Galerkin method for electromagnetic field discretization

In order to develop the numerical analogs of the electromagnetic field integral representations, we have to discretize, also, the field components and the Green s tensors within the anomalous domain D of integration. We can treat all integral representations, considered in this chapter, as operators acting on the vector functions, x, 

For example, we show here how to represent formula (9.44) written in operator form, 

following the conventional technique of the Galerkin method (Kress, 1999), we form the inner product of both sides of equation (9.183) with the basis 

The coefficients of the expansion (9.181) are determined as the solution of this system of linear equations (9.185), which can be obtained by one of the numerical methods described in Chapters 3, 4, and 5. 

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