Issue |
ESAIM: COCV
Volume 26, 2020
|
|
---|---|---|
Article Number | 56 | |
Number of page(s) | 16 | |
DOI | https://doi.org/10.1051/cocv/2019030 | |
Published online | 08 September 2020 |
Solving a Bernoulli type free boundary problem with random diffusion
Departement Mathematik und Informatik, Universität Basel,
Spiegelgasse 1,
4051
Basel, Switzerland.
* Corresponding author: helmut.harbrecht@unibas.ch
Received:
15
April
2018
Accepted:
27
April
2019
The present article is concerned with the numerical solution of a free boundary problem for an elliptic state equation with random diffusion. The domain under consideration is represented by a level set function which is evolved by the objective’s shape gradient. The state is computed by the finite element method, where the underlying triangulation is constructed by means of a marching cubes algorithm. The high-dimensional integral, which is induced by the random diffusion, is approximated by the quasi-Monte Carlo method. By numerical experiments, we validate the feasibility of the approach.
Mathematics Subject Classification: 35R35 / 35N25 / 65C05 / 65N75
Key words: Free boundary problem / random diffusion / shape optimization
© EDP Sciences, SMAI 2020
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