Frechet derivative calculation using finite difference methods

4-2 Frechet derivative calculation using finite difference methods The problem of the Frechet derivative, or sensitivity matrix calculation for electromagnetic field has been examined in many publications and was discussed in Chapter 

We can find the equations for the Prechet derivative by differentiating the corresponding electromagnetic field and potential equations. According to (9.48), the equations have the form 

Note that equation (12.88) has exactly the same structure as equation (12.10). Therefore, we can apply any of the differential methods, introduced in this chapter, to find the magnetic and electric field sensitivities (variations and E). 

For example, the corresponding system of finite difference equations is similar to system (12.35)  

If we would like to find the sensitivity of the electric field to the perturbation of the conductivity Sa in one cell, Vg, we have to substitute for e a vector which has only three nonzero components, i 

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