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CivilComp Proceedings
ISSN 17593433 CCP: 90
PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED AND GRID COMPUTING FOR ENGINEERING Edited by:
Paper 5
New Matrix General Formulas of DualPrimal Domain Decomposition Methods without recourse to Lagrange Multipliers I. Herrera^{1} and R.A. Yates^{2}
^{1}Institute of Geophysics, National Autonomous University of Mexico (UNAM), Mexico
I. Herrera, R.A. Yates, "New Matrix General Formulas of DualPrimal Domain Decomposition Methods without recourse to Lagrange Multipliers", in , (Editors), "Proceedings of the First International Conference on Parallel, Distributed and Grid Computing for Engineering", CivilComp Press, Stirlingshire, UK, Paper 5, 2009. doi:10.4203/ccp.90.5
Keywords: domain decomposition methods, dualprimal, Lagrange multipliers, preconditioners, discontinuous Galerkin, FETI, NeumannNeumann.
Summary
Nowadays parallel computing is the most effective means for increasing computational speed. In turn, the domain decomposition methods (DDM) are most efficient for applying parallelcomputing to the solution of partial differential equations. The nonoverlapping class of such methods, which are especially effective, is constituted mainly by the Schur complement and the nonpreconditioned FETI (or Neumann) methods, here grouped generically as the oneway methods, together with the NeumannNeumann and the preconditioned FETI methods, here grouped generically as the roundtrip methods. More recently, such methods have been improved by the introduction of the dualprimal methods, in which a relatively small number of continuity constraints across the interfaces are enforced. However, the treatment of roundtrip algorithms up to now has been done with recourse to Lagrange multipliers exclusively. Recently, however, Herrera and his collaborators [1,2,3,4] have introduced a more direct treatment, the multipliersfree formulation, in which the differential operators are applied to discontinuous functions, and the matrices are applied to discontinuous vectors. Among some other advantages of such a direct treatment, it allows the development of more explicit and general expressions of the algorithm matrices, which are here reported. Such matrixexpressions in turn allow the development of more robust and simple computational codes.
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