Ing. Jakub Šístek, Ph.D.

Článek

10.1016/j.cpc.2021.108199

Katedra aplikované matematiky

This work deals with the application of the Balancing Domain Decomposition by Constrains (BDDC) method to unsteady two-phase flow problems in porous media. We briefly describe the spatial discretization of the problem which is based on the mixed-hybrid finite element method (MHFEM) and semi-implicit time discretization. Then, we describe the BDDC method, in detail discuss the differences between the symmetric and nonsymmetric cases, and present the necessary modifications of the algorithm for the more complicated nonsymmetric case. We describe the parallel implementation of the method and highlight the critical steps of the algorithm that affect the performance and scalability. The parallel implementation is then tested on benchmark problems in 2D and 3D and its efficiency is investigated on various meshes. The numerical results indicate that the method preserves good computational efficiency for increasing number of processes and, therefore, allows solving problems on very fine meshes. In the case of unsteady problem, additional speed-up is achieved using the information from previous time steps for the solution in the current time step.

Článek

10.1016/j.matcom.2011.03.014

Katedra aplikované matematiky

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems. (c) 2011 IMACS. Published by Elsevier B.V. All rights reserved.