The Efield® FDTD Method

Applicability of Method

The Efield® Finite-Difference Time-Domain (FDTD) solver is suitable for a wide range of problems. Due to its computational efficiency and parallelization it is possible to use for large problems such as finite antenna arrays, printed circuits and lightning simulations on large structures. The availability of subcell models for a range of common small features such as thin layers and slots the EfieldTD FDTD solver pushes the limit even further. Functionality such as waveguide ports, S-parameter computation and a range of far-field transforms makes it well suited also for broadband analysis of microwave and antenna problems. For very complex geometries the structured grid may be limiting due to staircase effects.

  • Antenna design
  • Microwave design
  • EMI/EMC interaction

Surface currents in the interior of the Saab 2000 aircraft Tapered slot array antenna simulation
Figure 1: Large scale FDTD simulations of Saab 2000 aircraft (left) and tapered slot array antenna (right).

Description of method

FDTD is based on the solution of Maxwell's equations on a structured grid where the electric and magnetic field components are staggered in both time and space. The resulting scheme is extremely efficient in homogeneous media both regarding memory requirements and in terms of arithmetic operations for given accuracy requirements.

The FDTD unit cell Computational domain in FDTD

Figure 1: The FDTD method.

Solver features

Materials and boundary conditions

The Efield® FDTD 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® FDTD solver including

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


There are different ways to generate a source in the Efield® FDTD 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 transformations

The user can choose between three different near-to-far-field transformations in the Efield® FDTD 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® FDTD solver includes state-of-the-art subcell models for

  • Thin wires
  • Thin sheets
  • Thin slots


Output from the Efield® FDTD 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® FDTD 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.