TY - GEN A1 - Keller, Hedwig A1 - Bartels, Sören A1 - Wachsmuth, Gerd T1 - Numerical Approximation of Optimal Convex and Rotationally Symmetric Shapes for an Eigenvalue Problem arising in Optimal Insulation N2 - 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. KW - shape optimization KW - optimal insulation KW - convexity KW - rotational symmetry KW - PDE constraints KW - iterative solution Y1 - 2021 UR - https://arxiv.org/pdf/2111.03364.pdf ER - TY - GEN A1 - Bartels, Sören A1 - Keller, Hedwig A1 - Wachsmuth, Gerd T1 - Numerical Approximation of Optimal Convex Shapes in ℝ³ T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2311.13386 SP - 1 EP - 17 ER - TY - GEN A1 - Keller, Hedwig A1 - Bartels, Sören A1 - Wachsmuth, Gerd T1 - Numerical Approximation of Optimal Convex and Rotationally Symmetric Shapes for an Eigenvalue Problem arising in Optimal Insulation T2 - Computers & Mathematics with Applications Y1 - 2022 U6 - https://doi.org/10.1016/j.camwa.2022.05.026 SN - 1873-7668 SN - 0898-1221 VL - 119 SP - 327 EP - 339 ER -