JournalsifbVol. 21 , No. 1pp. 1–19

Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation

  • Sören Bartels

    Universität Freiburg, Freiburg im Breisgau, Germany
  • Giuseppe Buttazzo

    Università di Pisa, Italy
Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation cover
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Abstract

The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of corresponding eigenfunctions that determine the optimal layer thickness are addressed. Corresponding numerical experiments confirm the theoretical observation that a symmetry breaking occurs for the case of small available insulation masses and provide insight in the geometry of optimal films. An experimental shape optimization indicates that convex bodies with one axis of symmetry have favorable insulation properties.

Cite this article

Sören Bartels, Giuseppe Buttazzo, Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation. Interfaces Free Bound. 21 (2019), no. 1 pp. 1–19

DOI 10.4171/IFB/414