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4.3.2 Assembly of the ElectroThermal Problem
The discretization of the electrical and the thermal problem, (4.32) and (4.40), respectively, forms a nonlinear system of equations for a tetrahedral element given by
where
corresponds to

(4.78) 
and
to





(4.79) 
for
.
Applying Newton's method, the element Jacobian matrix for the electrothermal problem has the form

(4.80) 
Since the global system for the electrothermal problem is constructed following the assembly procedure described in Section 4.1.2, the Jacobian matrix is the nucleus matrix to be computed for each element of the mesh.
The matrix entries for the electrical equation (4.78) are given, in general, by
and the entries for the thermal equation (4.79) are computed by
The righthand side of the linear system (4.73) is assembled by the residuals
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R. L. de Orio: Electromigration Modeling and Simulation