By Alfredo Bermúdez de Castro, Dolores Gomez, Pilar Salgado

The ebook represents a simple help for a grasp path in electromagnetism orientated to numerical simulation. the most aim of the booklet is that the reader understands the boundary-value difficulties of partial differential equations that are meant to be solved on the way to practice machine simulation of electromagnetic procedures. in addition it incorporates a half dedicated to electrical circuit conception according to traditional differential equations. The ebook is especially orientated to electrical engineering functions, going from the overall to the categorical, particularly, from the entire Maxwell’s equations to the actual circumstances of electrostatics, direct present, magnetostatics and eddy currents types. except usual workouts concerning analytical calculus, the ebook contains a few others orientated to real-life purposes solved with MaxFEM loose simulation software.

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**Example text**

4. Compute the current intensity traversing the circuit in Fig. 4, considering that the power generator has no internal resistance and supplies an harmonic electromotive force with complex amplitude 120 V and frequency 1 Hz. 33 cos(2π t + π ). 5. Compute the current intensity traversing the circuit in Fig. 5, considering that all power generators have no internal resistance and that all of them supply a harmonic electromotive force with frequency 1 Hz. The complex amplitudes are 12, 6, 9, 10 and 4 V respectively.

The Schur complement linear system is built: → − →m+1 → − →0 →m − t− m − A DΔ−1 = A DΔ−1 t A V t ( E (tm+1 ) + C ( I , . . , I )) + Ψ (tm+1 ). 12) 3. For each edge j representing a generator without internal resistance: a. 12) (this amounts to adding a new row to matrix t A DΔ−1 t A ). b. A column is added to the above matrix to keep symmetry (this means to add a new unknown: the current intensity along edge j). In order to facilitate the computer implementation it is convenient to number the edges corresponding to generators without internal resistance at the end.

EE (t))t where E j (t) = 0 if there is no a power source at edge j. Moreover, let us denote by D the algebraic-differential linear operator defined on → − a vector of E functions of time, I (t), by: • if edge j is a resistor: → − D( I ) j (t) := R j I j (t); • if edge j is an uncoupled inductor: dI j → − (t); D( I ) j (t) := L j dt • if edge j is a capacitor: 1 → − (Q j (0) + D( I ) j (t) := Cj t 0 I j (s) ds); • if edge j is a power generator: → − D( I ) j (t) := r j I j (t); • if the subset of edges S = {lk : k = 1, .