D1.6 Full versus Partial System Matrix

One problem with the Newton method arises from the fact, that the Jacobian matrix cannot be calculated exactly. Especially as the model parameters depend on many other quantities consideration of all derivatives would be very complicated. These missing derivatives can cause divergence of the Newton method at the beginning of the iteration. As reported in [36] it is advantageous to ignore some of the derivatives of the system matrix at the beginning of the iteration process. This reduces the coupling of the equations and is especially useful in case of HD simulations where the derivatives of the carrier concentrations with respect to the carrier temperatures deteriorate the convergence properties. As default we ignore $\partial$n/$$\partial$$T_n and $\partial$p/$$\partial$$T_p when E₂(u) > E_th = 1.0 ^. V_T. This is specified by

HDBlock
{
   ignoreDer  = if (updateNorm > ignoreDerNorm, "EleDEtm,HolDHtm", "");
}