BDDC swMATH ID: 7232 Software Authors: Šístek, J. Author Profile; Mandel, J.; Sousedík, B.; Burda, P. Description: Parallel implementation of multilevel BDDC In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method. Homepage: http://rd.springer.com/chapter/10.1007%2F978-3-642-33134-3_72 Keywords: Balancing Domain Decomposition by Constraints Related Software: BDDCML; PETSc; METIS; MUMPS; PCBDDC; lobpcg.m; Trilinos; FreeFem++; ParMETIS; PARDISO; GitHub; SuperLU; hypre; Gmsh; BoomerAMG; FEMPAR; FEniCS; DOLFIN; xSDK; FROSch Cited in: 30 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Parallel implementation of multilevel BDDC. Zbl 1311.65178Šístek, J.; Mandel, J.; Sousedík, B.; Burda, P. 2013 all top 5 Cited by 48 Authors 6 Šístek, Jakub 5 Sousedík, Bedřich 4 Klawonn, Axel 4 Rheinbach, Oliver 4 Spillane, Nicole 3 Badia, Santiago 3 Burda, Pavel 3 Zampini, Stefano 2 Hanek, Martin 2 Lanser, Martin 2 Mandel, Jan 2 Marcinkowski, Leszek 2 Martín, Alberto F. 2 Principe, Javier R. 2 Rahman, Talal 2 Rixen, Daniel J. 2 Widlund, Olof B. 1 Březina, Jan 1 Brown, Jed 1 Čermák, Martin 1 Cirak, Fehmi 1 Dohrmann, Clark R. 1 Eikeland, Erik 1 Gosselet, Pierre 1 Hapla, Vaclav 1 He, Yunhui 1 Heinlein, Alexander 1 Hetmaniuk, Ulrich L. 1 Horák, David 1 Jolivet, Pierre 1 Kühn, Martin Joachim 1 Li, Ruipeng 1 MacLachlan, Scott P. 1 Matouš, Karel 1 Niehoff, Balthasar 1 Pierson, Kendall H. 1 Pospíšil, Lukáš 1 Radtke, Patrick 1 Román, Jose E. 1 Roux, François-Xavier 1 Saad, Yousef 1 Sojka, Radim 1 Subber, Waad 1 Tu, Xuemin 1 Vasatova, Alena 1 Verdugo, Francesc 1 Weber, Janine 1 Xi, Yuanzhe all top 5 Cited in 12 Serials 8 SIAM Journal on Scientific Computing 3 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 2 ETNA. Electronic Transactions on Numerical Analysis 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computing 1 Computational Mechanics 1 SIAM Journal on Matrix Analysis and Applications 1 Applications of Mathematics 1 Numerical Linear Algebra with Applications all top 5 Cited in 6 Fields 27 Numerical analysis (65-XX) 8 Mechanics of deformable solids (74-XX) 7 Fluid mechanics (76-XX) 5 Partial differential equations (35-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) Citations by Year