Discretization of the electromagnetic potential differential equations

Gauss theorem to the volume integral containing Laplacian and divergence operators  

We can evaluate now the volume and surface integrals in equation (12.54) approximately in terms of the discretized functions. This can be achieved by using the relationships, similar to (12.44) and (12.46). In particular  

The resulting system of linear algebraic equations and the accompanying boundary conditions for vector and scalar potentials can be expressed using matrix notations as 

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