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<p>Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem constrained by a nonlocal Dirichlet problem. Here, we focus on deriving the second shape derivative of the corresponding reduced functional and we further investigate a second-order optimization algorithm.</p>

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Second order shape optimization for an interface identification problem constrained by nonlocal models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月1日

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  • Matthias Schuster,
  • Volker Schulz

摘要

Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem constrained by a nonlocal Dirichlet problem. Here, we focus on deriving the second shape derivative of the corresponding reduced functional and we further investigate a second-order optimization algorithm.