Lecture 4 (FDTD) -- Electromagnetics and FDTD

[@QuentinLee2014]

It is really great course on FDTD. The speaker has profound understanding of the electromagnetic theory and numerical method, and could illustrate difficult things in a very easy way. I have listened to the lectures for three times, and have taken notes about the slides. Something really worth studying.

[@physicsfan8376]

Perfect course. Perfect teacher. I really enjoyed the physical meaning of equations, it makes them much more understandable.

[@empossible1577]

Thank you!!

[@SandipDhruba-v8j]

1:43 where on the website is it?

[@empossible1577]

The Lorentz force law? This typically is not used in FDTD. There is a variant called Particle in Cell (PIC) FDTD that uses it to simulate interaction with plasma. If you just want to learn more about the Lorentz force law, checkout Lectures 4e and 5d here: empossible.net/academics/emp3302/ Also, the course this video is from is here: empossible.net/academics/emp5304/ You may also be interested in a book we just published. It is intended to teach the art of computational electromagnetics to the complete beginner. The books goes all the way from basic concepts up to rather advanced simulations. Here is a link to the book website: empossible.net/fdfdbook/ Hope this helps!

[@nasserhussain5698]

Thanks, it is a great lecture.

[@sibichakravarthy037]

Very informative lecture!

[@Olenka181091]

At 22:58 the slide claims that the relative permeability is in range [1, inf] but the next slide with table 23:03 shows that for example for bismuth the value is

[@empossible1577]

Yes, the relative permeability is always greater than 1...except when it is not. ha ha Sorry for the confusion here. The answer is a bit involved, but whenever the parameters seem to have strange and magical values, it it usually a frequency-domain thing where parameters can easily have strange values depending on the frequency relative to where they are resonant. If you want to see more about this, checkout Topic 2 here: empossible.net/academics/emp6303/ BTW, let me point you to the official course website. Many of the lectures have been improved and revised. You can download the notes, get links to the latest videos, and more... empossible.net/academics/emp5304/ Also, you maybe interested in the following online courses in FDTD. They are intended for the complete beginner and even include extensive MATLAB codes. The first half of the first course is entirely free. empossible.thinkific.com/collections?category=FDTD-in-MATLAB Hope this helps!!

[@Olenka181091]

@@empossible1577 Thank you so much! This is a very helpful and comprehensive answer :)

[@Cringeupdates]

The function of D at 12:34 is actually the function of P, an extra term of epsilon_0*E is missing.

[@empossible1577]

P = eps_0 * chi * E D = eps * E eps = eps_0 * eps_r All equations at 12:34 look correct to me. Which equation is bothering you?

[@Cringeupdates]

@@empossible1577Boyd (non linear optics) defines P = epsilon_0*chi*E

[@empossible1577]

@@Cringeupdates Ah yes! I forgot a term in the third equation. ha ha. Thank you! I have fixed the notes that are available on the course website. When I rerecord, it will be in the video. empossible.net/academics/emp5304/

[@frankzack7294]

Great course.helped me a lot during coding my own simple Maxwell solver. I'm curious about the update equations for dispersive materials though. Taflove gives a very short summary for this..hard to follow. But fortunately theres no need for on-the-fly convolution or Fourier transformation,if I got it right. I didn't get the following: Is the E field still divergence-free in case of linear dispersion?

[@empossible1577]

This topic is covered in Lecture 10, but I only show one technique for incorporating dispersive materials. There are other many other methods.

[@tubupima5492]

In slide 36, why is the first order differential plus the function itself equals to zero? Thank you very much for the lecture by the way. It is the best.

[@empossible1577]

That just comes from the differential equation I chose for this example. Otherwise, there really is not a reason and it could change. I was just trying to keep it simple.

[@tubupima5492]

CEM Lectures Thank you!

[@salahuddinnur5054]

Hi, I have been folIowing this lecture series for learning EM/FDTD simulation. Can I cite this lecture series in my work? If yes, would you please provide the proper format. Thanks in advance ...

[@empossible1577]

Thank you! I am actually not sure how to cite KZbin videos. Perhaps you could cite the course website, which has links to the videos, latest version of the notes, and many other resources to help you. Here it is... emlab.utep.edu/ee5390fdtd.htm If you figure out how to cite this properly, please let me know!

[@salahuddinnur5054]

Thanks very much. I would cite the course website then ...

[@mikefredd3390]

I'm embarrassed to ask but what is meant by the convolution (*) operation?

[@empossible1577]

Ha ha. Glad you asked!! If you have not seen convolution before, it is a weird concept to grasp. It is sort of a blurring operation where you slide one function across another and report the overlap area as a function of the offset. You can take a look at the wikipedia article on convolution. en.wikipedia.org/wiki/Convolution Unless you are doing some more advanced FDTD, you do not need to understand convolution. The point is that the material properties are not constant, although it is usually an accurate approximation that really simplifies the simulation. However, imagine the permittivity changes with frequency. How do you account for this in a time-domain simulation when you potentially have a spectrum of frequencies all in the same simulation? I touch on this topic in Lecture 10. I also talk about another FDTD topic related to convolution in Lecture 12. Even though permittivity (and permeability) is a time-domain phenonemon, we like to report the permittivity as being a function of frequency. In the frequency-domain, the constitutive relation D=eps*E is a standard multiplication. However, when we Fourier transform to the time-domain, standard multiplication because convolution. BTW, here is a link to the course website. It as links to the lectures on KZbin, you can download the course notes, and get other resources that may help you develop your FDTD code.

[@mikefredd3390]

I can't seem to see the course website link can you resend? I'll start writing some code for lectures 5/6 in Python Saturday. Wish me luck.

[@empossible1577]

emlab.utep.edu/ee5390fdtd.htm

[@comment8767]

Sullivan eat your heart out!

[@mikefredd3390]

In the simulation can time flow backwards? Can I move sequentially clockwise and counter clockwise on this flow chart?

[@empossible1577]

Hmmm... I never thought about backward, but it seems to me the math works both ways. Give it a try!