NITSOL swMATH ID: 623 Software Authors: Pernice, Michael; Walker, Homer F. Description: We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods. The algorithm is implemented in a Fortran solver called NITSOL that is robust yet easy to use and provides a number of useful options and features. The structure offers the user great flexibility in addressing problem specificity through preconditioning and other means and allows easy adaptation to parallel environments. Features and capabilities are illustrated in numerical experiments. Homepage: http://users.wpi.edu/~walker/NITSOL/ Keywords: Newton iterative methods; truncated Newton methods; Newton-Krylov methods; inexact Newton methods; Krylov subspace methods; GMRES; BiCGSTAB; TFQMR; parallel computation; large-scale nonlinear systems; algorithm; preconditioning; numerical experiments Related Software: KELLEY; PETSc; AztecOO; Aztec; SUNDIALS; Trilinos; hypre; ML; ARPACK; LAPACK; MPSalsa; LANCELOT; Wesseling; BoomerAMG; Gmsh; GQTPAR; UMFPACK; MPI; L-BFGS-B; HSL Cited in: 99 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year NITSOL: A Newton iterative solver for nonlinear systems. Zbl 0916.65049Pernice, Michael; Walker, Homer F. 1998 all top 5 Cited by 211 Authors 6 Bellavia, Stefania 6 Keyes, David Elliot 6 Knoll, Dana A. 6 Morini, Benedetta 5 An, Hengbin 4 Crivellini, Andrea 4 Liu, Lulu 3 Alizard, Frédéric 3 Guo, Xueping 3 Newman, Christopher K. 3 Pernice, Michael 3 Robinet, Jean-Christophe 3 Tromeur-Dervout, Damien 3 Vassilevski, Yuri V. 3 Walker, Homer F. 2 Abgrall, Rémi 2 Bassi, Francesco 2 Berndt, Markus 2 Bonaldi, Francesco 2 Droniou, Jérôme 2 Franciolini, Matteo 2 Gould, Nicholas Ian Mark 2 Gruzdev, Arseniy P. 2 Hansen, Glen A. 2 Jimack, Peter K. 2 Kelley, Carl T. 2 Liu, Xu 2 Martineau, Richard C. 2 Masson, Roland 2 Melnikov, Nikolai B. 2 Mo, Zeyao 2 Nigro, Alessandra 2 Nourgaliev, Robert R. 2 Pasteau, Antoine 2 Shadid, John N. 2 Tocci, Michael D. 2 Toint, Philippe L. 1 Ahmed, Sarfraz 1 Allu, Srikanth 1 Ascher, Uri M. 1 Bai, Zhongzhi 1 Bailey, David S. 1 Barton, Paul I. 1 Berrill, Mark A. 1 Berrone, Stefano 1 Bertaccini, Daniele 1 Booth, Michael J. 1 Botti, Lorenzo 1 Boudouvis, Andreas G. 1 Brenner, Konstantin 1 Brown, Jed 1 Cai, Junwei 1 Cai, Xiao-Chuan 1 Calo, Victor Manuel 1 Catabriga, Lucia 1 Chacón, Luis 1 Chen, Ke 1 Cherubini, Stefania 1 Chua, Chek Beng 1 Clarno, Kevin T. 1 Colombo, Alessandro G. 1 Congedo, Pietro Marco 1 Coquel, Frédéric 1 Côrtes, Adriano M. A. 1 Coutinho, Alvaro L. G. A. 1 Dai, Pingfei 1 Dalcín, Lisandro D. 1 Dalton, Michael G. 1 De Bartolo, Carmine 1 De Simone, Valentina 1 De, Suvranu 1 Debusschere, Bert J. 1 DeHart, Mark D. 1 Deng, GanBo 1 Deuflhard, Peter 1 di Serafino, Daniela 1 Dilts, Gary A. 1 Dorf, Mikhail A. 1 Dorr, Milo R. 1 Duff, Iain S. 1 Evans, Katherine J. 1 Fang, Liang 1 Feng, Tao 1 Ford, Judith M. 1 Francois, Marianne M. 1 Frank, Florian 1 Garbey, Marc 1 Gasparo, Maria Grazia 1 Gaston, Derek R. 1 Gaul, André 1 Gérald, Sophie 1 Ghanem, Roger G. 1 Ghosh, Debojyoti 1 Ghosh, Supriyo 1 Godoy, William F. 1 Gomes-Ruggiero, Márcia Ap. 1 Goodyer, Christopher E. 1 Graves-Morris, Peter R. 1 Grippo, Luigi 1 Guiho, Florian ...and 111 more Authors all top 5 Cited in 38 Serials 23 Journal of Computational Physics 12 SIAM Journal on Scientific Computing 7 Computers and Fluids 7 Journal of Computational and Applied Mathematics 3 International Journal for Numerical Methods in Fluids 3 SIAM Journal on Numerical Analysis 3 Applied Numerical Mathematics 3 Physics of Fluids 2 Computer Methods in Applied Mechanics and Engineering 2 ACM Transactions on Mathematical Software 2 ETNA. Electronic Transactions on Numerical Analysis 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Inverse Problems 1 Applied Mathematics and Computation 1 Journal of Optimization Theory and Applications 1 Operations Research 1 Computational Mechanics 1 Journal of Scientific Computing 1 European Journal of Applied Mathematics 1 Annals of Operations Research 1 International Journal of Computer Mathematics 1 SIAM Journal on Optimization 1 Advances in Engineering Software 1 Computational Optimization and Applications 1 Communications in Numerical Methods in Engineering 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 European Journal of Mechanics. B. Fluids 1 Computational Geosciences 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Springer Series in Computational Mathematics 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Advances in Applied Mathematics and Mechanics 1 Set-Valued and Variational Analysis 1 Numerical Algebra, Control and Optimization 1 East Asian Journal on Applied Mathematics 1 Ural Mathematical Journal all top 5 Cited in 17 Fields 77 Numerical analysis (65-XX) 45 Fluid mechanics (76-XX) 20 Partial differential equations (35-XX) 9 Operations research, mathematical programming (90-XX) 6 Mechanics of deformable solids (74-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year