We finally present various numerical results in this chapter. Our main intention is to demonstrate that the results obtained by our stochastic approach differ significantly from those where, for example, all random variables are simply replaced by their expectations (especially see Section 5.1.1 in this context). Therefore, we particularly consider shape optimization applications where the desired behavior can be observed. In Section 5.1, we present some deterministic problem set-ups, together with some two-stage stochastic optimization counterparts based on the expectation value (cf. Definition 3.4). Subsequently, some first results for shape optimization problems with risk objectives (cf. Sections 3.3 and 3.4) are reported in Section 5.2. All computational results are obtained by Algorithm 4.10 or Algorithm 4.11, respectively, with the appropriate shape objective functional and its derivative as given in Section 4.2.
KeywordsOptimal Shape Excess Probability Surface Load Shape Optimization Problem Topological Derivative
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