Alzahrani, Hasnaa; Turkiyyah, George; Knio, Omar; Keyes, David Space-fractional diffusion with variable order and diffusivity: discretization and direct solution strategies. (English) Zbl 1513.35511 Commun. Appl. Math. Comput. 4, No. 4, 1416-1440 (2022). Reviewer: Abdallah Bradji (Annaba) MSC: 35R11 65F55 65R20 PDFBibTeX XMLCite \textit{H. Alzahrani} et al., Commun. Appl. Math. Comput. 4, No. 4, 1416--1440 (2022; Zbl 1513.35511) Full Text: DOI arXiv
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
Gao, Longfei; Keyes, David Simultaneous approximation terms for elastic wave equations on nonuniform grids. (English) Zbl 1509.65134 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, 125-133 (2020). MSC: 65N55 65N50 65N06 65M20 86A15 35Q86 35Q74 35R35 PDFBibTeX XMLCite \textit{L. Gao} and \textit{D. Keyes}, Lect. Notes Comput. Sci. Eng. 138, 125--133 (2020; Zbl 1509.65134) Full Text: DOI arXiv
Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. (English) Zbl 1453.65289 SIAM J. Sci. Comput. 42, No. 5, A3397-A3426 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 65M32 35Q93 49M25 49N45 65F10 65F99 65Y05 65Y10 78A46 PDFBibTeX XMLCite \textit{I. Ambartsumyan} et al., SIAM J. Sci. Comput. 42, No. 5, A3397--A3426 (2020; Zbl 1453.65289) Full Text: DOI arXiv
Litvinenko, Alexander; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel; Keyes, David Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability. (English) Zbl 1434.76016 GEM. Int. J. Geomath. 11, No. 1, Paper No. 10, 29 p. (2020). MSC: 76-10 76S05 35Q35 65M22 65M55 PDFBibTeX XMLCite \textit{A. Litvinenko} et al., GEM. Int. J. Geomath. 11, Paper No. 10, 29 p. (2020; Zbl 1434.76016) Full Text: DOI arXiv
Gao, Longfei; Del Rey Fernández, David C.; Carpenter, Mark; Keyes, David SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids. (English) Zbl 1412.65075 J. Comput. Appl. Math. 348, 421-444 (2019). MSC: 65M06 86A15 76Q05 65M50 35Q86 PDFBibTeX XMLCite \textit{L. Gao} et al., J. Comput. Appl. Math. 348, 421--444 (2019; Zbl 1412.65075) Full Text: DOI arXiv Link
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
Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz. (English) Zbl 1277.49037 J. Comput. Phys. 231, No. 17, 5822-5853 (2012). MSC: 49M15 35G20 65M99 PDFBibTeX XMLCite \textit{X. Yuan} et al., J. Comput. Phys. 231, No. 17, 5822--5853 (2012; Zbl 1277.49037) Full Text: DOI
Keyes, David E. Exaflop/s: the why and the how. (Exaflop/s : pourquoi et comment.) (English. French summary) Zbl 1221.00058 C. R., Méc., Acad. Sci. Paris 339, No. 2-3, 70-77 (2011). MSC: 00A71 35Q68 PDFBibTeX XMLCite \textit{D. E. Keyes}, C. R., Méc., Acad. Sci. Paris 339, No. 2--3, 70--77 (2011; Zbl 1221.00058) Full Text: DOI
Mallet, V.; Keyes, D. E.; Fendell, F. E. Modeling wildland fire propagation with level set methods. (English) Zbl 1186.65140 Comput. Math. Appl. 57, No. 7, 1089-1101 (2009). MSC: 65N06 35Q79 35Q92 35F20 PDFBibTeX XMLCite \textit{V. Mallet} et al., Comput. Math. Appl. 57, No. 7, 1089--1101 (2009; Zbl 1186.65140) Full Text: DOI arXiv
He, Yuan; Keyes, David E. PDE-based parameter reconstruction through Schur and Schwarz decompositions. (English) Zbl 1139.65313 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, 543-550 (2008). MSC: 65M32 35K57 35R30 92C55 65Y05 PDFBibTeX XMLCite \textit{Y. He} and \textit{D. E. Keyes}, Lect. Notes Comput. Sci. Eng. 60, 543--550 (2008; Zbl 1139.65313)
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
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)
McInnes, L. C.; Susan-Resiga, R.; Atassi, H. M.; Keyes, D. E. Parallel solution of Helmholtz problems using additive Schwarz methods. (English) Zbl 0940.65121 DeSanto, John A. (ed.), Mathematical and numerical aspects of wave propagation. Proceedings of the 4th international conference held at Mines in Golden, CO, USA, June 1-5, 1998. Philadelphia, PA: SIAM. Proc. Appl. Math. 623-625 (1998). MSC: 65N30 65F10 65Y05 65F35 35J05 PDFBibTeX XMLCite \textit{L. C. McInnes} et al., Proc. Appl. Math. 623--625, 623--625 (1998; Zbl 0940.65121)
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)
McInnes, Lois C.; Susan-Resiga, Romeo F.; Keyes, David E.; Atassi, Hafiz M. Additive Schwarz methods with nonreflecting boundary conditions for the parallel computation of Helmholtz problems. (English) Zbl 0910.65086 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, 325-333 (1998). MSC: 65N55 65N30 65Y05 35J05 65F10 65F35 PDFBibTeX XMLCite \textit{L. C. McInnes} et al., Contemp. Math. 218, 325--333 (1998; Zbl 0910.65086)
Kelley, C. T.; Keyes, David E. Convergence analysis of pseudo-transient continuation. (English) Zbl 0911.65080 SIAM J. Numer. Anal. 35, No. 2, 508-523 (1998). Reviewer: K.Najzar (Praha) MSC: 65M20 65M12 65L05 65H10 35K55 PDFBibTeX XMLCite \textit{C. T. Kelley} and \textit{D. E. Keyes}, SIAM J. Numer. Anal. 35, No. 2, 508--523 (1998; Zbl 0911.65080) 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
Ern, Alexandre; Giovangigli, Vincent; Keyes, David E.; Smooke, Mitchell D. Towards polyalgorithmic linear system solvers for nonlinear elliptic problems. (English) Zbl 0807.65027 SIAM J. Sci. Comput. 15, No. 3, 681-703 (1994). Reviewer: Z.Dostál (Ostrava) MSC: 65F10 65F35 65H10 65Y20 35J65 65N22 80A32 PDFBibTeX XMLCite \textit{A. Ern} et al., SIAM J. Sci. Comput. 15, No. 3, 681--703 (1994; Zbl 0807.65027) Full Text: DOI Link
Gropp, William D.; Keyes, David E. Domain decomposition as a mechanism for using asymptotic methods. (English) Zbl 0808.65124 Kaper, Hans G. (ed.) et al., Asymptotic and numerical methods for partial differential equations with critical parameters. Proceedings of the NATO Advanced Research Workshop on asymptotic-induced numerical methods for partial differential equations, critical parameters, and domain decomposition, Beaune (France), May 25-28, 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 384, 93-105 (1993). Reviewer: J.R.Kuttler (Laurel) MSC: 65N55 65N50 65N06 35B40 35J25 35B25 PDFBibTeX XMLCite \textit{W. D. Gropp} and \textit{D. E. Keyes}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 384, 93--105 (1993; Zbl 0808.65124)
Gropp, William D.; Keyes, David E. Domain decomposition with local mesh refinement. (English) Zbl 0756.65045 SIAM J. Sci. Stat. Comput. 13, No. 4, 967-993 (1992). Reviewer: R.Redlinger (Karlsruhe) MSC: 65F10 65N55 65N50 65N22 35J25 PDFBibTeX XMLCite \textit{W. D. Gropp} and \textit{D. E. Keyes}, SIAM J. Sci. Stat. Comput. 13, No. 4, 967--993 (1992; Zbl 0756.65045) Full Text: DOI Link
Keyes, David E. (ed.); Chan, Tony F. (ed.); Meurant, Gérard (ed.); Scroggs, Jeffrey S. (ed.); Voigt, Robert G. (ed.) Fifth international SIAM symposium on domain decomposition methods for partial differential equations, held in Norfolk, Virginia, USA, May 6-8, 1991. (English) Zbl 0758.00015 Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiii, 623 (1992). MSC: 00B25 35-06 65-06 PDFBibTeX XMLCite \textit{D. E. Keyes} (ed.) et al., Fifth international SIAM symposium on domain decomposition methods for partial differential equations, held in Norfolk, Virginia, USA, May 6-8, 1991. Philadelphia, PA: SIAM (1992; Zbl 0758.00015)
Gropp, William D.; Keyes, David E. Parallel performance of domain-decomposed preconditioned Krylov methods for PDEs with locally uniform refinement. (English) Zbl 0752.65083 SIAM J. Sci. Stat. Comput. 13, No. 1, 128-145 (1992). Reviewer: S.K.Rangarajan (Karaikudi) MSC: 65N55 65Y05 65F10 35J25 65Y20 PDFBibTeX XMLCite \textit{W. D. Gropp} and \textit{D. E. Keyes}, SIAM J. Sci. Stat. Comput. 13, No. 1, 128--145 (1992; Zbl 0752.65083) Full Text: DOI
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
Keyes, David E.; Gropp, William D. Domain-decomposable preconditioners for second-order upwind discretizations of multicomponent systems. (English) Zbl 0766.65103 Fourth international symposium on domain decomposition methods for partial differential equations, Proc. Symp., Moscow/Russ. 1990, 129-139 (1991). MSC: 65N55 65F35 65Y05 35K57 PDFBibTeX XMLCite \textit{D. E. Keyes} and \textit{W. D. Gropp}, in: Fourth international symposium on domain decomposition methods for partial differential equations. Proceedings of the symposium, held at Moscow, Russia, in May 21-25, 1990. Philadelphia, PA: SIAM. 129--139 (1991; Zbl 0766.65103)
Chan, Tony F.; Keyes, David E. Interface preconditionings for domain-decomposed convection-diffusion operators. (English) Zbl 0722.65060 Domain decomposition methods for partial differential equations, Proc. 3rd Int. Symp. Houston/TX (USA) 1989, 245-262 (1990). Reviewer: J.Mandel (Denver) MSC: 65N55 65F10 35J70 65F35 PDFBibTeX XML
Gropp, William; Keyes, David E. A domain decomposition method with locally uniform mesh refinement. (English) Zbl 0701.65079 Domain decomposition methods for partial differential equations, Proc. 3rd Int. Symp. Houston/TX (USA) 1989, 115-129 (1990). Reviewer: P.Kloucek MSC: 65N55 65N50 35J25 65F10 PDFBibTeX XML
Keyes, David E.; Gropp, William D. Domain decomposition techniques for the parallel solution of nonsymmetric systems of elliptic boundary value problems. (English) Zbl 0694.65048 Appl. Numer. Math. 6, No. 4, 281-301 (1990). Reviewer: J.Albrycht MSC: 65N22 65F10 80A32 35J25 PDFBibTeX XMLCite \textit{D. E. Keyes} and \textit{W. D. Gropp}, Appl. Numer. Math. 6, No. 4, 281--301 (1990; Zbl 0694.65048) Full Text: DOI
Smooke, M. D.; Mitchell, R. E.; Keyes, D. E. Numerical solution of confined axisymmetric laminar diffusion flames. (English) Zbl 0696.65087 Adaptive methods for partial differential equations, Proc. Workshop, Troy/NY (USA) 1988, 125-149 (1989). Reviewer: I.Grosu MSC: 65Z05 65N22 80A25 35Q99 PDFBibTeX XML
Gropp, William D.; Keyes, David E. Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations. (English) Zbl 0645.65069 SIAM J. Sci. Stat. Comput. 9, No. 2, 312-326 (1988). Reviewer: G.Stoyan MSC: 65N22 65Y05 68Q25 65F10 35J25 PDFBibTeX XMLCite \textit{W. D. Gropp} and \textit{D. E. Keyes}, SIAM J. Sci. Stat. Comput. 9, No. 2, 312--326 (1988; Zbl 0645.65069) Full Text: DOI
Keyes, D. E.; Smooke, M. D. Flame sheet starting estimates for counterflow diffusion flame problems. (English) Zbl 0656.65111 J. Comput. Phys. 73, 267-288 (1987). Reviewer: J.Prakash MSC: 65Z05 65C20 80A25 35Q99 PDFBibTeX XMLCite \textit{D. E. Keyes} and \textit{M. D. Smooke}, J. Comput. Phys. 73, 267--288 (1987; Zbl 0656.65111) Full Text: DOI
Keyes, David E.; Gropp, William D. A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation. (English) Zbl 0619.65088 SIAM J. Sci. Stat. Comput. 8, S166-S202 (1987). Reviewer: W.Schönauer MSC: 65N22 65F35 65F10 35J25 65Y05 PDFBibTeX XMLCite \textit{D. E. Keyes} and \textit{W. D. Gropp}, SIAM J. Sci. Stat. Comput. 8, S166--S202 (1987; Zbl 0619.65088) Full Text: DOI