## libMesh

 swMATH ID: 6657 Software Authors: B. S. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey Description: The libMesh library provides a framework for the numerical simulation of partial differential equations using arbitrary unstructured discretizations on serial and parallel platforms. A major goal of the library is to provide support for adaptive mesh refinement (AMR) computations in parallel while allowing a research scientist to focus on the physics they are modeling. libMesh currently supports 1D, 2D, and 3D steady and transient simulations on a variety of popular geometric and finite element types. The library makes use of high-quality, existing software whenever possible. PETSc is used for the solution of linear systems on both serial and parallel platforms, and LASPack is included with the library to provide linear solver support on serial machines. An optional interface to SLEPc is also provided for solving both standard and generalized eigenvalue problems. Homepage: http://libmesh.sourceforge.net/index.php Keywords: inverse problem; nonlinear optimization problem; material parameter identification; derivatives of eigenvalues and eigenvectors; adjoint problem Related Software: PETSc; deal.ii; FEniCS; Trilinos; Gmsh; FreeFem++; hypre; p4est; METIS; MOOSE; ParaView; MUMPS; DUNE; Matlab; GitHub; MFEM; BoomerAMG; GRINS; SLEPc; DOLFIN Cited in: 146 Publications Further Publications: http://libmesh.sourceforge.net/publications.php
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### Cited by 353 Authors

 11 Carey, Graham Francis 10 Coutinho, Alvaro L. G. A. 9 Knezevic, David J. 6 Cai, Xiao-Chuan 6 Griffith, Boyce E. 6 Luo, Li 6 Patera, Anthony T. 5 Bangerth, Wolfgang 5 Grave, Malú 5 Peterson, John W. 4 Botti, Lorenzo 4 Camata, Jose J. 4 Huynh, Dinh Bao Phuong 4 Kirk, Benjamin S. 4 Krause, Rolf H. 4 Oden, John Tinsley 4 Smetana, Kathrin 4 Stogner, Roy H. 4 Wang, Xiaoping 3 Caboussat, Alexandre 3 Garg, Vikram V. 3 Gourzoulidis, Dimitrios 3 Keyes, David Elliot 3 Kronbichler, Martin 3 Lima, Ernesto A. B. F. 3 Manzoni, Andrea 3 Nestola, Maria Giuseppina Chiara 3 Petersen, Steffen 3 Quarteroni, Alfio M. 3 von Estorff, Otto 2 Abdulle, Assyr 2 Almeida, Regina C. 2 Amaziane, Brahim 2 Ballani, Jonas 2 Ballarin, Francesco 2 Barone, Matthew F. 2 Barth, William Lee 2 Bauman, Paul T. 2 Berrone, Stefano 2 Bhalla, Amneet Pal Singh 2 Burstedde, Carsten 2 Chen, Xiaoqing 2 Corsini, Alessandro 2 Côrtes, Adriano M. A. 2 De Souza, Giacomo Rosilho 2 Di Pietro, Daniele Antonio 2 Dreyer, Daniel 2 Elias, Renato N. 2 Faghihi, Danial 2 Glowinski, Roland 2 Heister, Timo 2 Hoover, Alexander P. 2 Hormuth, David A. II 2 Jurak, Mladen 2 Kalashnikova, Irina 2 Knepley, Matthew G. 2 Murray, Bruce T. 2 Nguyen, Loi 2 Patankar, Neelesh A. 2 Picasso, Marco 2 Rispoli, Franco 2 Roberts, Nathan V. 2 Rochinha, Fernando Alves 2 Rossa, Andre L. 2 Rossi, Simone 2 Rozza, Gianluigi 2 Saar, Martin O. 2 Tezduyar, Tayfun E. 2 Valli, Andrea M. P. 2 Vogler, Daniel 2 von Planta, Cyrill 2 Yankeelov, Thomas E. 2 Žgaljić Keko, Ana 2 Zhang, Qian 1 Abukhdeir, Nasser Mohieddin 1 Acharya, Shashank 1 Aghav, Hrithik 1 Ahn, Hyung Taek 1 Akbarzadeh, Amir M. 1 Alhadeff, A. 1 Allu, Srikanth 1 Alves, José L. D. 1 Anderson, Michael L. 1 Andrade, Roberto Fernandes Silva 1 Andrs, David 1 Antiga, Luca 1 Arndt, Daniel 1 Arunajatesan, Srinivasan 1 Audigane, Pascal 1 Badia, Santiago 1 Baiges, Joan 1 Balajewicz, Maciej J. 1 Bale, Rahul 1 Barros, Gabriel F. 1 Bassi, Francesco 1 Bastian, Peter 1 Bayona, Camilo 1 Beni, Ali Naderi 1 Berger, Lorenz 1 Berrill, Mark A. ...and 253 more Authors
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### Cited in 41 Serials

 18 Journal of Computational Physics 15 Computer Methods in Applied Mechanics and Engineering 11 Computers and Fluids 11 SIAM Journal on Scientific Computing 9 International Journal for Numerical Methods in Engineering 8 International Journal for Numerical Methods in Fluids 6 Computational Mechanics 6 Computational Geosciences 5 Computers & Mathematics with Applications 5 ACM Transactions on Mathematical Software 4 Journal of Computational and Applied Mathematics 4 Journal of Scientific Computing 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Communications in Numerical Methods in Engineering 2 Journal of Fluid Mechanics 2 Applied Mathematics and Computation 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Advances in Computational Mathematics 2 European Journal of Mechanics. A. Solids 2 Archives of Computational Methods in Engineering 1 Acta Mechanica 1 Journal of Engineering Mathematics 1 BIT 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Finite Elements in Analysis and Design 1 Japan Journal of Industrial and Applied Mathematics 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Mathematical Programming. Series A. Series B 1 Archive of Applied Mechanics 1 Numerical Linear Algebra with Applications 1 International Journal of Computer Vision 1 International Journal of Computational Fluid Dynamics 1 Chaos 1 Nonlinear Analysis. Real World Applications 1 Computational Methods in Applied Mathematics 1 Unitext 1 Algorithms 1 International Journal for Numerical Methods in Biomedical Engineering 1 Statistics and Computing
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### Cited in 22 Fields

 99 Numerical analysis (65-XX) 64 Fluid mechanics (76-XX) 29 Mechanics of deformable solids (74-XX) 23 Partial differential equations (35-XX) 20 Biology and other natural sciences (92-XX) 10 Computer science (68-XX) 7 Geophysics (86-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Classical thermodynamics, heat transfer (80-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 2 Systems theory; control (93-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX)