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.


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)
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