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Electromagnetic field problems are often formulated as boundary value problems in unbounded regions. For this reason, the application of conventional numerical methods, such as the finite element method, is difficult. The paper describes a new technique to circumvent this difficulty. The technique is based on the reduction of the field equations in unbounded space to equivalent boundary Galerkin's criterion. Such criterion can be combined with the volume Galerkin's criterion for regions occupied by conductors. A new quasi-finite-element discretization based on the coupled boundary/volume Galerkin's criterion is presented.