# Comparison of FDTD, FEM and MOM techniques

1. ## Comparison of FDTD, FEM and MOM techniques

the application relates specifically to electrically large problems, for instance modeling various types of antennas (but resonant types), such as wire or MPA's on vehicles.

i have no practical experiencing solving any of these techniques, but am looking for a greater understanding as to why any solution technique would be better than another in different applications including the one mentioned above.

are these statements below generally true? (this is currently my line of thinking)

FEM (HFSS) and FDTD(CST) are different solution techniques, one in frequency and one in time, that generally require the same computational power (computer power) to solve problems. Because each of these solutions discretizes the problem and requires a radiation volume, generally their problem sizes are comparable.

MOM (FEKO, IE3D/FIDELITY) for instance, does not require a radiation boundary by imposing certain boundary conditions to the structure in its solution technique. however, because of these imposed boundary conditions this technique is not useful for complex 3-d volumes of non metallic surfaces so on....

i want to conclude that MOM can handle larger electrical problems, compared to FDTD and FEM, given the right set of circumstances (essentially the problem consists of PEC only)

is my understanding correct and if not can anyone discuss this with me? •

2. ## fdtd vs fem

A good rule of thumb is to have the mesh edge length to be less than a tenth of a wavelength. (This is true in time domain methods as well.) This parameter is called the linear meshing density, and if hold this parameter is held constant, we can compare the three methods. Since everybody likes acronyms, let's call this the LMD.

PDE methods, like FEM and FDTD, use volume meshing. So the number of unknowns increase with the cube of the linear meshing density. For these methods memory and solution time scale proportionally with number of unknowns. Thus memory and time are O(LMD^3). The constant of proportionality depends greatly on implementation and the type of problem. For an antenna problem, especially near resonance, FEM tends to have the advantage.

Integral equations (e.g. MoM) use a surface mesh, and the number of unknowns increase with the square of the linear meshing density. PDE methods produce sparse matrices while IE methods produce dense matrices. For a dense matrix using an iterative solver, the memory and solution time scale with square of the unknowns, or O(LMD^4). However, there are fast methods for integral equations which reduce memory and time to O(N log N) with respect to the number of unknowns. Or in terms linear meshing density, O(LMD^2 * log LMD).

So an MoM, using a fast method, will eventually beat FDTD or FEM. There are three basic types of fast methods:
1.) multipole methods (e.g. FMM)
2.) hierarchal matrices (e.g. ACA)
3.) pre-corrected FFT

I know Feko has a FMM code and Ansoft Designer uses a hierarchal matrix technique. I don't know of any other commercial codes that use fast methods, but I have not looked. If there are others, I am sure their users or other representative, will chime in. •

3. ## hfss fdtd

hey wiley thanks for the response. i sent you a pm because you seemed knowledgable on the subject matter and possibly dont mind discussing it a bit further. •

4. ## fdtd fem

use ADS-Momentum a MOM EM simulator
& try EM3DS & AMDS for antenna applications. 5. ## fem vs fdtd

Following up:

There are two ways for IE codes to handle dielectrics. Actually there are an infinite number of ways, but only two have obtain commercial viability.

The first is based on the equivalence principle. These IE codes can handle arbitrary dielectrics as long as those dielectrics are isotropic at the cost of doubling the number of unknowns on those surfaces. PDE methods have a definite advantage here. For small to medium problems, PDE methods are a better choice. As the number of unknowns increases, the IE method will eventually do better, but the crossover point is very high. (HFSS has always beaten my own IE code on these types of problems; so on a PC, I think the PDE methods are the way to go.)

The second method incorporates the dielectrics into the Green's function. These are the "layered media" codes, like IE3D, Sonnet, and Designer. The different dielectrics are handled analytically, and only the current on the conductors is solved. If the problem is planar, it is very difficult to get more efficient than these types of codes. (My own layered media code has always beaten HFSS.) 6. ## fem hfss

Hello,

It depends upon the type of structures & frequency of operation..
Useually MoM can do bigger structures at low frequencies...
The FEM technique is potentially too computer intensive for such large problems
where high accuracy is required ( Meshing of complex structures requires
considerable time/memory in FEM based solvers) where FDTD or MoM can help...

The following link has some more details on each method

---manju--- •

7. ## fdtd and tem

The MLFMM is a great way to accelerate IE (MoM) based codes, using surface equivalence principle (SEP) to model dielectrics. It stores sparse matrices so memory scaling is very efficient, as is solution time.

The drawback with MoM-SEP is that you can't model very complex dielectrics, e.g. a human head with many tissue properties. You should look for a hybrid solution. FEKO offers a MoM-FEM hybrid that works really well. You setup the the metallic areas of your problem to solve with the MoM (good for metallics by only meshing surfaces and wires) and then setup the complex dielectric regions of your model (e.g. a human head) with the FEM, which is great for this purpose and also stores spares matrices. The FEM is bound with SEP triangles, so coupling to infinity and the MoM region is rigorously taken into account. Check out the relevant pages on their website:

Simple dielectric structures with MoM and its extensions.

Electrically large structures with MLFMM.

Complex dielectric structures with MoM-FEM hybrid. --[[ ]]--