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.

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  1. Bracco, Cesare; Cho, Durkbin; Giannelli, Carlotta; Vázquez, Rafael: BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines (2021)
  2. Bucelli, Michele; Salvador, Matteo; Dede’, Luca; Quarteroni, Alfio: Multipatch isogeometric analysis for electrophysiology: simulation in a human heart (2021)
  3. Chen, Chun-Pei; Chen, Yaxiong; Subbarayan, Ganesh: Parametric stitching for smooth coupling of subdomains with non-matching discretizations (2021)
  4. Cho, D.; Pavarino, L. F.; Scacchi, S.: Overlapping additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity (2021)
  5. 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)
  6. 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)
  7. Xu, Chuang; Dong, Chunying; Dai, Rui: RI-IGABEM based on PIM in transient heat conduction problems of FGMs (2021)
  8. 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)
  9. Antolin, Pablo; Buffa, Annalisa; Coradello, Luca: A hierarchical approach to the \textitaposteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells (2020)
  10. Bosy, Michał; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia: A domain decomposition method for isogeometric multi-patch problems with inexact local solvers (2020)
  11. Bracco, Cesare; Giannelli, Carlotta; Kapl, Mario; Vázquez, Rafael: Isogeometric analysis with (C^1) hierarchical functions on planar two-patch geometries (2020)
  12. Brugiapaglia, Simone; Tamellini, Lorenzo; Tani, Mattia: Compressive isogeometric analysis (2020)
  13. Buffa, A.; Puppi, R.; Vázquez, R.: A minimal stabilization procedure for isogeometric methods on trimmed geometries (2020)
  14. 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)
  15. Bünger, Alexandra; Dolgov, Sergey; Stoll, Martin: A low-rank tensor method for PDE-constrained optimization with isogeometric analysis (2020)
  16. Cho, Durkbin: Optimal multilevel preconditioners for isogeometric collocation methods (2020)
  17. Cho, Durkbin: Overlapping Schwarz methods for isogeometric analysis based on generalized B-splines (2020)
  18. Coradello, Luca; Antolin, Pablo; Vázquez, Rafael; Buffa, Annalisa: Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach (2020)
  19. 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)
  20. Drzisga, Daniel; Keith, Brendan; Wohlmuth, Barbara: The surrogate matrix methodology: accelerating isogeometric analysis of waves (2020)

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