Numerical experiments to "inverse medium scattering for a nonlinear helmholtz equation"

TechnicalRemarks: This is a guide to generate the figures that have been used in the work

Inverse medium scattering for a nonlinear Helmholtz equation

by Roland Griesmaier, Marvin Knöller and Rainer Mandel.

You find all needed Matlab files to generate the figures.

An overview: -evaluategfun_z is supposed to generate the Herglotz density g, dependent on a possible shift z\in R^2 -Finalplots plots the figures at the end of the computation -funhandle_zAbs evaluates the function handle corresponding to the factorization method -funhanlde_zReal evaluates the function handle corresponding to the monotonicity method -getc and ToepPhi are used to evaluate the Toeplitz matrix in order to evaluate the 2d convolution from the nonlinear Lippmann Schwinger equation. Convolution is performed by using the 2d Fourier transform. -getUi_z generates incoming Herglotz fields, dependent on a possible shift z\in R^2 -mycon is the constraint used in the optimization -NLHH evaluates the far field given an incoming field. This function uses a fixed point iteration arising from the nonlinear Lippmann Schwinger equation. -nonlinear_qh2_scaled gives the (scaled) function handle corresponding to a kite made of fused silica.

The scripts Numerical_Example_Fac.m and Numerical_Example_Mon.m start the reconstruction of the kite using the factorization and the monotonicity method, respectively.

The computations have been carried out on a Cluster using 32 Cores. Generating an example from scratch takes approximately 4 days. Computations have been carried out using the Matlab 2018a version.

The code uses parallelization from the Matlab Parallelization Toolbox. The code uses optimization from the Matlab Optimization Toolbox.