Numerical methods for random Helmholtz problem

Date: Wed. October 27, 2021
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Title: Numerical methods for random Helmholtz problem

Speaker: Prof. Dr. Kai Zhang
Affiliation: Jilin University (China)

Abstract. In this talk, we discuss numerical methods for three kinds of random Helmholtz problems. For the random interface grating problems, by using the asymptotic perturbation approach via shape derivative, we estimate the expectation and the variance of the random solution in terms of the magnitude of the perturbation. For the optimal control problems constrained by random Helmholtz equation, we preprocess certain quantities before the ADMM iteration, so that nearly no random variable is in the inner iteration. For the inverse scattering problem, we propose a machine learning method for the data retrieval, which can effectively cope with the reconstruction under limited-aperture and/or phaseless far-field data. Numerical experiments verify the promising features of our schemes.



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