Linearized boundary control method for density reconstruction in acoustic wave equations
Year: 2024
Type: article
Abstract: We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagoves̆c̆enskiĭ's identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility.
Source: Inverse Problems
Authors: Lauri Oksanen, Tianyu Yang, Yang Yang
Institutions: University of Helsinki, Michigan State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
Awards: CAREER: Synergistic Inverse Wave Analysis and Computation, Acoustic Inverse Problems with Single and Multiple Measurements, Geometric inverse boundary value problems, ATD: An Edge-Based PDE Paradigm and Inverse Analysis for Spatiotemporal Information Diffusion and Threat Detection, Rapid 3D Ultrasound Tomography Reconstruction Methods for Guided Interventions, G8144583337, G8469057941
OpenAlex ID: W4404845598