Hi
I am working on two types of the inverse problem (reconstruction of the material properties) that involves solving the wave equation in the frequency domain for multiple right-hand sides. This problem is well known in geophysics (seismic inversion) and in biomedical imaging (Ultrasound imaging). Typically, this problem involves thousands of forward solves (FE simulation) as a result of sweeping overall frequency content and all sources (right-hand sides) at each iteration to the optimization (reconstruction).
Although I am just starting learning FEniCS and trying to switch to this new mindset, I can imagine how powerful FEniCS is especially for multiphysics simulation. However, I am still have some issues in deciding whether FEniCS is a suitable choice for my problems.
To be specific, the optimum framework that I am looking for is preferably having the following:
1- Can handle complex arithmetics (needed for solving the wave equation in the frequency domain)
2- Ability to modify the integration rule for specific region/regions of the domain (e.g. mid-point integration), this is needed to model a variant of the perfectly matched layer (PMDL) that acts as wave absorber.
3- Ability to update material properties after each optimization iteration in runtime without the need for updating the input.i file after each iteration.
So, if you could please give some pointers on the previous 3 points and some pointer on how to model an arbitrary, completely heterogeneous 3D domain (i.e each finite element in the mesh has different material property).
I really appreciate your response.