PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

Abstract

Abstract. A class of preconditioners based on balancing domain decomposition by constraints methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc). The algorithm and the underlying nonoverlapping domain decomposition framework are described with a specific focus on their current implementation in the library. Available user customizations are also presented, together with an experimental interface to the finite element tearing and interconnecting dual-primal methods within PETSc. Large-scale parallel numerical results are provided for the latest version of the code, which is able to tackle symmetric positive definite problems with highly heterogeneous distributions of the coefficients. Current limitations and future extensions of the preconditioner class are also discussed.

Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners

“…The 2D tests have been performed with a MATLAB code based on the GeoPDEs library [13]. The 3D parallel tests have been performed using the PETSc library [2] and its PCBDDC preconditioner (contributed to the PETSc library by Zampini; see [43]) and run on the parallel machine Shaheen of KAUST (http://www.hpc.kaust.edu.sa/content/shaheen-ii).…”

“…The results show clearly the robustness of BDDC, for both choices of primal spaces. Figure 3, we report results of parallel numerical experiments on a 3D NURBS domain shown in Figure 1(c) and using the PCBDDC PETSc objects (see [43]) to implement BDDC deluxe with the VEF par coarse space, i.e., with primal constraints for vertices (V), edges (E), and faces (F). We study only this primal choice because V par was the algorithm attaining the best performance in our 2D results.…”

Scalable and Robust BDDC Preconditioners for Reservoir and Electromagnetics Modeling

“…al. 2014); the implementation of the BDDC preconditioner has been contributed to PETSc by the corresponding author (Zampini 2015). SPD linear systems are always solved using the Preconditioned Conjugate Gradient (PCG) method using random right-hand sides, null initial guesses, relative residual reduction 10 −8 as a stopping criterion, and the BDDC as a preconditioner.…”

“…For additional details on the implementation of the method considered in the current work, see ref. (Zampini 2015). In what follows, we will refer to the adopted strategy as adaptive BDDC.…”

“…Also, using adaptive selection of constraints at the coarser level provides high-quality spectrally equivalent BDDC solvers, which do not compromise the global convergence properties of the method at the finest level. The computation of the local and coarse corrections involved in the coarser levels of the BDDC preconditioner can be overlapped and independently solved on different MPI communicators (Zampini 2015).…”