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i am working on a project concerning propagation modeling by means of MoM over irregular terrain profiles implemented in MATLAB.
I am supposed to load a topographic database (mountains, hills) and to apply MoM-(integral equations) for calculating the field strength.
Can anyone give any advice or hint how to apply the moments method over an irregular terrain?



You're gonna need a big computer. Really really big. Mind bogglingly big.


You should investigate the issue of intracability of large MoM problems. 'Terrain' is likely too large a problem space.

That problem might be more tractable using something like GTD/UTD.

Propagation over terrain is a problem that has already been done many times; but probably not using MoM under MatLab.


Thanks a lot VE1BILL...

I know that MoM may seem intractable but i should try to simulate MoM + irregular terrain in order to make the comparison with GTD, PWE, etc.
I will dare to ask you sth else.Do you know if i should treat the whole surface as one structure and apply the appropriate triangulation (RWG basis functions) or should i use point-matching method?
Or do i need to divide the terrain into smaller structures, depending on frequency?
Sorry for the "big questions"



Disclaimer - I'm not an expert in this field, just an observer.

MoM and the like break up the structure (in this case I think that your structure would be the terrain) into little 'finte-element' segments of 1/10 or 1/6 lambda. You can see that the problem size goes up as something like N^3 (by linear size, and inversely by frequency).

Modeling even a big airplane (~50m) at UHF is computationally very intensive. Modeling extended "terrain" (km scale) with MoM is probably completely intractable. Intractability might mean that you would need to fill the entire volume of the known Universe with neutrino-sized super-computers and it would still take forever to execute.

The model probably needs to be derived again for every significant change of frequency band. Otherwise you'll be doing many more calculations than necessary. 2:1 linear scale ratio is 8:1 computational effort ratio.

GTD/UTD works the other way. The canonical elements need to be a certain minimum size for the approximations to be valid. Again, the working model changes with frequency to keep it valid.

You should really look into commercial products and see what they do. Propagation over terrain is pretty-much a solved problem.


The largest Mom dimensions we'd even think of is 10 Lambda per side cube. Unless you're working in the 1 kHz frequency region and have measured terrain properties from the largest property measurement device on the planet, MoM codes won't make it.

Sounds like a manager gave you an assignment from the outer limits of space.


"The largest Mom dimensions we'd even think of is 10 Lambda per side cube."

And 18 months later when computer speeds have roughly doubled (i.a.w. Moore's Law), you'd be able to do about 12.5 Lambda per side cube.


Only partly true VE1BLL, (we actually do 6x7x10 lambda now max.). Our computer has 12 gig's of RAM, and uses that within about an hour of processing and going to the hard drive slows life down. Some of our runs are 1-2 weeks long.

The dual processor 64 bit machines are great, but we'd really  like to have 200+ gig's of ram to really make full use of our capability. It's costly though.



I was trying to make it clear that the Cube Law pretty much defeats Moore's Law: 18 months gives you roughly double the processing power and memory, but only a 25% increase in linear problem space using MoM.

On the other hand, the practical limits of GTD/UTD works in the opposite way. GTD/UTD starts to becomes practical just where MoM-type algorithms begin to choke any reasonable computer.

For many applications (like pattern prediction), GTD/UTD (done well) gives useful results in minutes on a normal PC. The algorithm speed allows one to check the results for inconsistencies or obvious errors 'six ways from Sunday' in mere hours (*). A moderate sized project (say a dozen antennas) could include several thousand runs if you wish to be careful.

* Assuming that the geometrical model of your 'structure', built from the limited set of allowed canonical elements, is already at hand.

For those that haven't seen GTD/UTD, it is reportedly derived (I mean formally derived, mathematically) from first principles (diffraction and all that). In other words, it is a perfectly valid approximation and the results should be just as good as the care you take with your .geo model.

People in this field have demonstrated good agreement with measured results (often limited by the quality of the measured results...).

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