Geodesic
Large splitting iterative methods and parallel solution of variational inequalities
Lobachevskii journal of mathematics, Tome 8 (2001), pp. 167-184

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Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied: convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analysed in the case when both operators are linear, self-adjoint and positive definite. The results are applied for the mesh variational inequalities which are solved using a non-overlapping domain decomposition method and the splitting iterative procedure. Parallel solution of a mesh scheme for continuous casting problem is presented and the dependence of the calculation time on the number of processors is discussed. 
@article{LJM_2001_8_a3,
     author = {E. Laitinen and A. V. Lapin and J. Piesk\"a},
     title = {Large splitting iterative methods and parallel solution of variational inequalities},
     journal = {Lobachevskii journal of mathematics},
     pages = {167--184},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2001_8_a3/}
}
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E. Laitinen; A. V. Lapin; J. Pieskä. Large splitting iterative methods and parallel solution of variational inequalities. Lobachevskii journal of mathematics, Tome 8 (2001), pp. 167-184. http://geodesic.mathdoc.fr/item/LJM_2001_8_a3/