In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then rescheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments that includes weak scalability analyses with structured and unstructured meshes for the three-dimensional Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-memory machines. This experimental study reveals remarkable weak scalability in the solution of problems with thousands of millions of unknowns on several tens of thousands of computational cores.

S. Badia, H. Nguyen. Relaxing the Roles of Corners in BDDC by Perturbed Formulation. (2017) DOI 10.1007/978-3-319-52389-7_41

O. Colomés, S. Badia. Segregated Runge-Kutta methods for the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Engng 105(5) (2015) DOI 10.1002/nme.4987

E. Neiva, S. Badia, A. Martín, M. Chiumenti. A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing. Int J Numer Methods Eng 119(11) (2019) DOI 10.1002/nme.6085

S. Badia, A. Martín, J. Principe. Multilevel Balancing Domain Decomposition at Extreme Scales. SIAM J. Sci. Comput. 38(1) DOI 10.1137/15m1013511

S. Zampini. PCBDDC: A Class of Robust Dual-Primal Methods in PETSc. SIAM J. Sci. Comput. 38(5) DOI 10.1137/15m1025785

S. Badia, H. Nguyen. Balancing Domain Decomposition by Constraints and Perturbation. SIAM J. Numer. Anal. 54(6) DOI 10.1137/15m1045648

S. Badia, M. Olm. Space-Time Balancing Domain Decomposition. SIAM J. Sci. Comput. 39(2) DOI 10.1137/16m1074266

S. Badia, A. Martín, H. Nguyen. Physics-Based Balancing Domain Decomposition by Constraints for Multi-Material Problems. J Sci Comput 79(2) (2018) DOI 10.1007/s10915-018-0870-z

L. Riha, M. Merta, R. Vavrik, T. Brzobohaty, A. Markopoulos, O. Meca, O. Vysocky, T. Kozubek, V. Vondrak. A massively parallel and memory-efficient FEM toolbox with a hybrid total FETI solver with accelerator support. The International Journal of High Performance Computing Applications 33(4) (2018) DOI 10.1177/1094342018798452

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E. Casoni, A. Jérusalem, C. Samaniego, B. Eguzkitza, P. Lafortune, D. Tjahjanto, X. Sáez, G. Houzeaux, M. Vázquez. Alya: Computational Solid Mechanics for Supercomputers. Arch Computat Methods Eng 22(4) (2014) DOI 10.1007/s11831-014-9126-8

S. Badia, A. Martín, J. Principe. FEMPAR: An Object-Oriented Parallel Finite Element Framework. Arch Computat Methods Eng 25(2) (2017) DOI 10.1007/s11831-017-9244-1

L. Yang, S. Badia, R. Codina. A pseudo-compressible variational multiscale solver for turbulent incompressible flows. Comput Mech 58(6) (2016) DOI 10.1007/s00466-016-1332-9