## PETSc

 swMATH ID: 4012 Software Authors: S. Balay, W.D. Gropp, L.C. McInnes, B.F. Smith Description: The Portable, Extensible Toolkit for Scientiﬁc Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear, nonlinear equation solvers and time integrators that may be used in application codes written in Fortran, C, C++, Python, and MATLAB (sequential). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous ﬂexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++ or Fortran and experience using a debugger such as gdb or dbx, it may require a signiﬁcant amount of time to take full advantage of the features that enable efﬁcient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efﬁcient implementation of many application codes simpler than “rolling them” yourself. Homepage: http://www.mcs.anl.gov/petsc/ Keywords: partial differential equations Related Software: FEniCS; hypre; MUMPS; SLEPc; Trilinos; Gmsh; deal.ii; BoomerAMG; libMesh; LAPACK; METIS; Firedrake; Matlab; DOLFIN; FreeFem++; GitHub; p4est; UMFPACK; SyFi; ParaView Cited in: 1,594 Publications
all top 5

### Cited by 3,069 Authors

 53 Cai, Xiao-Chuan 35 Pavarino, Luca Franco 29 Scacchi, Simone 26 Bassi, Francesco 23 Zampini, Stefano 22 Keyes, David Elliot 22 Klawonn, Axel 21 Rheinbach, Oliver 20 Yang, Haijian 19 Hwang, Fengnan 19 Román, Jose E. 19 Yang, Chao 18 Dalcín, Lisandro D. 16 Crivellini, Andrea 16 Knepley, Matthew G. 15 Griffith, Boyce E. 14 Colli Franzone, Piero 14 Waisman, Haim 13 Colombo, Alessandro G. 13 Gibou, Frédéric 13 Widlund, Olof B. 12 Jolivet, Pierre 12 Mitchell, Lawrence 11 Bangerth, Wolfgang 11 Botti, Lorenzo 11 Chen, Rongliang 11 Ghidoni, Antonio 11 Krause, Rolf H. 11 Parsani, Matteo 11 Stern, Fred 10 Carrica, Pablo M. 10 Ghattas, Omar N. 10 Heister, Timo 10 Kronbichler, Martin 10 Smith, Barry F. 9 Badia, Santiago 9 Barba, Lorena A. 9 Beilina, Larisa 9 Biros, George 9 Cotter, Colin John 9 Farrell, Patrick E. 9 Luo, Li 9 Maier, Matthias Sebastian 8 Bhalla, Amneet Pal Singh 8 Denner, Fabian 8 Gómez, Héctor J. 8 Heltai, Luca 8 Horák, David 8 Knezevic, David J. 8 Lanser, Martin 8 Martín, Alberto F. 8 McInnes, Lois Curfman 8 Patankar, Neelesh A. 8 Pelteret, Jean-Paul 8 Plank, Gernot 8 Prud’homme, Christophe 8 Rhebergen, Sander 8 Saad, Yousef 8 Sahin, Mehmet 8 Szyld, Daniel B. 8 Turcksin, Bruno 7 Arndt, Daniel 7 Aulisa, Eugenio 7 Barker, Andrew T. 7 Čiegis, Raimondas 7 Dawson, Clint N. 7 Di Pietro, Daniele Antonio 7 Farrell, Patrick Emmet 7 Kahle, Christian 7 Kirby, Robert C. 7 McAuliffe, Colin 7 Medale, Marc 7 Ollivier-Gooch, Carl F. 7 Pain, Christopher C. 7 Sun, Shuyu 7 van Wachem, Berend G. M. 6 Adams, Mark F. 6 Baiges, Joan 6 Berger-Vergiat, Luc 6 Calo, Victor Manuel 6 Campos, Carmen 6 Casquero, Hugo 6 Chang, Justin 6 Del Rey Fernández, David C. 6 Franchina, Nicoletta 6 Ganapathysubramanian, Baskar 6 Hapla, Vaclav 6 Huang, Jizu 6 Kamensky, David 6 Masson, Roland 6 Nakshatrala, K. B. 6 Nigro, Alessandra 6 Rebay, Stefano 6 Schütz, Jochen 6 Storti, Mario Alberto 6 Wechsung, Florian 6 Xie, Dexuan 5 Augustin, Christoph M. 5 Bourdin, Blaise 5 Brown, Jed ...and 2,969 more Authors
all top 5

### Cited in 188 Serials

 288 Journal of Computational Physics 166 Computer Methods in Applied Mechanics and Engineering 155 SIAM Journal on Scientific Computing 112 Computers and Fluids 46 ACM Transactions on Mathematical Software 36 Computers & Mathematics with Applications 36 Journal of Scientific Computing 32 International Journal for Numerical Methods in Engineering 32 Journal of Computational and Applied Mathematics 30 Computational Mechanics 27 International Journal for Numerical Methods in Fluids 26 Computer Physics Communications 26 Journal of Fluid Mechanics 21 Computational Geosciences 18 Numerical Linear Algebra with Applications 14 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 International Journal of Computational Fluid Dynamics 11 SIAM Journal on Numerical Analysis 10 Applied Numerical Mathematics 9 Mathematical Biosciences 9 Mathematics and Computers in Simulation 9 ETNA. Electronic Transactions on Numerical Analysis 9 Journal of Numerical Mathematics 8 Applied Mathematics and Computation 8 Numerische Mathematik 8 Parallel Computing 8 Communications in Computational Physics 7 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 7 Archives of Computational Methods in Engineering 6 Journal of the Mechanics and Physics of Solids 5 Inverse Problems 5 BIT 5 SIAM Journal on Matrix Analysis and Applications 5 Applied Mathematical Modelling 5 Communications in Numerical Methods in Engineering 5 Advances in Computational Mathematics 5 Computing and Visualization in Science 5 International Journal of Computational Methods 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 SIAM/ASA Journal on Uncertainty Quantification 4 Mathematics of Computation 4 Journal of Non-Newtonian Fluid Mechanics 4 Optimization Methods & Software 4 European Journal of Mechanics. A. Solids 4 European Journal of Mechanics. B. Fluids 4 Concurrency and Computation: Practice & Experience 4 Mathematical Geosciences 3 Journal of Engineering Mathematics 3 Calcolo 3 Physica D 3 Applied Mathematics Letters 3 Applications of Mathematics 3 Numerical Algorithms 3 International Journal of Computer Mathematics 3 SIAM Journal on Applied Mathematics 3 Mathematical Programming. Series A. Series B 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 3 Engineering Analysis with Boundary Elements 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Combustion Theory and Modelling 3 Journal of High Energy Physics 3 Optimization and Engineering 3 Mathematical Modelling and Analysis 3 Software - Environments - Tools 3 Acta Mechanica Sinica 3 International Journal for Numerical Methods in Biomedical Engineering 3 Journal of Theoretical Biology 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 3 SMAI Journal of Computational Mathematics 3 Communications on Applied Mathematics and Computation 3 Journal of Computational and Theoretical Transport 2 Classical and Quantum Gravity 2 IMA Journal of Numerical Analysis 2 Journal of Mathematical Biology 2 Bulletin of Mathematical Biology 2 Journal of Optimization Theory and Applications 2 Meccanica 2 Finite Elements in Analysis and Design 2 Numerical Methods for Partial Differential Equations 2 Computational Mathematics and Mathematical Physics 2 Mathematical Problems in Engineering 2 Mathematics and Mechanics of Solids 2 Informatica (Vilnius) 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Lobachevskii Journal of Mathematics 2 Multiscale Modeling & Simulation 2 Acta Numerica 2 International Journal of Numerical Analysis and Modeling 2 Journal of Computational Acoustics 2 International Journal of Parallel, Emergent and Distributed Systems 2 GAMM-Mitteilungen 2 Springer Series in Computational Mathematics 2 Lecture Notes in Computational Science and Engineering 2 Inverse Problems and Imaging 2 Discrete and Continuous Dynamical Systems. Series S 2 Applied and Computational Mathematics 2 GEM - International Journal on Geomathematics 2 Journal of Mathematics in Industry 2 SN Partial Differential Equations and Applications ...and 88 more Serials
all top 5

### Cited in 38 Fields

 1,084 Numerical analysis (65-XX) 678 Fluid mechanics (76-XX) 283 Mechanics of deformable solids (74-XX) 281 Partial differential equations (35-XX) 134 Biology and other natural sciences (92-XX) 92 Computer science (68-XX) 83 Geophysics (86-XX) 75 Optics, electromagnetic theory (78-XX) 64 Statistical mechanics, structure of matter (82-XX) 46 Calculus of variations and optimal control; optimization (49-XX) 38 Operations research, mathematical programming (90-XX) 32 Classical thermodynamics, heat transfer (80-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 23 Quantum theory (81-XX) 15 Probability theory and stochastic processes (60-XX) 14 Statistics (62-XX) 12 Integral equations (45-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Relativity and gravitational theory (83-XX) 8 General and overarching topics; collections (00-XX) 6 Ordinary differential equations (34-XX) 6 Systems theory; control (93-XX) 5 Combinatorics (05-XX) 5 Mechanics of particles and systems (70-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Operator theory (47-XX) 3 Astronomy and astrophysics (85-XX) 3 Information and communication theory, circuits (94-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Mathematics education (97-XX)