A novel time-domain iterative method for a three-dimensional inverse acoustic obstacle scattering problem
This work addresses the inverse obstacle scattering problem for acoustics, offering a new computational approach with improved stability, but the results are incremental given the lack of quantitative comparison to existing methods.
The paper introduces a novel time-domain iterative method for reconstructing both the shape and location of a rigid obstacle in 3D acoustic scattering. Numerical experiments demonstrate effectiveness and robustness, though no specific accuracy or speed numbers are provided.
This paper concerns the three-dimensional forward and inverse acoustic obstacle scattering problem in the time domain. For the forward problem, a retarded potential formulation discretized by convolution quadrature and Galerkin methods is introduced. By introducing the retarded boundary integral defined on a homothetic surface, we propose a novel time-domain convolution quadrature based iterative method to reconstruct both the shape and location of a rigid obstacle. The retarded integral in the time domain is reformulated into a system of integrals in the s-domain. The resulting s-domain integrals are very fast to compute, as they only involve non-singular integrals over the homothetic surfaces. Moreover, the Fréchet derivative with respect to the boundary can be derived straightforwardly. We also prove that the scattered field generated by the homothetic surface converges to the exact field in the time domain. To improve the stability of the inversion algorithm, an incremental truncation technique is proposed, and numerical experiments confirm the effectiveness and robustness of our method.