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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 14
Edited by: B.H.V. Topping and A.I. Khan
Paper XIII.5

A Domain Decomposition Polynomial Preconditioning for Parallel Processing

M. Papadrakakis and S. Bitzarakis

Institute of Structural Analysis & Aseismic Research, National Technical University of Athens, Greece

Full Bibliographic Reference for this paper
M. Papadrakakis, S. Bitzarakis, "A Domain Decomposition Polynomial Preconditioning for Parallel Processing", in B.H.V. Topping, A.I. Khan, (Editors), "Information Technology for Civil & Structural Engineers", Civil-Comp Press, Edinburgh, UK, pp 257-263, 1993. doi:10.4203/ccp.14.13.5
A conjugate gradient algorithm based on a domain decomposition formulation is proposed for the solution of large-scale problems resulting from the application of the finite element method. A polynomial type preconditioning is employed in which the approximate inverse of the global coefficient matrix is expressed by a second-order Neumann series, where an additive composition of the preconditioning matrix by its subdomain contributions is achieved. This local nature of the preconditioning matrix makes it suitable for parallel implementation. Block type preconditioning, where full elimination is performed inside each block, is also studied and compared with the proposed polynomial preconditioning.

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