Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
Year: 2026
Type: preprint
Abstract: This paper considers an inverse shape problem for recovering an unknown impenetrable clamped obstacle in two dimensions from near-field point source and dipole measurements for the biharmonic Helmholtz equation in the frequency domain. The measured data consist of the scattered field and its normal derivative on a closed measurement curve surrounding the obstacle. Since the associated near-field operator does not directly admit the symmetric factorization required by the factorization method, we introduce a far-field transformation. This transformation is defined independently of the obstacle and augments the near-field operator into the associated far-field operator which does admit a symmetric factorization. This yields a rigorous complete characterization of the obstacle by the factorization method theory and leads to a practical reconstruction algorithm based on the spectral data of the transformed operator. Numerical experiments are presented to demonstrate the effectiveness of the proposed method, with synthetic near-field data generated using the method of fundamental solutions. We also consider reconstructions using only scattered-field measurements generated by point sources, demonstrating the potential for reduced the amount of measured data.
Source: arXiv (Cornell University)
Authors: Ozochiawaeze, General, Harris, Isaac
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7213581283