Non-overlapping domain decomposition methods in structural mechanics

Non-overlapping Domain Decomposition Methods in Structural Mechanics

The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family of large ill-conditioned linear systems. In this paper we study strategies to efficiently solve to linear system based on non-overlapping domain decompositio...

Non-overlapping Domain Decomposition Methods

Our intention in this paper is to give a uniied investigation on a class of non-overlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring type methods and the Neumann-Neumann type methods. The basic framework used for analysis is the parallel subspace correction m...

Overlapping Domain Decomposition Methods

Overlapping domain decomposition methods are efficient and flexible. It is also important that such methods are inherently suitable for parallel computing. In this chapter, we will first explain the mathematical formulation and algorithmic composition of the overlapping domain decomposition methods. Afterwards, we will focus on a generic implementation framework and its applications within Diff...

Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods

We present a new parallelizable preconditioner that is used as the local component for a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attracting numerical behaviour and compare it to the regular BPS. Finally, to alleviate the construction cost of this new preconditioner, that requires the explicit computat...

Non - Overlapping Domain Decomposition