Numerical solution of a nonlinear eigenvalue problem arising in optimal insulation
Provides numerical methods for a specific optimal insulation problem, with incremental insights into symmetry breaking and shape optimization.
The paper solves a nonlinear eigenvalue problem for optimal insulation, showing symmetry breaking for small insulation masses and identifying convex bodies with one symmetry axis as favorable.
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.