Wyniki wyszukiwania - BazTech

1

A regularized Newton method in electrical impedance tomography using shape Hessian information

Eppler K., Harbrecht H.

Control and Cybernetics

|

2005

|

Vol. 34, no 1

203-225

EN

The present paper is concerned with the identification of an obstacle or void of different conductivity included in a two-dimensional domain by measurements of voltage and currents at the boundary. We employ a reformulation of the given identification problem as a shape optimization problem as proposed by Roche and Sokolowski (1996). It turns out that the shape Hessian degenerates at the given hole which gives a further hint on the ill-posedness of the problem. For numerical methods, we propose a preprocessing for detecting the barycentre and a crude approximation of the void or hole. Then, we resolve the shape of the hole by a regularized Newton method.

2

Optimal Shape Design for Elliptic Equations Via Bie-Methods

Eppler K.

International Journal of Applied Mathematics and Computer Science

|

2000

|

Vol. 10, no 3

487-516

EN

A special description of the boundary variation in a shape optimization problem is investigated. This, together with the use of a potential theory for the state, result in natural embedding of the problem in a Banach space. Therefore, standard differential calculus can be applied in order to prove the Frechet-differentiability of the cost function for appropriately chosen data (sufficiently smooth). Moreover, necessary optimality conditions are obtained in a similar way as in other approaches, and are expressed in terms of an adjoint state for more regular data.

3

Second derivatives and sufficient optimality conditions for shape funetionals

Eppler K.

Control and Cybernetics

|

2000

|

Vol. 29, no 2

485-511

EN

For sorne heuristic approaches to boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for these approaches the functionals are Frechet-differentiable in some sense, because at least a local embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.