AI Chat AI Image Generator AI Video Text to Speech

Numerical Approximation of Optimal Convex and Rotationally Symmetric Shapes for an Eigenvalue Problem arising in Optimal Insulation

11/05/2021

∙

by Hedwig Keller, et al.

∙

∙

We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in ℝ^3, the restriction to rotationally symmetric domains is used to reduce shape optimization problems to a two-dimensional setting. For the optimization of an eigenvalue arising in a problem of optimal insulation, the existence of an optimal domain is proven. An algorithm is proposed that can be applied to general shape optimization problems under the geometric constraints of convexity and rotational symmetry. The approximated optimal domains for the eigenvalue problem in optimal insulation are discussed.

Hedwig Keller
1 publication
Sören Bartels
24 publications
Gerd Wachsmuth
1 publication

research

∙ 09/10/2023

Riemannian Acceleration with Preconditioning for symmetric eigenvalue problems

In this paper, we propose a Riemannian Acceleration with Preconditioning...

0 Nian Shao, et al. ∙

research

∙ 06/14/2021

Optimizing Rayleigh quotient with symmetric constraints and their applications to perturbations of the structured polynomial eigenvalue problem

For a Hermitian matrix H ∈ℂ^n,n and symmetric matrices S_0, S_1,…,S_k ∈ℂ...

0 Anshul Prajapati, et al. ∙

research

∙ 11/13/2019

A new preconditioner for elliptic PDE-constrained optimization problems

We propose a preconditioner to accelerate the convergence of the GMRES i...

0 Hamid Mirchi, et al. ∙

research

∙ 02/28/2023

Non-convex shape optimization by dissipative Hamiltonian flows

Shape optimization with constraints given by partial differential equati...

0 Matthias Bolten, et al. ∙

research

∙ 07/03/2022

On shape and topological optimization problems with constraints Helmholtz equation and spectral problems

Coastal erosion describes the displacement of sand caused by the movemen...

0 Mame Gor Ngom, et al. ∙

research

∙ 03/14/2020

Nonlinear eigenvalue problems for coupled Helmholtz equations modeling gradient-index graphene waveguides

We discuss a quartic eigenvalue problem arising in the context of an opt...

0 Jung Heon Song, et al. ∙

research

∙ 07/12/2023

Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

In this article, we propose a reduced basis method for parametrized non-...

0 Yonah Conjungo Taumhas, et al. ∙