PUMA - Rapid Enriched Simulation Application Development. The PUMA software toolkit allows engineers to quickly implement simulation applications using generalized finite element techniques based on the partition of unity method (PUM). Compared to classical finite element methods (FEM), a PUM can directly utilize user insight, domain-specific information and physics-based basis functions in order improve the approximation properties of the model and to reduce the computational cost substantially. PUMA thus allows for the rapid evaluation of novel models. An introduction to the PUM can be found in M. A. Schweitzer. A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, Volume 29 of Lecture Notes in Computational Science and Engineering, Springer, 2003.

References in zbMATH (referenced in 31 articles )

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  1. Iqbal, M.; Stark, D.; Gimperlein, H.; Mohamed, M. S.; Laghrouche, O.: Local adaptive (q)-enrichments and generalized finite elements for transient heat diffusion problems (2020)
  2. Albrecht, Clelia; Klaar, Constanze; Pask, John Ernest; Schweitzer, Marc Alexander; Sukumar, N.; Ziegenhagel, Albert: Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem (2018)
  3. Banerjee, Subhajit; Sukumar, N.: Exact integration scheme for planewave-enriched partition of unity finite element method to solve the Helmholtz problem (2017)
  4. Dahlke, Stephan; Keding, Philipp; Raasch, Thorsten: Quarkonial frames with compression properties (2017)
  5. Griebel, Michael (ed.); Schüller, Anton (ed.); Schweitzer, Marc Alexander (ed.): Scientific computing and algorithms in industrial simulations. Projects and products of Fraunhofer SCAI (2017)
  6. Schweitzer, Marc Alexander; Ziegenhagel, Albert: Embedding enriched partition of unity approximations in finite element simulations (2017)
  7. Kergrene, Kenan; Babuška, Ivo; Banerjee, Uday: Stable generalized finite element method and associated iterative schemes; application to interface problems (2016)
  8. Griebel, Michael; Rieger, Christian; Zwicknagl, Barbara: Multiscale approximation and reproducing kernel Hilbert space methods (2015)
  9. Sillem, A.; Simone, A.; Sluys, L. J.: The orthonormalized generalized finite element method-OGFEM: efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions (2015)
  10. Tian, Rong; Wen, Longfei: Improved XFEM -- an extra-DoF free, well-conditioning, and interpolating XFEM (2015)
  11. Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng: A partition of unity method for a class of fourth order elliptic variational inequalities (2014)
  12. Krause, Dorian; Fackeldey, Konstantin; Krause, Rolf: A parallel multiscale simulation toolbox for coupling molecular dynamics and finite elements (2014)
  13. Dahlke, Stephan; Oswald, Peter; Raasch, Thorsten: A note on quarkonial systems and multilevel partition of unity methods (2013)
  14. Schweitzer, Marc Alexander: Multilevel partition of unity method for elliptic problems with strongly discontinuous coefficients (2013)
  15. Tian, Rong: Extra-dof-free and linearly independent enrichments in GFEM (2013)
  16. Babuška, I.; Banerjee, U.: Stable generalized finite element method (SGFEM) (2012)
  17. Schweitzer, Marc Alexander: Generalizations of the finite element method (2012)
  18. Fackeldey, Konstantin; Krause, Dorian; Krause, Rolf; Lenzen, Christoph: Coupling molecular dynamics and continua with weak constraints (2011)
  19. Schweitzer, Marc Alexander: Multilevel particle-partition of unity method (2011)
  20. Schweitzer, Marc Alexander: Stable enrichment and local preconditioning in the particle-partition of unity method (2011)

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