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 98 articles , 1 standard article )

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  1. Yu, Bo; Cao, Geyong; Huo, Wendong; Zhou, Huanlin; Atroshchenko, Elena: Isogeometric dual reciprocity boundary element method for solving transient heat conduction problems with heat sources (2021)
  2. Antolin, Pablo; Buffa, Annalisa; Coradello, Luca: A hierarchical approach to the \textitaposteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells (2020)
  3. Bosy, Michał; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia: A domain decomposition method for isogeometric multi-patch problems with inexact local solvers (2020)
  4. Bracco, Cesare; Giannelli, Carlotta; Kapl, Mario; Vázquez, Rafael: Isogeometric analysis with (C^1) hierarchical functions on planar two-patch geometries (2020)
  5. Brugiapaglia, Simone; Tamellini, Lorenzo; Tani, Mattia: Compressive isogeometric analysis (2020)
  6. Buffa, A.; Puppi, R.; Vázquez, R.: A minimal stabilization procedure for isogeometric methods on trimmed geometries (2020)
  7. Bu, Ling-Ze; Zhao, Wei; Wang, Wei: Tensor train-Karhunen-Loève expansion: new theoretical and algorithmic frameworks for representing general non-Gaussian random fields (2020)
  8. Bünger, Alexandra; Dolgov, Sergey; Stoll, Martin: A low-rank tensor method for PDE-constrained optimization with isogeometric analysis (2020)
  9. Cho, Durkbin: Optimal multilevel preconditioners for isogeometric collocation methods (2020)
  10. Coradello, Luca; Antolin, Pablo; Vázquez, Rafael; Buffa, Annalisa: Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach (2020)
  11. Ding, Chensen; Deokar, Rohit R.; Lian, Haojie; Ding, Yanjun; Li, Guangyao; Cui, Xiangyang; Tamma, Kumar K.; Bordas, Stéphane P. A.: Resolving high frequency issues via proper orthogonal decomposition based dynamic isogeometric analysis for structures with dissimilar materials (2020)
  12. Drzisga, Daniel; Keith, Brendan; Wohlmuth, Barbara: The surrogate matrix methodology: low-cost assembly for isogeometric analysis (2020)
  13. Du, Xiaoxiao; Zhao, Gang; Wang, Wei; Guo, Mayi; Zhang, Ran; Yang, Jiaming: NLIGA: a MATLAB framework for nonlinear isogeometric analysis (2020)
  14. Garotta, Fabrizio; Demo, Nicola; Tezzele, Marco; Carraturo, Massimo; Reali, Alessandro; Rozza, Gianluigi: Reduced order isogeometric analysis approach for PDEs in parametrized domains (2020)
  15. Gervasio, Paola; Dedè, Luca; Chanon, Ondine; Quarteroni, Alfio: A computational comparison between isogeometric analysis and spectral element methods: accuracy and spectral properties (2020)
  16. Hu, Xindi; Zhu, Shengfeng: Isogeometric analysis for time-fractional partial differential equations (2020)
  17. Loli, Gabriele; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia: An efficient solver for space-time isogeometric Galerkin methods for parabolic problems (2020)
  18. Montardini, Monica; Negri, Matteo; Sangalli, Giancarlo; Tani, Mattia: Space-time least-squares isogeometric method and efficient solver for parabolic problems (2020)
  19. Sajavičius, Svajūnas; Takacs, Thomas: Imposing nonlocal boundary conditions in Galerkin-type methods based on non-interpolatory functions (2020)
  20. Ummidivarapu, Vinay K.; Voruganti, Hari K.; Khajah, Tahsin; Bordas, Stéphane Pierre Alain: Isogeometric shape optimization of an acoustic horn using the teaching-learning-based optimization (TLBO) algorithm (2020)

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