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Numerical realization of a fictitious domain approach used in shape optimization. I: Distributed controls. (English) Zbl 0854.49004
The authors deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.

##### MSC:
 49J20 Existence theories for optimal control problems involving partial differential equations 49Q10 Optimization of shapes other than minimal surfaces 49M30 Other numerical methods in calculus of variations (MSC2010)
##### Keywords:
optimal shape design; fictitious domain method
##### References:
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