Paul Hüttl

Paul Hüttl
Universität Regensburg | UR

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5
Publications
578
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9
Citations
Citations since 2017
5 Research Items
9 Citations
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20172018201920202021202220230123456

Publications

Publications (5)
Article
Full-text available
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to represent the shapes over which we minimize. The idea behind this method is to modify the Laplace operator by introdu...
Preprint
Full-text available
We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [21] formulated for the principal eigenvalue of the Dirichlet--Laplacian. The shape, that is to be optimized, is represented by a phase-field function mapping into in the interval $[0,1]$. We show that any minimiz...
Preprint
Full-text available
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to represent the shapes over which we minimize. The idea behind this method is to modify the Laplace operator by introdu...
Article
Full-text available
A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality condi...
Preprint
Full-text available
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and differentiability of the eigenvalues and we establish the existence of a global minimizer to our optimization problem. We furt...

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Projects

Project (1)
Project
The goal is to optimize the shape/topology of an object described by a (multi-)phase-field equation. In this context, the shape/topology corresponds to the interface of the phase-field variable. For instance, compliance and eigenvalue optimization of elastic structures are investigated.