*
*## E. Laitinen, A.V. Lapin, J.Pieska

## Splitting iterative methods and parallel solution of
variational inequalities

*
*## (Lobachevskii Journal of Mathematics,

## Vol.8, pp.167-184)

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.

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