New matrix general formulas of dual-primal domain decomposition methods without recourse to lagrange multipliers
Por:
Herrera I., Yates R.A.
Publicada:
1 ene 2009
Resumen:
Nowadays parallel computing is the most effective means for increasing computational speed. In turn, the domain decomposition methods (DDM) are most efficient for applying parallel-computing to the solution of partial differential equations. The non-overlapping 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 Neumann-Neumann and the preconditioned FETI methods, here grouped generically as the round-trip methods. More recently, such methods have been improved by the introduction of the dual-primal methods, in which a relatively small number of continuity constraints across the interfaces are enforced. However, the treatment of round-trip algorithms up to now has been done with recourse to Lagrange multipliers exclusively. Recently, however, Herrera and his collaborators have introduced a more direct treatment, the "multipliers-free method", in which the differential operators are applied to discontinuous functions, and the matrices are applied to 'discontinuous vectors'. The multipliers-free method possesses significant advantages, many of them derived from the directness of its approach; among them, 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. © Civil-Comp Press, 2009.
Filiaciones:
Herrera I.:
Institute of Geophysics, National Autonomous University of Mexico (UNAM), Mexico
Yates R.A.:
Alternativas en Computación, S.A. de C.V., Mexico
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