Volume 26, 2020
|Number of page(s)||16|
|Published online||08 September 2020|
Solving a Bernoulli type free boundary problem with random diffusion
Departement Mathematik und Informatik, Universität Basel,
* Corresponding author: email@example.com
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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