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Numerical Green's Function (NGF)

Numerical Green's Function
Identifying static elements
in MoM matrices


The solution of problems that are analysed where some elements are modified may be sped up significantly by initially identifying static parts of the geometry and re-using the solution of these static parts in subsequent simulations where dynamic parts of the model are modified.  This domain decomposition method is called a Numerical Green's Function (NGF).

Examples of problem classes where an NGF is valuable include:

  • Optimisation of dynamic elements of an otherwise static model, e.g. slot dimensions in a slot coupled microstrip patch antenna.
  • Antenna placement investigations, e.g. changing the mounting position of an antenna on a vehicle, while the vehicle geometry remains static.

Investigation of optimal antenna position on a helicopter using NGF


An aperture coupled microstrip patch antenna is optimised with respect to its coupling slot dimensions.  The substrate, feed line and radiating top patch are identified as static sub-domains for the NGF, while the slot itself is a dynamic sub-domain.

In the first run, the NGF computes the mathematical response of the static domains as well, without a significant difference in solution requirements.

Default NGF active
CPU time (MoM matrix fill) [sec] 1 790 1 793
CPU time (MoM solution) [sec] 47 59 
Memory used [MByte] 56.3 56.3 

Computing a MoM solution while storing NGF data - Aperture coupled microstrip patch antenna configuration #1

In the second solution run, the NGF uses the already computed solution of the static sub-domains and only recomputes the contribution of the dynamic sub-domain (i.e. the slot).  In this instance a very significant saving is made in the amount of time required to compute the new solution.

Default NGF active
CPU time (MoM matrix fill) [sec] 2 249 844
CPU time (MoM solution) [sec] 51 44 
Memory used [MByte] 60.9 61.0 

Computing a MoM solution using NGF data - Aperture coupled microstrip patch antenna configuration #2