BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

Abstract

a b s t r a c tA high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for large-scale, convection-dominated problems. The algorithm is applied to the linear system arising from the discretization of the two-dimensional advection-diffusion equation and Euler equations for compressible, inviscid flow. A Robin-Robin interface condition is extended to the Euler equations using entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization of the diffusion-dominated flows, and achieves low iteration count in the advection-dominated regime. The BDDC method based on inexact local solvers with incomplete factorization and p = 1 coarse correction maintains the performance of the exact counterpart for the wide range of the Peclet numbers considered while at significantly reduced memory and computational costs.

Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows

“…Here we use a direct method for the serial case and one application of BDDC preconditioner when parallel solvers are treated. We refer to [33] for the application of the BDDC preconditioner to nonsymmetric problems. For a more detailed description of the implementation and algorithms used for the recursive block-preconditioning technique we refer to [25].…”

Massively parallel implementation of finite element, meshless and isogeometric analysis methods in computational mechanics

“…Since their introduction, non-overlapping DDM have been widely used for solving large-scale problems in a number of fields in computational mechanics. Some recent indicative applications are in contact problems [28], porous media problems [29], heterogeneous problems [30], stochastic finite elements [31], [32], inequality-constrained quadratic programming [33], Navier-Stokes equations [34], Helmholtz problems [35], Galerkin least-squares methods [36].…”

“…3.5. 18 ( 35,36) 19 ( 37,38) 20 ( 39,40) In order to maintain domain continuity, boundary node displacements must be equal in both subdomains:…”