In this paper, the Cauchy problem for the Helmholtz equation is investigated. The objective is to recover the missing data on some part of the boundary of a bounded domain from overspecified data on the remaining part...
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In this paper, the Cauchy problem for the Helmholtz equation is investigated. The objective is to recover the missing data on some part of the boundary of a bounded domain from overspecified data on the remaining part of the boundary. We propose a preconditioned Krylov algorithm to solve this ill-posed problem, based on the represen-tation of the solution with surface integral equations and the Steklov-Poincare operator. We give a theoretical and numerical validation of the proposed method conducted in the 3D setting. We show the fast convergence of the proposed algorithm tested on various synthetic examples. The numerical results show a high precision of the reconstruction obtained for different levels of noisy data.(c) 2022 Elsevier B.V. All rights reserved.
This paper proposes a method that combines a data completion algorithm with the Reciprocity Gap-Linear Sampling Method (RG-LSM) to detect cracks in a non-homogeneous multi-layer domain with a modified impedance bounda...
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This paper proposes a method that combines a data completion algorithm with the Reciprocity Gap-Linear Sampling Method (RG-LSM) to detect cracks in a non-homogeneous multi-layer domain with a modified impedance boundary condition. The data completion algorithm recovers missing information using Cauchy data from the exterior boundary, extending the RG-LSM's application in such domains. We validate the robustness of the method through a theoretical analysis and 3D numerical tests, showing its effectiveness on various crack shapes and different noise levels.
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