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.

References in zbMATH (referenced in 134 articles , 1 standard article )

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  1. Degen, Denise; Veroy, Karen; Wellmann, Florian: Certified reduced basis method in geosciences. Addressing the challenge of high-dimensional problems (2020)
  2. Favino, Marco; Hunziker, Jürg; Caspari, Eva; Quintal, Beatriz; Holliger, Klaus; Krause, Rolf: Fully-automated adaptive mesh refinement for media embedding complex heterogeneities: application to poroelastic fluid pressure diffusion (2020)
  3. Grave, M.; Camata, José J.; Coutinho, Alvaro L. G. A.: Residual-based variational multiscale 2D simulation of sediment transport with morphological changes (2020)
  4. Kaczmarczyk, Łukasz; Ullah, Zahur; Lewandowski, Karol; Meng, Xuan; Zhou, Xiao-Yi; Athanasiadis, Ignatios; Nguyen, Hoang; Chalons-Mouriesse, Christophe-Alexandre; Richardson, Euan J.; Miur, Euan; Shvarts, Andrei G.; Wakeni, Mebratu; Pearce, Chris J.: MoFEM: An open source, parallel nite element library (2020) not zbMATH
  5. Kopaničáková, Alena; Krause, Rolf: A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020)
  6. Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E.: Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids (2020)
  7. Smetana, Kathrin: Static condensation optimal port/interface reduction and error estimation for structural health monitoring (2020)
  8. Vadala-Roth, Ben; Acharya, Shashank; Patankar, Neelesh A.; Rossi, Simone; Griffith, Boyce E.: Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity (2020)
  9. Abdulle, Assyr; De Souza, Giacomo Rosilho: A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations (2019)
  10. Caboussat, Alexandre; Glowinski, Roland; Gourzoulidis, Dimitrios; Picasso, Marco: Numerical approximation of orthogonal maps (2019)
  11. Cerveny, Jakub; Dobrev, Veselin; Kolev, Tzanio: Nonconforming mesh refinement for high-order finite elements (2019)
  12. Feng, Xinzeng; Hormuth, David A. II; Yankeelov, Thomas E.: An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging (2019)
  13. Fritz, Marvin; Lima, Ernesto A. B. F.; Nikolić, Vanja; Oden, J. Tinsley; Wohlmuth, Barbara: Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation (2019)
  14. Garg, Vikram V.; Stogner, Roy H.: Local enhancement of functional evaluation and adjoint error estimation for variational multiscale formulations (2019)
  15. Gesenhues, Linda; Camata, José J.; Côrtes, Adriano M. A.; Rochinha, Fernando A.; Coutinho, Alvaro L. G. A.: Finite element simulation of complex dense granular flows using a well-posed regularization of the (\mu(I))-rheology (2019)
  16. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  17. Robert Anderson, Julian Andrej, Andrew Barker, Jamie Bramwell, Jean-Sylvain Camier, Jakub Cerveny, Veselin Dobrev, Yohann Dudouit, Aaron Fisher, Tzanio Kolev, Will Pazner, Mark Stowell, Vladimir Tomov, Johann Dahm, David Medina, Stefano Zampini: MFEM: a modular finite element methods library (2019) arXiv
  18. Roberts, Nathan V.: Camellia: a rapid development framework for finite element solvers (2019)
  19. Rong, Junjie; Ye, Wenjing: Topology optimization design scheme for broadband non-resonant hyperbolic elastic metamaterials (2019)
  20. Sváček, Petr: On implementation aspects of finite element method and its application (2019)

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