# Finite Element Method (FEM)

Finite Element Method (FEM)
 Full coupling between MoM and FEM regions.

### General Applicability of the Technique

The FEM is applicable to the modelling of electrically large or inhomogeneous dielectric bodies, which are not efficiently solvable with FEKO's extensions to the MoM. The FEM is a volume meshing technique that employs tetrahedra to accurately mesh arbitrarily shaped volumes where the dielectric properties may vary between neighbouring tetrahedra.

### Technical Foundation (Hybrid FEM/MoM)

The FEM/MoM hybridisation features full coupling between metallic wires and surfaces in the MoM region and heterogeneous dielectric bodies in the FEM region. The MoM part of the solution is calculated first, which results in equivalent magnetic and electric currents that form the radiation boundary of the FEM region. This hybrid technique makes use of the strengths of both the MoM and the FEM in the following ways:

• The MoM is used for the efficient modelling of open boundary radiating structures where no 3D space discretisation is required.
• The FEM is used for the efficient modelling of inhomogeneous dielectric bodies in term of field distributions inside the volume.

The FEM region may include complex surfaces, including:

• Metallic surfaces where a skin effect is significant.
• Thin dielectric sheets.
• Metallic surfaces with a finite surface impedance.
• Metallic surfaces with an electrically thin surface coating.

The intrinsic power of the FEM can also be harnessed for solutions of closed problems that are bounded by metallic surfaces.  When the FEM and MoM is decoupled and a structure is analysed that is bounded by metallic surfaces and is completely meshed as tetrahedra, FEKO will recognize that the problem can be solved with just the FEM, i.e. a fully sparse matrix solution.  This method uses very little memory and solves very fast, compared to the coupled FEM/MoM.

Magic Tee Waveguide Coupler
Ku-band Cavity Waveguide Filter
Two-path Cut-off Waveguide Filter
Runtime (3 GHz CPU)
(per frequency sample)
33.4 sec
17.2 sec
13.7 sec
Memory
62.3 MByte
99.2 MByte
31.3 MByte
Feed method
FEM modal port
(fundamental mode)
FEM modal port
(fundamental mode)
FEM modal port
(fundamental mode)
Model

### Accelerating the FEM/MoM - Parallelization and FEM/MLFMM Hybridisation

The parallelised FEM/MoM hybrid provides two significant solution features:

• All solution phases of the FEM/MoM hybrid have been parallelized and as such much faster solution times are achievable.
• Electrically larger or dielectrically more complex FEM/MoM problems can now be solved on less expensive computing platforms.  This is achieved through the use of distributed memory computing clusters, rather than shared memory platforms.

The FEM/MoM hybridisation is further optimized by hybridisation with the MLFMM.  The MLFMM method solves the MoM part of the FEM/MoM hybridisation very efficiently, making the following possible:

• Analysis of dielectrically complex antennas on large platforms, e.g. a microstrip antenna on an aircraft.
• Analysis of radiation hazards for humans in close proximity to high powered radiating antennas, e.g. humans inside a vehicle with a transmitting communication radio.

 Radiation hazard analysis for humans inside a vehicle with transmitting communication antennas

### Typical Application of the FEM

Typical applications of the FEM/MoM and FEM/MLFMM hybrid methods include antenna simulations, radiation hazard investigations where humans interact with RF equipment, the modelling of waveguide filters with dielectric blocks in the filter and the modelling of microstrip patches on finite substrates.

 Modelling a conformal linear array microstrip antenna on an air defence missile. 10g cube localised SAR peak in a FEM phantom wearing a metallic stab-proof jacket and a TETRA personal radio.