A procedure for defining behavior of weight functions near the edge for best convergence using the Galerkin method

A general procedure is described for calculating linear functionals of the electromagnetic theory. The procedure is based on the equivalence of two methods of calculating such functionals-the GM and the variational method (VM). To implement the procedure the sought linear functional is expressed as a variational functional. The stationarity condition of the latter leads to some auxiliary problems. Due to the equivalence the WF behavior near the edge is the same as that obtained from the solution of the auxiliary problem. The efficiency of the procedure, i.e., the high speed of convergence, is illustrated by two examples: (1) calculation of the equivalent circuit shunt impedance of the capacitive diaphragm in a plane waveguide, and (2) calculation of the capacitance of a metal tube segment filled with dielectric