Lower Bounds in Domain Decomposition

Brenner, Susanne C.

doi:10.1007/978-3-540-34469-8_3

Cited by 2 publications

(3 citation statements)

References 23 publications

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“…The estimate κ(B h A h ) δ −2 ≈ H −2 is consistent with the observed linear growth of the number of iterations for the preconditioned system as H decreases. Such a condition number estimate for the one-level additive Schwarz preconditioner is known to be sharp for standard finite element methods [1].…”

Section: Numerical Resultsmentioning

confidence: 99%

A One-Level Additive Schwarz Preconditioner for a Discontinuous Petrov–Galerkin Method

Barker

Brenner

Park

et al. 2014

Lecture Notes in Computational Science and Engineering

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Discontinuous Petrov-Galerkin (DPG) methods are new discontinuous Galerkin methods [3,4,5,6,7,8] with interesting properties. In this article we consider a domain decomposition preconditioner for a DPG method for the Poisson problem.Let Ω be a polyhedral domain in R d (d = 2, 3), Ω h be a simplicial triangulation of Ω . Following the notation in [8], the model Poisson problem (in an ultraweak formulation) is to find

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Section: Numerical Resultsmentioning

confidence: 99%

A One-Level Additive Schwarz Preconditioner for a Discontinuous Petrov–Galerkin Method

Barker

Brenner

Park

et al. 2014

Lecture Notes in Computational Science and Engineering

Self Cite

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“…This three-equation system (10) is the starting point from a rich zoology of methods, most of which possess strong connections we will try to emphasis on. Before going further in the exploration of these methods, we propose to introduce local condensed operators that represent a subdomain on its interface, then a set of synthetic notations.…”

Section: Basic Equationsmentioning

confidence: 99%

“…Once equipped with their best preconditioners and coarse problems, mathematical results [39,65,10] provide theoretical scalability of the methods. For instance for 3D elasticity problems, if h is the diameter of finite elements and H the diameter of subdomains, condition number κ of the interface problem reads (C is a real constant):…”

Section: Introductionmentioning

confidence: 99%

Non-overlapping domain decomposition methods in structural mechanics

Gosselet

Rey

2006

Arch Computat Methods Eng

137

166

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SummaryThe 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 decomposition methods. We present a review of most employed approaches and their strong connections. We outline their mechanical interpretations as well as the practical issues when willing to implement and use them. Numerical properties are illustrated by various assessments from academic to industrial problems. An hybrid approach, mainly designed for multifield problems, is also introduced as it provides a general framework of such approaches.

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Lower Bounds in Domain Decomposition

Cited by 2 publications

References 23 publications

A One-Level Additive Schwarz Preconditioner for a Discontinuous Petrov–Galerkin Method

A One-Level Additive Schwarz Preconditioner for a Discontinuous Petrov–Galerkin Method

Non-overlapping domain decomposition methods in structural mechanics

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