Analysis of two-level domain decomposition preconditioners based on aggregation

Analysis of Two-level Domain Decomposition Preconditioners Based on Aggregation

In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothe...

Convergence of some two-level overlapping domain decomposition preconditioners with smoothed aggregation coarse space

We study two-level overlapping preconditioners with smoothed aggregation coarse spaces for the solution of sparse linear systems arising from finite element discretizations of second order elliptic problems. Smoothed aggregation coarse spaces do not require a coarse triangulation. After aggregation of the fine mesh nodes, a suitable smoothing operator is applied to obtain a family of overlappin...

Local preconditioners for two-level non-overlapping domain decomposition methods

Domain-decomposition based H-LU preconditioners

Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations

Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The onelevel domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach converg...