JournalsifbVol. 1, No. 1pp. 3–16

Parallel algorithms for the solution of variational inequalities

  • Pierre-Louis Lions

    Collège de France, Paris, France
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Abstract

One of the many ways of solving free-boundary problems is, when possible, to put them (perhaps after suitable transformations) in the framework of variational or quasi-variational inequalities. It then remains to solve them numerically, a task which has been studied by Glowinski, Lions, & Tremolieres [9] without reference to parallel algorithms. On the other hand, systematic attempts to decompose the problems of the calculus of variations and of control theory have been made by Bensoussan, Lions, & Temam [4], using, among other things, ideas arising from splitting methods (see Marchuk [25] and the bibliography therein). We propose here a general method for obtaining, in infinitely many ways, stable parallel algorithms for the solution of variational inequalities of evolution. This method was introduced in [12] for equations of evolution. We show here how it can be adapted to variational inequalities (what is needed from [12] is recalled here).

Cite this article

Pierre-Louis Lions, Parallel algorithms for the solution of variational inequalities. Interfaces Free Bound. 1 (1999), no. 1, pp. 3–16

DOI 10.4171/IFB/1