Best explanation i came across by far. Starting with the basics and going into details, and everything is well explained. I wish my teacher did it this way, so i could avoid all the pain and headache. Every time i come back to this channel.

@empossible1577

4 ай бұрын

That is awesome to hear!!!

This is pure gold, thank you!

Really good lecture, thanks for this. Very clear and practical explanations.

Really helpful lectures ,which is used to gain a lot of knowledge about variational methods.

Great explanation , the best video ever about finite elements method

@empossible1577

4 жыл бұрын

Thank you!

You are god mate, cant figured out this for two years and finally i can do , thanks a lot. Cheers from VŠCHT Prague.

@empossible1577

7 жыл бұрын

Great! Thank you!!

Thanks a lot Prof. great lectures....

thanks Professor, you made the whole image more clear!

@empossible1577

3 жыл бұрын

Great to hear!

Great lecture ! Thank you Professor This clarified some ambiguities that I was dealing with for two years ! nice

@empossible1577

3 жыл бұрын

That is great to hear!! Thank you!!!

Great lecture!

great thanks for this lecture

I hope it is not too late to thank you for the great job.

@empossible1577

4 жыл бұрын

Ha ha. Never to late!! Thank you!

Saved my course, finally variational method is making sense to me, thank you!!!

@empossible1577

8 жыл бұрын

+Samson Victor You are welcome!

There's a minor mistake at 6:14 (slide 7), for linear operators in general, they are not commutative. It is not always the case that L1[L2[f(x)]] = L2[L1[f(x)]]. The rule is probably not required, i haven't seen it used.

@empossible1577

Ай бұрын

Thank you for pointing this out! I am not sure why I wrote this down. In linear algebra, it is well known you cannot usually reverse the order because linear operations are not in general commutative. I am embarrassed! LOL

Bookmarks Summary of Galerkin's method 15:23 Example using ODE 17:07

This explanation is the best I have seen on KZread so far about variational methods, I only have a question about the method of weighted residuals, why do you need to chose a set weighting functions? Why do you need to test both sides with Wm(x)? It is not already sufficient with the previous steps to solve the differential equation?

@empossible1577

2 жыл бұрын

The main purpose of the method is to convert something into a matrix equation that can be solved numerically. It is easy to imagine a case where the problem does not have an analytical solution. A numerical solution is obtained this way. In order of a numerical solution to be obtained, the equation and functions have to be made discrete. In this method, they are made discrete by only storing the weights of the basis functions. The testing step give a final equation that can be solved to calculate the unknown weights of the solution.

@SiriusFuenmayor

2 жыл бұрын

@@empossible1577 thank you for your response, I think I was able to see the answer to my question, sometimes things in math are really obvious and you don't see it right away, I think that the reason to multiply of the second set of basis functions is that the main idea is to get the coefficients a_n. If you have a common vector x expanded in a orthonormal basis e_i for example x = a_1*e_1 + a_2*e_2 + a_3*e_3 you get the coefficients by making the dot product with the corresponding basis vector, for example to get a_1 you do = a_1* + a_2* + a_3* = a_1 + 0 + 0 = a_1 since the basis is orthonormal the same must be happening here, what do you think?

CEM Lectures, can you tell the difference between Galerkin and Rayleigh Ritz method, what is the main difference in between them ,, do you have any video on rayleigh ritz method?

Thank you so much for making and sharing these beautiful lectures with the rest of the world! Might there still be a way to get a pdf or some kind which contain the lecture slides? I saw someone else asked about that a few years ago but the link does not work anymore

@empossible1577

4 жыл бұрын

Thank you! Here is a link to the PDF version of the notes. These have seen quite a bit of revisions, corrections, additions, and other revisions since the videos were recorded. empossible.net/academics/emp5337/

GREEEEAAAAATTTT!!!

Is this method of weighted residuals also how density functional theory works? And just how linear combination of atomic orbitals functions in general?

Thank you a lot.

@empossible1577

Жыл бұрын

You are welcome!!

Thank you very much for this introduction .ive been looking for something like this. Please could you recommend a book for multipole and BEM methods and higher order BEM?

@empossible1577

2 жыл бұрын

I am not sure these are the best, but here are the books on my shelf... www.amazon.com/Boundary-Electrical-Engineers-Engineering-Electromagnetics/dp/1845640330/ref=sr_1_1?crid=WVV8T27PENS4&keywords=boundary+element+method+electromagnetics&qid=1643318428&s=books&sprefix=boundary+element+method+electromagnetics%2Cstripbooks%2C86&sr=1-1 www.amazon.com/Multilevel-Large-Scale-Computational-Electromagnetics-Electromagnetic/dp/111997741X/ref=sr_1_1?crid=ZJNLQJTI3JDD&keywords=fast+multipole+electromagnetics&qid=1643318476&s=books&sprefix=fast+multipole+electromagnetics%2Cstripbooks%2C87&sr=1-1

Your videos are very helpful as a starting point to understanding the literature. Do you plan on making a video dedicated to MoM or even Spectral Domain MoM? I'm interested reflectarrays and I'm trying to get my head around Pozar's famous paper on them.

@empossible1577

6 жыл бұрын

I do plan on doing that, but that will not likely happen any time soon. I think that needs to be done with a semester long course covering all variational methods like finite element, method of moments, spectral domain, boundary element, etc. Very sorry!!!

@wussup331

6 жыл бұрын

CEM Lectures No worries! I look forward to it.

In the slide in the beginning of the lecture where you were describing some functions of MOM and FEM. I am confused regarding something. It says that MOM is used specially for surface meshing and FEM is used specially for volume meshing. My question is, consider a rectangular cuboid, it has both volume and surface. In this case I can use both volume and surface meshing. Especially in edges I have to use surface meshing to get accurate results. So does that mean I need to use two types of computational methods to solve for a single problem, does this type of solution exist? Thank you

@empossible1577

7 жыл бұрын

So MoM and FEM do not do meshing. The meshing is a separate step. MoM uses a surface mesh, but does not generate it. FEM uses a volume mesh, but does not generate it. For your rectangular cuboid thing, if it is metal, you can describe it by just meshing its surface and nothing else. There is no need to mesh the interior of the cube. MoM would operate with just the surface mesh to calculate scattering or whatever else you might be doing. If you use FEM, you will have to mesh the volume of the cube, some space outside of the cube, and then think about boundary conditions at the edge of your mesh.

Thank you, interesting lecture and well explained Professor ! A small request please if possible, Is it possible to get a pdf of the slides? Because sometimes its quicker and easier to check some stuff than go/search over the whole video again

@empossible1577

7 жыл бұрын

Yes, absolutely. I posted them to the course website along with links to the videos and other resources for you. I have made many revisions and corrects to the notes so they may not match the videos exactly. Here is the course website: emlab.utep.edu/ee5390cem.htm

@paulamiroy953

7 жыл бұрын

Thanks ! May I ask a question out of curiosity? What type of projects one can do as final project in Computational EM? Could you please share or suggest some topics or problems?

@empossible1577

7 жыл бұрын

I get this questions a lot. Before I answer, I always ask several things: (1) What kind of research are you currently doing? (2) What topics in the course seemed most interesting or wanted to learned more? (3) What types of research or devices are you most interested in? Based on this I might advise they add some feature to an algorithm. For example, maybe they include anisotropy into their formulation and code. Or, perhaps, they simulate a new or interesting device like a photonic crystal. If you can answer those questions, hopefully I can be of more help.

Really helpful, thanks! Any chance u could recommend some literature about the math u skipped? Interested in FEM, Ritz - Galerkin.

@empossible1577

8 жыл бұрын

+Milos Cadek www.amazon.com/Finite-Element-Method-Electromagnetics/dp/0471438189/ref=sr_1_3?s=books&ie=UTF8&qid=1457731461&sr=1-3&keywords=fem+electromagnetics

@MrMcada

8 жыл бұрын

+CEM Lectures Thanks!

My present understanding from this lecture is that FEM is similar to FDFD, FDTD, except in the meshing part. In FDFD, FDTD we use rectangular mesh. While FEM uses a more sophisticated meshing strategy. However the way the equations are solved is through Finite Differencing. Is that correct? This and the next lecture on Optimization is not in the CEM playlist. Do you have any plans of releasing lecture videos on method of moments? Thank you

@empossible1577

7 жыл бұрын

FEM and FDFD are similar in that they are both frequency-domain methods where you assemble a huge set of equations into a matrix equation and solve that to calculate the fields. Post processing the results is also very similar. The math behind the methods is very different. FDFD discretizes Maxwell's equations by approximating the derivatives with finite-differences. Each row in the matrix equation comes from a finite-difference equation from one point on the grid. FEM uses variational calculus or Galerkin method to discretize Maxwell's equations. This is used to develop a small set of equations that couple the unknowns within an element. This small set of equations is then inserted into several rows of the global matrix. Hope this is meaningful!

Sir i got to say this But i will that is YEEEAAAAAAH.

Thats a good lecture. The problem is that FEM was presented wrong and it isn't about Variational Methods at all

@empossible1577

6 жыл бұрын

You are sort of right. The finite element method is commonly formulated one of two ways. First, applying variational calculus and the second using the Galerkin method. I chose to use the Galerkin method because I "think" it is more intuitive. The same matrices are derived in the end so I am not sure I would call the material presented wrong, but perhaps confusing or misleading. Thank you for the observation!

instructive, a small correction at 45:31, fast multipole not multiple

@empossible1577

4 жыл бұрын

Thank you! I have fixed the notes but not the video.

Dear Sir In your opinion which book is best to learn this course(Finite element Method or Analysis) as whole from general prespective or general point of view.

@empossible1577

4 жыл бұрын

I don't like anything I have seen. They all throw equations out there, but do not describe the over all algorithm very well. If you find something good, please let me know!

@husnainhyder6713

4 жыл бұрын

@@empossible1577 All right Sure no problem. Thanks

@wolfwolf7121

3 жыл бұрын

@@empossible1577 Good day! I study the FEM from this book - MATLAB-based Finite Element Programming in Electromagnetic Modeling by Özlem Özgün, Mustafa Kuzuoğlu. It is very helpful for me. Maybe you will like this book. Thank you for your lectures!