Efield® FDTD-FEM method
Applicability of method
The combination of structured and unstructured grids in the EfieldTD 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 makes this approach extremely powerful.
- Antenna design
- Microwave design
- EMI/EMC interaction
- Antenna integration
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 bodyconforming unstructured grids.
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.
- Frequency domain Near-to-Farfield transforms
- CW near-to-far field transforms
- TD near-to-far field transform
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.
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Thin sheets The sheets are defined in FDTD as Cartesian plates with a certain normal direction. The implementation is very general allowing for intersecting and overlapping sheets. The discontinuous electric field components at the sheet are taken into account by introducing additional degrees of freedom. The parameters that are attached to each sheet are: the thickness, relative permittivity, the conductivity and relative permeability.
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Thin wires To grid wires independent of the volumetric grid greatly simplifies modelling for the engineer. This useful model is offered both in FDTD and FEM. The wire is composed of straight segments of a certain length, radius and resistivity. Voltages and current sources can be applied as well as loads with arbitrary impedance. For low frequency problems a simpler wire model is available that forces the wire to follow Cartesian grid edges and completely avoids interpolation since an electric field component is always collocated with a current node. Wires can run from the FDTD to the FEM region.
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Thin slots The thin slot model is based on a dual formulation to the thin wire model and can be used for slots located in both the FDTD and FEM regions. The slots are located in a PEC screen but can otherwise have arbitrary location. It is assumed that the length is much larger than the width and that both the depth and width are electrically small. A symmetric coupling between slot and field variables ensures stability.
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