tIGAr swMATH ID: 32525 Software Authors: Kamensky, David; Bazilevs, Yuri Description: tIGAr: Automating isogeometric analysis with FEniCS. This paper introduces tIGAr, a library for using the open-source finite element (FE) automation software FEniCS to perform isogeometric analysis (IGA). The library uses a global variant of Bézier extraction to avoid modifying the finite element assembly procedures of FEniCS. This makes much of the convenient functionality of FEniCS directly available for IGA. General rational splines are implemented through an abstraction that sees only an extracted representation of the IGA function space. Through this abstraction, an enormous variety of spline spaces can be used for analysis, so long as a corresponding preprocessor is developed for each one, implementing a simple interface. As examples, we discuss preprocessors for B-splines specified analytically, non-uniform rational B-splines (NURBS) designed using the open-source software igakit, and T-splines designed using commercial software. We then demonstrate the implementation of solvers for several non-trivial partial differential equations that benefit from IGA. We also evaluate the parallel performance of tIGAr on a distributed-memory supercomputer. Finally, we outline possibilities for further development of IGA in FEniCS. Source code for tIGAr is continuously updated online at https://github.com/david-kamensky/tIGAr. Homepage: https://www.sciencedirect.com/science/article/pii/S0045782518304985 Source Code: https://github.com/david-kamensky/tIGAr Dependencies: FEniCS Keywords: isogeometric analysis; software; extsc{FEniCS}; NURBS; T-splines; Bézier extraction Related Software: ShNAPr; PETSc; FEniCS; DOLFIN; CouDALFISh; UFL; GitHub; TSFC; PetIGA; Matlab; ISOGAT; Python; petsc4py; Firedrake; mpi4py; Igatools; GeoPDEs; CutFEM; ParaView; top88.m Cited in: 17 Publications all top 5 Cited by 52 Authors 8 Kamensky, David 5 Bazilevs, Yuri 5 Hsu, Ming-Chen 3 Evans, John A. 3 Johnson, Emily L. 3 Rajanna, Manoj R. 2 Krishnamurthy, Adarsh 2 Liu, Ning 2 Lua, Jim 2 Phan, Nam 2 Xiang, Ru 2 Xu, Fei 2 Zhao, Han 1 Akkerman, Ido 1 Alaydın, Mert Deniz 1 Balu, Aditya 1 Burkhart, Harold M. 1 Chakrabarti, Anupam 1 Chowdhury, Rajib 1 Crisp, Caroline E. 1 Du, Xiaoxiao 1 Fernando, Milinda 1 Fletcher, Andrew H. 1 Fromm, Jennifer E. 1 Ganapathysubramanian, Baskar 1 Gao, Boshun 1 Guo, Mayi 1 Gupta, Abhinav 1 Hwang, John T. 1 Karuthedath, Philip Luke 1 Khanwale, Makrand A. 1 Khara, Biswajit 1 Khristy, Joel 1 Laurence, Devin W. 1 Lee, Chung-Hao 1 Li, Xiliang 1 Li, Xin 1 Liu, Xiangbei 1 Mamindlapelly, Bhagath 1 Maute, Kurt 1 Mir, Arshid 1 Moutsanidis, Georgios 1 Saurabh, Kumar 1 Shende, Shaunak 1 Sundar, Hari 1 ten Eikelder, Marco F. P. 1 Tong, Guoxiang Grayson 1 Wang, Wei 1 Wunsch, Nils 1 Xu, Songzhe 1 Yang, Jiaming 1 Zhao, Gang all top 5 Cited in 6 Serials 8 Computer Methods in Applied Mechanics and Engineering 4 Computers & Mathematics with Applications 1 Computers and Fluids 1 Numerische Mathematik 1 Computer Aided Geometric Design 1 Computational Mechanics all top 5 Cited in 8 Fields 10 Mechanics of deformable solids (74-XX) 9 Numerical analysis (65-XX) 5 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) Citations by Year