The code constitutes of four different .edp files:

1. "parameters.eps"

File that contains the physical and geometrical parameters of the medium where the waves will propagate. For each scatterer (circle, kite, or kite2), we have two medium type possibilities: a layered or in a non-layered one (these can be chosen changing the values of the string variables 'scatterer' and 'MediumType', respectively). Once that both the scatterer and medium type are chosen, one can decide the (piecewise constant) material properties: mu = rmu + 1.iimu and eps = rn + 1.iin, where the equation considered is div( mu^-1 grad(u)) + k^2 eps u = 0

This files generates two meshes: the one that "FFback.edp" will use and the one that "FFcrack.edp" will use (the background media mesh, and the mesh for the media with a -or a couple of- crack).

2. "FFback.edp" File that computes the Fourier coefficients of the far-field pattern associated to the acoustic scattered wave for different incident plane waves. Outputs:

3. The matlab file "filenameBack.m" (filenameBack is a variable that can be found in parameters.edp), that contains a Ninc x nbfpro matrix called Aback. Here Ninc = number of incident waves, nbfpro = truncation level for the Fourier series expansion.

4. The matlab file "RHS.m" that contains a Ninc x Nsample matrix called rhs, where Ninc = number of incident waves, Nsample = number of sample points along the curve gamma where we will reccord the value of the solution, later used as a right hand side for the LSM in the crack problem.

5. "FFcrack.edp" File that computes the Fourier coefficients of the far-field pattern associated to the acoustic scattered wave for different incident plane waves. The medium here is the same as in FFback.edp, except that there are some (1 or 2) cracks at the interface of two materials. The 'scatterer' variable in "parameters.edp" corresponds to different geometries for both the scatterer and the cracks: circle - Circular scatterer and 1 single crack kite - kite-shaped scatterer and 1 single crack kite2 - kite-shaped scatterer and 2 cracks

Output:

1. The unique output of "FFcrack.edp" is the matlab file "filenameCrack.m" (filenameCrack is a variable that can be found in parameters.edp), that contains a Ninc x nbfpro matrix called Adef. Here Ninc = number of incident waves, nbfpro = truncation level for the Fourier series expansion.

2. "auxfunc.edp" This file contains few auxiliary functions used by "FFback.edp" and "FFcrack.edp": i) the one that integrates functions in the FE space, against the Fourier basis function on the external circle (to make a change of basis to Fourier one), and which is very useful in the construction of both the DtN map and the far-field patterns. ii) Functions that save the outputs of "FFback.edp" and "FFcrack.edp" as matlab files