Cost Function Noise

The numerical calculation of the electromagnetic field introduces various sources of noise to the cost function, particularly because of changes in the finite element mesh. You must provide the optimizer with an estimate of the noise. The noise indicates whether a change during the solution process is significant enough to support achievement of the cost function.

For example, if the cost function, c, is

where |S₁₁| is the magnitude of the reflection coefficient, at the minimum, |S₁₁| is expected to be very small, .

From the solution setup, the error in |S₁₁| is expected to be . The perturbed cost function is therefore

Near the minimum, the error in the cost function E_c is given by

Therefore, the cost function noise would be 1.0.