Symbolic computational systems introduce some unique features in computational engineering. There have been several papers published on the solution of differential equations under given boundary conditions by symbolic systems. The finite element formalism has received prime attention in the course of development of symbolic computation in engineering. The main idea has been to develop a symbolic FEM package to reduce the burden of manual algebra, eliminate errors introduced by numerical quadrature, and improve the efficiency of element generation.
This work discusses a symbolic solution to electromagnetic linear antenna problems. The solution is a method of moments that transforms Pocklington's integral equation to a matrix equation. The symbolic system is used to produce (1) analytical integration, ( 2 ) the parametric expression for the input impedance and (3) computational code for forward and reverse problem of the input impedance.
1. Introduction
A symbolic computation system has many possible roles in engineering. It can be used to do analytical differentiation, polynomial manipulation, transformation, integration, solving systems of linear equations, matrix operations, power series and so It can be used to perform symbolic computations which result in parametric representation of the solutions or numerical calculation with automatically bounding error.4 We may benefit from it for problems involving high precision and high speed. For example, if one can establish through a symbolic system an internally consistent method of moments formalism for an electromagnetic computation, then one may port this algorithm to a network of fast machines. The same transfer from interpretive code t o compiled code such as Fortran and C makes it possible to handle larger problems.s
There are many advantages of expressing engineering problems with symbolic systems. Traditional mathematical formulas give relations and results, but cannot capture the processes of calculation that lead to them. Thus, for example, a traditional formula might give the solution to a particular kind of equation, but cannot trace the process by which such a solution is found.
Most papers on the symbolic computation in engineering have been focused on the application to the finite element methods."-"' In this work we introduce an application of symbolic computation to the antenna problem through the method of moments.'l The example to be discussed is a linear dipole antenna loaded by two lumped impedances and fed at the centre.
2. EXAMPLE
In this section we develop a symbolic approach to the method of moments (point matching) formalism for the analysis of a dipole antenna. Pocklington's integral equationt2 is a good elementary example for antenna studies involving the use of the symbolic computation for forward ~~ ~