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A Comparison of Additive Schwarz Preconditioners for Parallel Adaptive Finite Elements

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

We consider a second order elliptic boundary value problem in the variational form: find uH01(Ω), for a given polygonal (polyhedral) domain \(\varOmega \subset \mathbb{R}^{d},\,d = 2,3\) and a source term fL2(Ω), such that
$$\displaystyle{ \underbrace{\mathop{\int _{\varOmega }\nabla u^{{\ast}}(x) \cdot \nabla v(x)\,dx}}\limits _{\equiv a(u^{{\ast}},v)} =\underbrace{\mathop{ \int _{\varOmega }f(x)v(x)\,dx}}\limits _{\equiv (f,v)},\quad \text{for all }v \in H_{0}^{1}(\varOmega ). }$$
(1)
The Bank–Holst parallel adaptive meshing paradigm [1–3] is utilised to solve (1) in a combination of domain decomposition and adaptivity.

Notes

Acknowledgements

This work was supported by the Numerical Algorithms and Intelligent Software Centre funded by the UK EPSRC grant EP/G036136 and the Scottish Funding Council.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsHeriot-Watt University, Riccarton, EdinburghSchwarzUK

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