The Efield® hybrid FDTD-FEM method

Applicability of method

The combination of structured and unstructured grids in the Efield® hybrid FDTD-FEM solver makes it particularly well suited for problems with different geometrical scales. A common example is antenna integration on large structures where a detailed model of the antenna is often necessary to obtain accurate antenna characteristics. Models for complex materials and subcell features are available in both the FDTD and FEM regions which together with the possibility of wide-band response in a single simulation make this approach extremely powerful.

  • Antenna design
  • Microwave design
  • EMI/EMC interaction
  • Antenna integration

Hybrid mesh around the aperture in a waveguide antenna Hybrid mesh around the nose of the Saab 2000 aircraft

Figure 1: Hybrid mesh details.

Description of method

The Efield® time-domain solver combines an FDTD solver on Cartesian grids with an FEM solver on unstructured grids. The underlying philosophy of this approach is to take advantage of the strengths of the individual solvers without suffering from their weaknesses. FDTD is used on a staggered Cartesian grid and is very efficient in homogeneous regions but not suitable for complex geometries due to the staircasing error. The FEM solver enables accurate modeling of complex geometries through the use of body conforming unstructured grids.

Solver features

Materials and boundary conditions

The Efield® hybrid FDTD-FEM solver can handle a wide variety of materials as

  • Dielectric & magnetic
  • Dispersive (Debye, Lorentz, General)
  • Lumped circuit elements (RLC)
  • Impedance boundary conditions
The option General Dispersive material is an option where the user can define a specific set of poles and residues of the electric susceptibility function.

Outer boundary conditions

Several different boundary conditions can be applied in the Efield® hybrid FDTD-FEM solver including

  • Absorbing boundary conditions (PML, UPML, Mur)
  • Periodic boundary condition


There are different ways to generate a source in the Efield® hybrid FDTD-FEM solver such as

  • Plane waves
  • Voltage and current sources on wires
  • Lumped circuit source
  • Waveguide mode excitation using 2D numerical or analytical eigenmode solver (homogeneous or inhomogeneous)
  • Point sources

Near-to-far-field transformation.

The user can choose between three different near-to-far-field transformations in the Efield® hybrid FDTD-FEM solver as

  • FD near-to-far-field transform. This transform is useful if the user wants the far-field information at a number of prescribed frequencies. A compensation procedure has been implemented for significantly reduce the dispersion error of the incoming wave.

  • CW near-to-far-field transform. For problems where a continuous wave source with a single frequency is used and an efficient continuous wave near-to-far-field transformation can be utilized.

  • TD near-to-far-field transform. This transform directly computes the scattered or radiated field versus time during the FDTD time stepping. The frequency domain fields can then be obtained by FFT post-processing.

Subcell models

The ability to model features that are small relative to the cell size is often important. Thus accurate models that characterize the physics of such features without the need for highly resolved grids are often essential. The Efield® hybrid FDTD-FEM solver includes state-of-the-art subcell models for

  • Thin wires
  • Thin sheets
  • Thin slots


Output from the Efield® hybrid FDTD-FEM solver include

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

Multi-block solver

The Efield® hybrid FDTD-FEM solver is parallelized using MPI multi-block technique. An optimal load balance is calculated and used for solving the problem based on the hardware regarding number of FLOPS, communication bandwidth and memory per processor.