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<p>We consider the geometric inverse problem of determining an immersed obstacle in a 2D linear wave equation from overspecified boundary data. We use the topological gradient method to solve this problem. The unknown obstacle is reconstructed using the leading term of the Khon–Vogelius shape function variation. We propose a simple and fast detection algorithm. The efficiency and accuracy of the proposed approach are illustrated by some numerical examples.</p>

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A Non-iterative Reconstruction Method For The Geometric Inverse Problem For The Wave Equation

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Hamza Kahlaoui

摘要

We consider the geometric inverse problem of determining an immersed obstacle in a 2D linear wave equation from overspecified boundary data. We use the topological gradient method to solve this problem. The unknown obstacle is reconstructed using the leading term of the Khon–Vogelius shape function variation. We propose a simple and fast detection algorithm. The efficiency and accuracy of the proposed approach are illustrated by some numerical examples.