Calculus of Variations and Geometric Measure Theory

S. Bartels - G. Buttazzo

Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation

created by buttazzo on 12 Aug 2017


Submitted Paper

Inserted: 12 aug 2017
Last Updated: 12 aug 2017

Year: 2017


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.

Keywords: optimal insulation, symmetry breaking, numerical scheme