Numerical solution of a nonlinear eigenvalue problem arising in optimal\n insulation

2017/08/12 by Sören Bartels, Bartels, Sören, Giuseppe Buttazzo +1 · 3 citations
Engineering · Mathematics · #35J25 #49R04 #65N12 #65N25 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1708.03762

openalex publication_date 2017/08/12 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/01

Abstract

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

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