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 25 articles , 1 standard article )

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  1. 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)
  2. Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio: Isogeometric analysis and proper orthogonal decomposition for parabolic problems (2017)
  3. Beirão da Veiga, Lourenço; Buffa, Annalisa; Sangalli, Giancarlo; Vázquez, Rafael: An introduction to the numerical analysis of isogeometric methods (2016)
  4. Beirão da Veiga, Lourenco; Pavarino, Luca F.; Scacchi, Simone; Widlund, O.B.; Zampini, Stefano: BDDC deluxe for isogeometric analysis (2016)
  5. Cazzani, Antonio; Malagù, Marcello; Turco, Emilio: Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches (2016)
  6. Charawi, Lara Antonella: Isogeometric overlapping additive Schwarz solvers for the bidomain system (2016)
  7. 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)
  8. Sangalli, Giancarlo; Tani, Mattia: Isogeometric preconditioners based on fast solvers for the Sylvester equation (2016)
  9. Vázquez, R.: A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0 (2016)
  10. Pauletti, M.Sebastian; Martinelli, Massimiliano; Cavallini, Nicola; Antolin, Pablo: Igatools: an isogeometric analysis library (2015)
  11. Buffa, A.; Sangalli, G.; Vázquez, R.: Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations (2014)
  12. 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)
  13. Gao, Longfei; Calo, Victor M.: Fast isogeometric solvers for explicit dynamics (2014)
  14. Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo: Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models (2014)
  15. Heltai, Luca; Arroyo, Marino; DeSimone, Antonio: Nonsingular isogeometric boundary element method for Stokes flows in 3D (2014)
  16. Malagù, M.; Benvenuti, E.; Duarte, C.A.; Simone, A.: One-dimensional nonlocal and gradient elasticity: assessment of high order approximation schemes (2014)
  17. Mantzaflaris, Angelos; Jüttler, Bert: Exploring matrix generation strategies in isogeometric analysis (2014)
  18. Auricchio, F.; Beirão da Veiga, L.; Kiendl, J.; Lovadina, C.; Reali, A.: Locking-free isogeometric collocation methods for spatial Timoshenko rods (2013)
  19. Beirão da Veiga, L.; Cho, D.; Pavarino, L.F.; Scacchi, S.: Isogeometric Schwarz preconditioners for linear elasticity systems (2013)
  20. Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.: Multigrid methods for isogeometric discretization (2013)

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