HYBRID NEWTON METHOD FOR RECOVERING MULTIPLE OBSTACLES BASED ON GENETIC ALGORITHM
基于遗传算法重建多个散射体的组合Newton法

This paper mainly studies the inverse problem of acoustic scattering to reconstruct the shapes of multiple sound-soft obstacles from a given incident field and its corresponding far field pattern of the scattered field. After constructing a nonlinear operator that maps the unknown boundary into the total field and its Fréchet differential, we investigate the hybrid Newton method via the single-layer potential. The convergence of the hybrid Newton method is established by transforming it into an optimal problem of a cost function. Furthermore, based on Genetic algorithm and the model function method for choosing regularization parameters, we present the numerical realization of the hybrid Newton method to recover multiple obstacles. Three numerical examples, which are to recover one obstacle, two obstacles and three obstacles, are given at last to show the feasibility of the method proposed in this paper.