A framework for solving the inverse scattering problem based on the Ultra Weak Variational Formulation
DOI:
https://doi.org/10.35819/remat2024v10iespecialid7053Keywords:
inverse problems, mild-slope equation, ultra weak variational formulationAbstract
This study focuses on two-dimensional inverse scattering problems, where information about an inaccessible region is inferred from measurements taken in accessible areas. The main focus is on the iterative resolution of the refraction-diffraction coefficient in the Helmholtz equation, using a regularized minimum square problem to cope with the ill-posed nature of the problem. To solve the corresponding direct problem, the Ultra Weak Variational Formulation (UWVF) method was applied, a method known for its computational efficiency, requiring fewer resources and allowing for analytical calculations. The methodology developed here was successfully applied to determine the bathymetry in coastal regions from the knowledge of waves in deep waters and along the coastline, yielding reliable and precise results.
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