Applicability of method

The EfieldFD MoM-PO and MLFMM-PO solvers are suitable for analysis of very large problems where the electrical size is to large for MoM or MLFMM. Typical applications include

  • Radar cross section (RCS) analysis
  • Antenna integration on large structures
  • Reflector antenna design

Description of method

The MoM-PO and MLFMM-PO solvers use a domain decomposition of the problem into a MoM or MLFMM domain and a PO domain. In Figure 1 two examples of domain decomposition are shown for (left) a reflector antenna and (right) a UAV. In the Efield® mesh generation a tool for creating curvature based decompositions and detection of free edges are included which makes it easy for the user to create a suitable decomposition for the MoM-PO or MLFMM-PO solvers.

The EfieldFD MoM-PO and MLFMM-PO solvers are based on an iterative technique between the MoM or MLFMM and PO domain. First a solution is computed in the MoM or MLFMM region using the MoM or MLFMM solver. After this solution has been computed a solution in the PO region is solved for using the MoM or MLFMM solution as a source together with the excitation. After the PO solution has been computed a new solution is computed in the MoM or MLFMM region using the MoM or MLFMM solver with the PO solution as a source together with the excitation. The procedure is continued until convergence or until a preset number of iterations has been reached.

When using the MoM-PO or MLFMM-PO large savings in memory and solution time are achieved by instead of solving the whole problem with MoM or MLFMM one smaller MoM or MLFMM problem is solved and one larger PO problem.

Domain decomposition for MoM/MLFMM-PO MoM/MLFMM-PO decomposition of UAV Figure 1: MoM/MLFMM-PO decomposition of UAV

In Figure 2 and 3 an example of a MLFMM-PO simulation compared with a MLFMM simulation is shown. The directivity in the E-plane at 1.3 GHz for a Cassegrain antenna with diameter 7.5 m in azimuth direction and 5.0 m in elevation direction is computed using MLFMM and MLFMM-PO. The total number of unknowns was 154 665 for MLFMM and for the MLFMM-PO simulation these unknowns was decomposed into 141 139 PO and 13 526 MLFMM unknowns. In the MLFMM-PO simulation the MLFMM was used for the horn and the sub-reflector and PO for the main reflector as can be seen in Figure 2. As can be seen in Figure 3 the accuracy of the directivity in the E-plane in the MLFMM-PO simulation is very good. The simulation time for the MLFMM was in this case 1115 seconds compared to 307 seconds for the MLFMM-PO simulation giving a significantly reduction in simulation time.

MLFMM-PO decomposition
Figure 2: MLFMM-PO decomposition with MLFMM part shown in green (horn and sub-reflector) and PO part shown in red (main reflector)

Directivity E-plane
Figure 3: Directivity in E-plane

Solver features

Material and Boundary conditions

In the PO domain only PEC are allowed. In the MoM or MLFMM region the following material and boundary conditions are available.

  • Dielectric and magnetic materials, lossy and loss free
  • PEC
  • PMC
  • IBC
  • RBC
  • Lumped elements (RLC)


Available excitations in the EfieldFD MoM-PO and MLFMM-PO solvers are:

  • Plane wave
  • Dipole
  • Voltage excitations on surface edges
  • Waveguide mode excitations using 2D numerical or analytical eigenmode solver
  • General field distributions


Output from the MoM-PO and MLFMM-PO solvers includes:

  • S-parameters
  • Input impedance
  • SVWR
  • Reflection loss
  • Far-fields (2D, 3D, directivity, gain, field pattern and polarisation)
  • Radar Cross section (RCS) calculation, bistatic and monostatic
  • Near-fields
  • Surface and wire currents
  • Far field power
  • Power through user defined surfaces

Parallelization and out-of-core

The MoM-PO is fully parallelized for both distributed and shared memory machines. The MLFMM-PO is fully parallelized for shared memory machines using OpenMP.