Efield® time-domain solvers

Due to its computational efficiency and parallelization it is possible to use the Efield® time-domain solvers for both small and large problems in a wide range of applications such as finite antenna arrays, on-chip embedded passives, IC packages, lightning and EMC/EMI.

Time-domain modeling has the advantage of providing broadband results, for example S-parameters and far-field, in a single simulation using pulse excitation. Furthermore, 3D visualization of the time evolution of fields and currents can often give deeper understanding of electromagnetic effects in complicated environments.

Solver modes

The solver modes available in EfieldTD are the FDTD mode and the FDTD-FEM hybrid mode.

The FDTD mode

The Efield® FDTD method is the basic time-domain solver which is multi-block parallelized on a Cartesian grid. Functionality includes plane waves, waveguide ports, voltage sources, S-parameter computation and a range of far-field transforms which makes the EfieldŽ FDTD method well suited for broadband analysis of microwave and antenna problems.

The hybrid FDTD-FEM mode

Efield® is the first commercial software vendor offering a hybrid FDTD-FEM solver allowing unstructured grids for modeling complex geometries and small details, together with a structured grid for the rest of the domain. The Efield® hybrid FDTD-FEM solver combines a parallel FDTD solver on a Cartesian (structured) grid with a FEM solver on unstructured grids. The underlying philosophy is to take advantage of the strengths of the individual solvers without suffering from their weaknesses. The FEM solver enables accurate modeling of complex geometries through the use of body-conforming unstructured grids, while the FDTD solver enables optimal performance in homogeneous regions.

The hybrid solver allows local spatial refinement of the unstructured grids to resolve geometrical details or to model field singularities near sharp corners, edges or points. Stability is guaranteed through a careful design of the coupling of the FDTD and FEM solvers.

Hybrid meshing

The generation of the Efield® hybrid grid is an automatic process that gives the user the option to choose which type of grid that should be used for different parts of the geometry. An important feature is that there may be several disconnected unstructured grids in the same problem.

Materials and boundary conditions

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

  • Dielectric & magnetic
  • Dispersive (Debye, Lorentz, General)
  • Lumped circuit elements (RLC)
  • Impedance boundary conditions

Outer boundary conditions

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

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


There are different ways to generate a source in the Efield® FDTD and hybrid FDTD-FEM solvers 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

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 and hybrid FDTD-FEM solvers includes state-of-the-art subcell models for

  • Thin wires
  • Thin sheets
  • Thin slots


The Efield® FDTD and hybrid FDTD-FEM solvers include:

  • S-parameters
  • Input impedance
  • Reflection loss
  • Far fields (2D, 3D, directivity, gain, field pattern, polarization 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 and hybrid FDTD-FEM solvers are 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.

Detail of the hybrid mesh around the nose of a Saab 2000 aircraft

Surface currents on the interior walls of a shielded enclosure. The simulation was done using FDTD and subcell models.

Saab 2000 lightning simulation using the FDTD-FEM solver.

Interior currents in the Saab 2000 aircraft after a simulated lightning strike (FDTD).

Near field from an FDTD simulation of a tapered slot array.

Surface currents on a patch U-slot antenna from an FDTD-FEM simulation