GeoPDEs: a research tool for isogeometric analysis of PDEs. GeoPDEs ( is a suite of free software tools for applications on isogeometric analysis (IGA), see [T. J. R. Hughes, J. A. Cottrell and Y. Bazilevs, Comput. Methods Appl. Mech. Eng. 194, No. 39–41, 4135–4195 (2005; Zbl 1151.74419)]. Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-splines and non-uniform rational B-splines (NURBS), while being flexible enough to allow users to implement new and more general methods with a relatively small effort. This paper presents the philosophy at the basis of the design of GeoPDEs and its relation to a quite comprehensive, abstract definition of IGA.

References in zbMATH (referenced in 33 articles , 1 standard article )

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  1. Cho, D.; Pavarino, L. F.; Scacchi, S.: Isogeometric Schwarz preconditioners for the biharmonic problem (2018)
  2. Garau, Eduardo M.; Vázquez, Rafael: Algorithms for the implementation of adaptive isogeometric methods using hierarchical B-splines (2018)
  3. Beirão da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Adaptive selection of primal constraints for isogeometric BDDC deluxe preconditioners (2017)
  4. Beirão da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Parallel sum primal spaces for isogeometric deluxe BDDC preconditioners (2017)
  5. Horger, Thomas; Wohlmuth, Barbara; Wunderlich, Linus: Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics (2017)
  6. Perotto, S.; Reali, A.; Rusconi, P.; Veneziani, A.: Higamod: a hierarchical isogeometric approach for model reduction in curved pipes (2017)
  7. Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio: Isogeometric analysis and proper orthogonal decomposition for parabolic problems (2017)
  8. Beirão da Veiga, L.; Buffa, A.; Sangalli, G.; Vázquez, R.: An introduction to the numerical analysis of isogeometric methods (2016)
  9. Beirão da Veiga, Lourenço; Buffa, Annalisa; Sangalli, Giancarlo; Vázquez, Rafael: An introduction to the numerical analysis of isogeometric methods (2016)
  10. Beirão da Veiga, Lourenço; Pavarino, Luca F.; Scacchi, Simone; Widlund, O. B.; Zampini, Stefano: BDDC deluxe for isogeometric analysis (2016)
  11. Cazzani, Antonio; Malagù, Marcello; Turco, Emilio: Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches (2016)
  12. Charawi, Lara Antonella: Isogeometric overlapping additive Schwarz solvers for the bidomain system (2016)
  13. Lai, Yicong; Liu, Lei; Zhang, Yongjie Jessica; Chen, Joshua; Fang, Eugene; Lua, Jim: Rhino 3D to Abaqus: a T-spline based isogeometric analysis software framework (2016)
  14. Sangalli, Giancarlo; Tani, Mattia: Isogeometric preconditioners based on fast solvers for the Sylvester equation (2016)
  15. Vázquez, R.: A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0 (2016)
  16. Pauletti, M. Sebastian; Martinelli, Massimiliano; Cavallini, Nicola; Antolin, Pablo: Igatools: an isogeometric analysis library (2015)
  17. Buffa, A.; Sangalli, G.; Vázquez, R.: Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations (2014)
  18. Chen, De-Xiang; Xu, Zi-Li; Liu, Shi; Feng, Yong-Xin: Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations (2014)
  19. Gao, Longfei; Calo, Victor M.: Fast isogeometric solvers for explicit dynamics (2014)
  20. Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo: Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models (2014)

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