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 124 articles , 1 standard article )

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  1. Arf, Jeremias; Simeon, Bernd: A space-time isogeometric method for the partial differential-algebraic system of Biot’s poroelasticity model (2022)
  2. Behnoudfar, Pouria; Loli, Gabriele; Reali, Alessandro; Sangalli, Giancarlo; Calo, Victor M.: Explicit high-order generalized-(\alpha) methods for isogeometric analysis of structural dynamics (2022)
  3. Bombarde, Dhiraj S.; Agrawal, Manish; Gautam, Sachin S.; Nandy, Arup: Hellinger-Reissner principle based stress-displacement formulation for three-dimensional isogeometric analysis in linear elasticity (2022)
  4. Buffa, Annalisa; Chanon, Ondine; Vázquez, Rafael: Analysis-aware defeaturing: problem setting and \textitaposteriori estimation (2022)
  5. Egger, Herbert; Harutyunyan, Mané; Löscher, Richard; Merkel, Melina; Schöps, Sebastian: On torque computation in electric machine simulation by harmonic mortar methods (2022)
  6. Hosseini, S. B.; Niiranen, J.: 3D strain gradient elasticity: variational formulations, isogeometric analysis and model peculiarities (2022)
  7. Kapidani, Bernard; Merkel, Melina; Schöps, Sebastian; Vázquez, Rafael: Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains (2022)
  8. Loli, Gabriele; Sangalli, Giancarlo; Tani, Mattia: Easy and efficient preconditioning of the isogeometric mass matrix (2022)
  9. Xu, Chuang; Zhan, Yunsheng; Dai, Rui; Yang, Huashi; Liu, Xiangyang; Dong, Chunying: RI-IGABEM for 3D viscoelastic problems with body force (2022)
  10. Bracco, Cesare; Cho, Durkbin; Giannelli, Carlotta; Vázquez, Rafael: BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines (2021)
  11. Bucelli, Michele; Salvador, Matteo; Dede’, Luca; Quarteroni, Alfio: Multipatch isogeometric analysis for electrophysiology: simulation in a human heart (2021)
  12. Chen, Chun-Pei; Chen, Yaxiong; Subbarayan, Ganesh: Parametric stitching for smooth coupling of subdomains with non-matching discretizations (2021)
  13. Cho, D.; Pavarino, L. F.; Scacchi, S.: Overlapping additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity (2021)
  14. Coradello, Luca; Kiendl, Josef; Buffa, Annalisa: Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach (2021)
  15. Coradello, Luca; Loli, Gabriele; Buffa, Annalisa: A projected super-penalty method for the (C^1)-coupling of multi-patch isogeometric Kirchhoff plates (2021)
  16. Ding, Chensen; Tamma, Kumar K.; Lian, Haojie; Ding, Yanjun; Dodwell, Timothy J.; Bordas, Stéphane P. A.: Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method (2021)
  17. Dwarka, V.; Tielen, R.; Möller, M.; Vuik, C.: Towards accuracy and scalability: combining isogeometric analysis with deflation to obtain scalable convergence for the Helmholtz equation (2021)
  18. Elasmi, Mehdi; Erath, Christoph; Kurz, Stefan: Non-symmetric isogeometric FEM-BEM couplings (2021)
  19. Li, Richen; Wu, Qingbiao; Zhu, Shengfeng: Isogeometric analysis with proper orthogonal decomposition for elastodynamics (2021)
  20. Montardini, M.; Remonato, F.; Sangalli, G.: Isogeometric methods for free boundary problems (2021)

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