IETI swMATH ID: 19412 Software Authors: S.K. Kleiss, C. Pechstein, B. Jüttler, S. Tomar Description: IETI - Isogeometric tearing and interconnecting. Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method. Homepage: http://www.sciencedirect.com/science/article/pii/S0045782512002599 Related Software: GeoPDEs; G+Smo; ISOGAT; PetIGA; Igatools; GitHub; PCBDDC; PETSc; MUMPS; Total FETI; PetIGA-MF; Wesseling; Matlab; Trilinos; Eigen; BDDCML; IRIT; EBF3PanelOpt; DFVLR-SQP; SciPy Cited in: 68 Publications all top 5 Cited by 94 Authors 9 Pavarino, Luca Franco 9 Sangalli, Giancarlo 9 Scacchi, Simone 8 Beirão da Veiga, Lourenço 7 Buffa, Annalisa 7 Jüttler, Bert 7 Takacs, Stefan 6 Hofer, Christoph D. 6 Langer, Ulrich 5 Cho, Durkbin 5 Vazquez, Rafael 5 Widlund, Olof B. 5 Zampini, Stefano 4 Toulopoulos, Ioannis 3 Hofreither, Clemens 3 Kapl, Mario 3 Kleiss, Stefan K. 3 Mantzaflaris, Angelos 3 Schneckenleitner, Rainer 3 Takacs, Thomas 3 Tomar, Satyendra K. 2 Anitescu, Cosmin 2 Buchegger, Florian 2 Coox, Laurens 2 Desmet, Wim 2 Donatelli, Marco 2 Gahalaut, K. P. S. 2 Garoni, Carlo 2 Greco, Francesco 2 Kraus, Johannes K. 2 Kunoth, Angela 2 Manni, Carla 2 Rabczuk, Timon 2 Serra-Capizzano, Stefano 2 Speleers, Hendrik 2 Tani, Mattia 2 Vandepitte, Dirk 2 Vitrih, Vito 2 Zulehner, Walter 1 Antolin, Pablo 1 Atak, Onur 1 Bercovier, Michel 1 Birner, Katharina 1 Bosy, Michał 1 Bouclier, Robin 1 Brivadis, Ericka 1 Bucelli, Michele 1 Chan, Chiu Ling 1 Charawi, Lara Antonella 1 Collin, Annabelle 1 De La Riva, Alvaro Pe 1 de Prenter, Frits 1 Deckers, Elke 1 Dede’, Luca 1 Elguedj, Thomas 1 Evans, John A. 1 Gaspar, Francisco José 1 Gervasio, Paola 1 Gillot, Frederic 1 Goyal, Anmol 1 Harbrecht, Helmut 1 Hirschler, Thomas 1 Hughes, Thomas J. R. 1 Jézéquel, Louis 1 Kargaran, S. 1 Kosinka, Jiří 1 Lei, Zhen 1 Marini, Federico 1 Maurin, Florian Paul Robert 1 Mi, Yongzhen 1 Montardini, Monica 1 Moore, Stephen Edward 1 Morlier, Joseph 1 Papadrakakis, Manolis 1 Pechstein, Clemens 1 Puppi, Riccardo 1 Quarteroni, Alfio M. 1 Reali, Alessandro 1 Rodrigo, Carmen 1 Salvador, Matteo 1 Schillinger, Dominik 1 Scholz, Felix 1 Scott, Michael A. 1 Simeon, Bernd 1 Stavroulakis, George M. 1 Tsapetis, Dimitris 1 Van Brummelen, Harald 1 Verhoosel, Clemens V. 1 Wei, Xiaodong 1 Wohlmuth, Barbara I. 1 Wunderlich, Linus 1 Zheng, Hui 1 Zhuang, Xiaoying 1 Zore, Urška all top 5 Cited in 16 Serials 27 Computer Methods in Applied Mechanics and Engineering 7 Computers & Mathematics with Applications 5 SIAM Journal on Scientific Computing 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Computer Aided Geometric Design 2 Mathematics and Computers in Simulation 2 SIAM Journal on Numerical Analysis 2 Computational Methods in Applied Mathematics 1 Journal of Computational Physics 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Applied Mathematical Modelling 1 Computing and Visualization in Science 1 Journal of Applied Mathematics and Computing 1 Acta Numerica all top 5 Cited in 9 Fields 68 Numerical analysis (65-XX) 13 Partial differential equations (35-XX) 10 Mechanics of deformable solids (74-XX) 4 Approximations and expansions (41-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Fluid mechanics (76-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) Citations by Year