Edge finite elements - neural networks modelling for crosstalk in electronic printed circuit boards

The Hopfield Artificial Neural Network (ANN) algorithm is combined with the vector Finite Element Method (FEM) from the standpoint of the topological analogy between FEM and ANN. The ANN and FEM are combined as follows: the neurons are arranged on all the corresponding FEM elements, and the synaptic weights of each neuron are predetermined using FEM´s formulation. The unknown inputs of the network are updated using the Back-Propagation (BP) technique, and the Conjugate-Gradient (CG) algorithm is used for training the BP network. To show the validity of the method, the cross-talk interference and cutoff frequencies of the printed circuit board (PCB) are computed using this technique and compared with the analytical solutions. A MATLAB computer program is written to implement the method.