Method of Moment (MoM)

Applicability of method

The EfieldFD MoM solver is suitable for analysis of electrically small structures and applications include antennas and waveguides. Typically structures of the size up to five or ten wavelengths can be treated. Typical applications include

  • Antenna design
  • Waveguide design

Surface currents of horn antenna Far field of horn antenna
Figure 1: Standard gain horn antenna computed with MoM

Description of method

In the MoM mode the classical Gaussian elimination process is used to solve the matrix system. This requires solution time proportional to N3 and memory usage proportional to N2, where N is the number of unknowns in the system. However, since the Efield® MoM solver is parallelized and the resulting matrix and right hand side can be stored on disc the size of the problem that can be treated can be increased quite a lot using a cluster of computers.

Solver features

Direct Solvers

Solution of the matrix system is done using LDLT- or LU-factorization.

Material and Boundary conditions

The EfieldFD MoM solver can handle lossy and loss free dielectrics and magnetic materials, perfect electric and magnetic conductors as well as imperfectly conducting conductors. Boundary conditions that can be used are perfect electric and magnetic conductors (PEC/PMC) as well as imperfect conductors which are modeled using impedance boundary conditions (IBCs) or resistive boundary conditions (RBCs). Lumped elements (RLC) can be used on wire nodes and surface edges.

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

Thin Wires

The EfieldFD solvers incorporate a wire method that stays stable even for small wire segment discretization. Wire-wire junctions as well as surface-wire junctions can be handled.


Available excitations in the EfieldFD MoM solver are:

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


Output from the EfieldFD MoM solver 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 formulation leads to a linear system of equations and depending on the problem size, the memory need to store the system matrix can exceed the available main memory on the computer system. There are two different options in this case. One is to run the EfieldFD solver on a parallel computer and use the memory on the PCs or workstations. The other is to store the system matrix (and right hand side) on disc rather then in the main memory using the EfieldFD out-of-core solver.

All EfieldFD solvers are parallelized and the solvers will run effectively on both shared memory and distributed memory machines. The solvers can be run either in out-of-core mode or in in-core mode depending on available memory. In the case of out-of-core mode the storage is on files on disc whereas for the in-core mode storage is only in the internal memory.