Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives (Q1706404)
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scientific article; zbMATH DE number 6852045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives |
scientific article; zbMATH DE number 6852045 |
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Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives (English)
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22 March 2018
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The author considers a shape optimization issue for an eigenvalue Dirichlet boundary value problem attached to the Laplace equation. For this problem, a standard Ritz-Galerkin f. e. m. approximation along with its weak variational formulation are used during shape evolution. Then the author analyses two cases, a geometry constrained one and another unconstrained. Both are solved by two shape gradient descent algorithms based on shape sensitive analysis. Some interesting numerical experiments are carried out.
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shape optimization
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eigenvalue
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Eulerian derivative
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shape functional
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shape gradient
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Galerkin finite element
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