# Computational Benefits of Using Symmetry

Exploiting symmetry in model affects the calculation of the matrix equation, which can lead to a reduction in runtime and memory requirements.

## Geometric Symmetry

The arbitrarily placed sources lead to unsymmetrical current distributions. As a result, all unknown coefficients on all the mesh must be solved. The matrix equation being solved is, as a result, the same as it would have been, without symmetry being considered.

The computation time is however reduced for setting up the matrix equation. This reduction is achieved by exploiting the interaction between any two basis functions is the same as that between their symmetrical counterparts.

## Electric / Magnetic Symmetry

When using electric / magnetic symmetry, less computational time is required to calculate the matrix equation entries. The major benefit of using symmetry is that the number of unknown coefficients is reduced by a factor of two. The system of linear equations to be solved has only half of the dimension, in comparison to a model without electric / magnetic symmetry.

The impact for the method of moments (MoM) is a reduction by a factor four (=2*2) in memory requirement, as the MoM has fully populated matrices.

The impact for the finite element method (FEM) is a reduction by a factor two in memory requirement, as the FEM leads to sparsely populated matrices. The reduction in unknowns also leads to a dramatic lowering of matrix equation solution time.