Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
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.
Related
- Spatial layout planning of cable based on a hybrid method combining interference obstacle local post-insertion and improved Dubins curves
- A Factorization Method for Support Recovery in Magnetic Induction Tomography
- PDNQP: A GPU-based Factorization-free Method for Large-scale Nonconvex Quadratic Programming
- A One-Factorization Predictor-Corrector Long-Step Arc-Search Method and a Curvature-Amplified Variant for Semidefinite Programming with a Homogeneous Self-Dual Embedding
- A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions
BibTeX
@misc{ozochiawaeze2026factorization,
title = {{Factorization method for a clamped obstacle from near-field measurements via a far-field transformation}},
author = {General Ozochiawaeze and Isaac Harris},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20528},
eprint = {2609.20528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20528},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
AU - General Ozochiawaeze
AU - Isaac Harris
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20528
UR - https://arxiv.org/abs/2609.20528
AB - 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.
ER -