1. FDTD is a time based formulation, while MoM is a frequency based technique.

2. FDTD is suitable for problems which are of transient nature or wideband , while MoM is used for frequency sweep responses.

3. FDTD uses grid based Yee cells for volume based discretization. MoM on the other hand discretizes only the surface of the source. 

4. Since the entire solution domain needs to be meshed, the number of mesh elements are higher for FDTD, while since MoM only meshes the surface of the source, number of mesh elements are smaller in case of MoM

5. FDTD solves for fields E, and H., while MoM solves for current density Js or charge density Qs.

6. FDTD solves the 1st order Maxwell's differential equation of combined spatial and temporal type, while MoM solves the integral form of Helmholtz equation.

7.FDTD is suitable for complex geometries involving multiple dielectrics etc. MoM is more suited to radiation problems, and for electrically large structures MoM combined with fast techniques like Fast Multipole Method, is the best bet.

Nowadays, the problem for the designer is basically time of simulation. From my experience, the longest time for simulation is with FDTD method (CST Microwave Studio), then the FEM method (HFSS, CST) and the shortest will be MoM (IE3D).

In another point of view, if we compare about the accuracy, i think the FEM and FDTD is more accurate than MoM. Then, the hardware requirement for FEM is always bigger than FDTD. If you have enough hardware resource, never mind to choose FEM method. However, if you don't have enough hardware, you can think about FDTD but time for simulation will be extended.

In my opinion, i used MoM for the initial step of parametric studies with determined RF structure. Then, when i got the clearer picture and fixed the most important parameters, i'll switch to FEM or FDTD method to get more accurate results.

I hope this can help you.

Dear Dat Nguyen sir I need some more clarification on this. CST works on FIT (Finite Integration Technique), which solves integral equations, but in some material as you mentioned they refer CST Microwave Studio works under the principle of FDTD. I'm confused in this Please clarify me.

Dear Yuvaraj Siva,

In my opinion, because i worked with the broadband applications. So, if i use the FEM and keep the accuracy, the time of simulation should be very long because of incrementation in frequency points.

I am not expert of EM simulation but some professors said to me that FDTD is such an effective simulator for dispersive material. Especially, FDTD is quite accurate for the biological applications that the EM distribution is very sensitive to the change in EM properties of biological object (tissue, muscle...).

Thank you Dat Nguyen.

It depends on the problem. If you have a problem with many dielectric layers the best choice would be FDTD. However if you have many metallic object far from each other ( for example array of dipoles) then the best choice would be MoM.

FDTD/CFDTD is a good choice if you actually need the time response, or you are especially interested in a large bandwidth. FDTD is also a good choice if your problem geometry is particularly inhomogeneous, perhaps a mixture of dielectric or even magnetic material and even including electronic devices such as diodes. If you are interested in narrower frequency ranges and want to do some optimization, maybe MOM has an advantage. Also for problems with dielectric stratifications where the Green´s function can be used, then MOM also has a clear advantage as it will not have to sample inside the dielectric, unless you put your source there of course. If your problem has very small structure as well as very large structure, then MOM might be at an advantage since the meshing is not restricted to a rectangular grid. On the optimization point, this is usually done in the frequency domain and MOM thus has an advantage. If the problem is highly dispersive then FDTD has an advantage. If you actually want to visualize the fields, again FDTD has an advantage. FIT and FDTD are similar approaches, the difference being the choice of state variable. CFDTD can be implemented in practically the same way as FIT, as far as I am aware.

Compared with Method of Moments, FIT and FDTD can be considered as the same method. MoM is faster for some problems FDTD is faster for others. MoM can pick out small features (eg on a PCB) and does not need to mesh the vacuum with anything like the same resolution. MoM is likely faster for many small and medium sized antenna problems. OTOH behaviour inside dielectrics (especially dispersive ones) are hard in MoM, and given your other questions about PIC modelling, really FDTD integrates with PIC much better as there is less computational effort in reading off or interpolating the fields at a given point in space. Also FDTD can be configured to provide strong parallel 'scaling' on high performance computing systems, so for electrically large problems where waves/structure/particles are interacting over an electrically large region, FDTD can win out again. What this means is that a twice-as-big problem can be solved in (almost) the same time if one throws twice as many processor cores at it, on those systems set up for it.

1. FDTD is a time based formulation, while MoM is a frequency based technique.

2. FDTD is suitable for problems which are of transient nature or wideband , while MoM is used for frequency sweep responses.

3. FDTD uses grid based Yee cells for volume based discretization. MoM on the other hand discretizes only the surface of the source. 

4. Since the entire solution domain needs to be meshed, the number of mesh elements are higher for FDTD, while since MoM only meshes the surface of the source, number of mesh elements are smaller in case of MoM

5. FDTD solves for fields E, and H., while MoM solves for current density Js or charge density Qs.

6. FDTD solves the 1st order Maxwell's differential equation of combined spatial and temporal type, while MoM solves the integral form of Helmholtz equation.

7.FDTD is suitable for complex geometries involving multiple dielectrics etc. MoM is more suited to radiation problems, and for electrically large structures MoM combined with fast techniques like Fast Multipole Method, is the best bet.

Generally the MoM as implemented in commercial codes is frequency based, but that is not a requirement of MoM, only the specific software. Leonard Bennett did his PhD at Purdue for time-domain HFIE and mine was at Illinois for the time-domain EFIE -- so it is not a limitation of the method, but the software design. Each of the packages have their good and bad points. FEM (and FDTD) are useful for anisotropic or inhomogeneous media, while MoM is best for basic antenna problems.

Packages like FEKO allow MoM, FDTD, FEM, GO, and UTD to be combined in various forms to solve problems. For instance, FEM might be used to model the head and MoM the exterior antenna problem. UTD and GO help a lot of the large problems. There is varied opinion on methods, but each really has a realm where it is most useful and in most cases all give about the same answer (a few folks have done comparisons, though not typically published). In those cases, the issues are memory and time trade offs. When doing comparisons, you have to be careful to compare things in a compatible way. The user can also screw things up royally by not really having a feel for the limitations of the techniques. If you are going to use EM simulation software, you should really study the techniques a bit to get a feel for what is being done, rather than blindly using the software -- actually that goes for circuit and other simulation software as well. All have limitations and the good user learns those limitations.

A question was asked about CST and FIT. FIT is just another method to develop the FDTD equations, coming from an integral approach to get the equations rather than a finite-difference form. The results are basically the same.

The above answers are so,interesting and complete. I can just specify that:

* MoM is compliant especially for planar structures to benefit from the less time computation.

* Each method is used to resolve either a differential problem (FEM FDTD  FVM ) or integral one (MoM)  (You now that Maxwell's Equations have two forms differential and integral)

* To valid your simulation (especially when you can't make experiment work, The recommendation (as in indicated in joint paper talking about a EM simulators survey)  is to make simulation by using 2 simulators from different families (one differential and the other integral) and valid results when they convergent and they are nearly similar (that I do in my whole papers I work with FEKO usin MoM and HFSS using FEM).