guoping Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations. (English) Zbl 1168.65344 J. Comput. Appl. Math. 228, No. 1, 296-303 (2009). MSC: 65H05 41A25 65D32 PDFBibTeX XMLCite \textit{L. Fang} and \textit{G. He}, J. Comput. Appl. Math. 228, No. 1, 296--303 (2009; Zbl 1168.65344) Full Text: DOI
Arnal, Josep; Migallón, Violeta; Penadés, José; Szyld, Daniel B. Newton additive and multiplicative Schwarz iterative methods. (English) Zbl 1137.65033 IMA J. Numer. Anal. 28, No. 1, 143-161 (2008). Reviewer: Aniket Mahanti (Saint John) MSC: 65H10 65Y05 PDFBibTeX XMLCite \textit{J. Arnal} et al., IMA J. Numer. Anal. 28, No. 1, 143--161 (2008; Zbl 1137.65033) Full Text: DOI Link
Bellavia, Stefania; Berrone, Stefano Globalization strategies for Newton-Krylov methods for stabilized FEM discretization of Navier-Stokes equations. (English) Zbl 1388.76122 J. Comput. Phys. 226, No. 2, 2317-2340 (2007). MSC: 76M10 65H20 65N30 76D05 PDFBibTeX XMLCite \textit{S. Bellavia} and \textit{S. Berrone}, J. Comput. Phys. 226, No. 2, 2317--2340 (2007; Zbl 1388.76122) Full Text: DOI
Pernice, Michael; Philip, Bobby Solution of equilibrium radiation diffusion problems using implicit adaptive mesh refinement. (English) Zbl 1099.65071 SIAM J. Sci. Comput. 27, No. 5, 1709-1726 (2006). MSC: 65M06 35K55 65H10 65M55 PDFBibTeX XMLCite \textit{M. Pernice} and \textit{B. Philip}, SIAM J. Sci. Comput. 27, No. 5, 1709--1726 (2006; Zbl 1099.65071) Full Text: DOI Link
Chacón, L.; Lapenta, G. A fully implicit, nonlinear adaptive grid strategy. (English) Zbl 1083.65110 J. Comput. Phys. 212, No. 2, 703-717 (2006). MSC: 65N50 65N55 65H10 65F35 65K10 49J20 PDFBibTeX XMLCite \textit{L. Chacón} and \textit{G. Lapenta}, J. Comput. Phys. 212, No. 2, 703--717 (2006; Zbl 1083.65110) Full Text: DOI
Marcinkowski, Leszek; Cai, Xiao-Chuan Parallel performance of some two-level ASPIN algorithms. (English) Zbl 1066.65057 Kornhuber, Ralf (ed.) et al., Domain decomposition methods in science and engineering. Selected papers of the 15th international conference on domain decomposition, Berlin, Germany, July 21–25, 2003. Berlin: Springer (ISBN 3-540-22523-4/pbk). Lecture Notes in Computational Science and Engineering 40, 639-646 (2005). MSC: 65H10 65Y05 76D05 65F35 76M20 PDFBibTeX XMLCite \textit{L. Marcinkowski} and \textit{X.-C. Cai}, Lect. Notes Comput. Sci. Eng. 40, 639--646 (2005; Zbl 1066.65057) Full Text: DOI
Hwang, Feng-Nan; Cai, Xiao-Chuan Improving robustness and parallel scalability of Newton method through nonlinear preconditioning. (English) Zbl 1067.65052 Kornhuber, Ralf (ed.) et al., Domain decomposition methods in science and engineering. Selected papers of the 15th international conference on domain decomposition, Berlin, Germany, July 21–25, 2003. Berlin: Springer (ISBN 3-540-22523-4/pbk). Lecture Notes in Computational Science and Engineering 40, 201-208 (2005). MSC: 65H10 65N30 35Q30 65Y05 76D05 76M10 PDFBibTeX XMLCite \textit{F.-N. Hwang} and \textit{X.-C. Cai}, Lect. Notes Comput. Sci. Eng. 40, 201--208 (2005; Zbl 1067.65052)
Byrd, Richard H.; Marazzi, Marcelo; Nocedal, Jorge On the convergence of Newton iterations to non-stationary points. (English) Zbl 1072.90038 Math. Program. 99, No. 1 (A), 127-148 (2004). Reviewer: Christian Grossmann (Dresden) MSC: 90C30 90C51 65H10 90C55 PDFBibTeX XMLCite \textit{R. H. Byrd} et al., Math. Program. 99, No. 1 (A), 127--148 (2004; Zbl 1072.90038) Full Text: DOI
Knoll, D. A.; Keyes, D. E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. (English) Zbl 1036.65045 J. Comput. Phys. 193, No. 2, 357-397 (2004). MSC: 65H10 65F35 65M06 65R20 35Q35 45G10 65Z05 76M25 PDFBibTeX XMLCite \textit{D. A. Knoll} and \textit{D. E. Keyes}, J. Comput. Phys. 193, No. 2, 357--397 (2004; Zbl 1036.65045) Full Text: DOI
Coffey, Todd S.; Kelley, C. T.; Keyes, David E. Pseudotransient continuation and differential-algebraic equations. (English) Zbl 1048.65080 SIAM J. Sci. Comput. 25, No. 2, 553-569 (2003). Reviewer: Rudolf Scherer (Karlsruhe) MSC: 65L80 65H10 65H20 34A09 PDFBibTeX XMLCite \textit{T. S. Coffey} et al., SIAM J. Sci. Comput. 25, No. 2, 553--569 (2003; Zbl 1048.65080) Full Text: DOI
Peinado, Jesús; Vidal, Antonio M. A parallel Newton-GMRES algorithm for solving large scale nonlinear systems. (English) Zbl 1027.65510 Palma, José M. L. M. (ed.) et al., High performance computing for computational science - VECPAR 2002. 5th international conference, Porto, Portugal, June 26-28, 2002. Selected papers and invited talks. Berlin: Springer. Lect. Notes Comput. Sci. 2565, 328-342 (2003). MSC: 65H10 65Y05 PDFBibTeX XMLCite \textit{J. Peinado} and \textit{A. M. Vidal}, Lect. Notes Comput. Sci. 2565, 328--342 (2003; Zbl 1027.65510) Full Text: Link
Keyes, David E. Terascale implicit methods for partial differential equations. (English) Zbl 1018.65121 Feng, Xiaobing (ed.) et al., Recent advances in numerical methods for partial differential equations and applications. Proceedings of the 2001 John H. Barrett memorial lectures trends in computational mathematics, Univ. of Tennessee, Knoxville, TN, USA, May 10-12, 2001. Providence, RI: AMS, American Mathematical Society. Contemp. Math. 306, 29-84 (2002). MSC: 65M55 65F35 65H10 65M60 35Q30 76M10 65Y05 76D05 76N15 PDFBibTeX XMLCite \textit{D. E. Keyes}, Contemp. Math. 306, 29--84 (2002; Zbl 1018.65121)