Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1703.06494

Coupling parallel adaptive mesh refinement with a nonoverlapping domain decomposition solver

Pavel Kůs·Jakub Šístek
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the effect of adaptive mesh refinement on a parallel domain decomposition solver of a linear system of algebraic equations. These concepts need to be combined within a parallel adaptive finite element software. A prototype implementation is presented for this purpose. It uses adaptive mesh refinement with one level of hanging nodes. Two and three-level versions of the Balancing Domain Decomposition based on Constraints (BDDC) method are used to solve the arising system of algebraic equations. The basic concepts are recalled and components necessary for the combination are studied in detail. Of particular interest is the effect of disconnected subdomains, a typical output of the employed mesh partitioning based on space-filling curves, on the convergence and solution time of the BDDC method. It is demonstrated using a large set of experiments that while both refined meshes and disconnected subdomains have a negative effect on the convergence of BDDC, the number of iterations remains acceptable. In addition, scalability of the three-level BDDC solver remains good on up to a few thousands of processor cores. The largest presented problem using adaptive mesh refinement has over 10^9 unknowns and is solved on 2048 cores.

Explore related subjects

math.NAcs.MScs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pavel Kůs, Jakub Šístek. 2017-03-19. Coupling parallel adaptive mesh refinement with a nonoverlapping domain decomposition solver. https://doi.org/10.1016/j.advengsoft.2017.03.012

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗