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 86 articles , 1 standard article )

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  1. Antolin, Pablo; Buffa, Annalisa; Coradello, Luca: A hierarchical approach to the \textitaposteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells (2020)
  2. 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)
  3. Bünger, Alexandra; Dolgov, Sergey; Stoll, Martin: A low-rank tensor method for PDE-constrained optimization with isogeometric analysis (2020)
  4. Coradello, Luca; Antolin, Pablo; Vázquez, Rafael; Buffa, Annalisa: Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach (2020)
  5. 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)
  6. Drzisga, Daniel; Keith, Brendan; Wohlmuth, Barbara: The surrogate matrix methodology: low-cost assembly for isogeometric analysis (2020)
  7. Du, Xiaoxiao; Zhao, Gang; Wang, Wei; Guo, Mayi; Zhang, Ran; Yang, Jiaming: NLIGA: a MATLAB framework for nonlinear isogeometric analysis (2020)
  8. Gervasio, Paola; Dedè, Luca; Chanon, Ondine; Quarteroni, Alfio: A computational comparison between isogeometric analysis and spectral element methods: accuracy and spectral properties (2020)
  9. Montardini, Monica; Negri, Matteo; Sangalli, Giancarlo; Tani, Mattia: Space-time least-squares isogeometric method and efficient solver for parabolic problems (2020)
  10. 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)
  11. Beck, Joakim; Tamellini, Lorenzo; Tempone, Raúl: IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains (2019)
  12. Carraturo, Massimo; Giannelli, Carlotta; Reali, Alessandro; Vázquez, Rafael: Suitably graded THB-spline refinement and coarsening: towards an adaptive isogeometric analysis of additive manufacturing processes (2019)
  13. Deparis, Simone; Iubatti, Antonio; Pegolotti, Luca: Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space (2019)
  14. Dölz, Jürgen; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix: Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples (2019)
  15. Georg, Niklas; Ackermann, Wolfgang; Corno, Jacopo; Schöps, Sebastian: Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking (2019)
  16. Horger, Thomas; Reali, Alessandro; Wohlmuth, Barbara; Wunderlich, Linus: A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems (2019)
  17. Kaltenbacher, Barbara; Nikolić, Vanja: The Jordan-Moore-Gibson-Thompson equation: well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time (2019)
  18. Kamensky, David; Bazilevs, Yuri: \textsctIGAr: automating isogeometric analysis with \textscFEniCS (2019)
  19. Muhr, Markus; Nikolić, Vanja; Wohlmuth, Barbara; Wunderlich, Linus: Isogeometric shape optimization for nonlinear ultrasound focusing (2019)
  20. Nikolić, Vanja; Wohlmuth, Barbara: A priori error estimates for the finite element approximation of Westervelt’s quasi-linear acoustic wave equation (2019)

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