Geodesic
Parallel algorithms for the solution of variational inequalities
Jacques-Louis Lions1
1Collège de France, Paris, France
Interfaces and free boundaries, Tome 1 (1999) no. 1, pp. 3-16

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DOI

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).
DOI : 10.4171/ifb/1
Classification : 46-XX, 00-XX
Mots-clés : Parallel algorithms, variational inequalities

Jacques-Louis Lions  1

1 Collège de France, Paris, France 
Jacques-Louis Lions. Parallel algorithms for the solution of variational inequalities. Interfaces and free boundaries, Tome 1 (1999) no. 1, pp. 3-16. doi: 10.4171/ifb/1
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