The work discusses several extentions to the method of moments (MoM), considered in the context of electromagnetics. The topics include the interpolating multiple domain basis functions (MDBF), and improvement to the condition number of the impedance matrix. The main focus in the work is on a realization of the novel composite multiple domain basis functions (MDBF), enabling an efficient treatment for curved structures, which is backward compatible with most of the existing MoM codes. The MDBF is a profiled linear combination of common basis functions (BF), such as piecewise linear (PWL). The method also permits to extend the thin wire approximation. Several automatic algorithms were developed to implement the method. The method realizing MDBFs has been applied to several examples, demonstrating an order of magnitude reduction in the number of unknowns required and translating into a hundred-fold memory saving. Furthermore, a theoretical basis for applying higher order polynomial basis functions has been introduced. Most of the methods introduced in the work may be applied in other computational fields, e.g. structural analysis.