The finite-difference Time-domain method (FDTD)
Applicability of method
The EfieldTD FDTD solver is suitable for a wide range of problems. Due to its computational effiency 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
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.
Figure 1: The FDTD method. |
Solver features
Materials and boundary conditions
The Efield® time-domain solvers can handle a wide variety of materials. This includes inhomogeneous dielectric and diamagnetic materials as well linear dispersive material of Debye and Lorentz type. For dispersive materials there is also the option to define poles and residues of the electric susceptibility function to model a general linear dispersive material.
- PEC/PMC
- 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-FEM hybrid solver including metallic boundary conditions such as PEC and PMC. Absorbing boundary conditions (ABC’s) such as Mur, PML and UPML are available and can be selected by the user.
- Absorbing boundary conditions (PML, UPML, Mur)
- PEC/PMC
- Periodic boundary condition
Excitations
There are different ways to generate a source in the Efield® FDTD-FEM hybrid solver. Huygens’ sources are used to generate plane waves of arbitrary propagation direction and point sources are used to model dipoles. The plane waves can be defined using Cartesian as well as spherical polar coordinates. Other source options include ports, current sources, voltage sources on thin wires and point sources.
- 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-FEM hybrid solver. A frequency domain transform, a continuous wave (CW) transform and a time domain transform (TD).
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Frequency domain Near-to-Farfield transforms This transform is useful if you want to have 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.
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CW near-to-far field transforms For problems where a continuous wave source with a single frequency is used and an efficient continuous wave near-to-farfield 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 postprocessing.
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 EfieldTD solver includes state-of-theart subcell models for thin wires, thin slots and thin sheets.
- Thin wires
- Thin sheets
- Thin slots
Post-processing
Output from the EfieldTD solver includes:
- S-parameters
- Input impedance
- Reflection loss
- Far fields (2D, 3D, directivity, gain, field pattern, polarisation, power...)
- Radar Cross section (RCS) calculation, bistatic and monostatic
- Surface and wire currents
- Power through user defined surfaces