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.
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.
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
Dear Professor. I have some questions for your lecture. In slide 24, how do we know that solution is the exact solution if we do not solve the problem before? In another word, how do we know when the result converge or not? In slide 39, how do we get the value of components of global matrix K? Thank you very much.
@@camlainguyen3545 In this case, if we kept adding terms the solution would stay the same. In this sense, the answer converges and that is how we know it is the final answer. Deriving the components of the element matrix is a lot more involved and depends heavily on the element and order of the element chosen. That is a bit outside the simple purpose of this set of notes. The short answer is that it is derived using the Galerkin method (or many other approaches). Given this matrix, the global matrix is really just an assembly of all the element matrices. I hope some day I can make a series of videos on this topic.
This explanation is the best I have seen on RUclips 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?
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.
@@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?
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 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
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/
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?
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
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
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
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?
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.
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.
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!!!
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
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.
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
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!
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.
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!
@@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!
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!
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
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.
That is awesome to hear!!!
Just came to the comments section to say the same words. Totally agree with your statement. A very big thank you to the creator of this video.
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.
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
Great explanation , the best video ever about finite elements method
Thank you!
Great explanation! Thank you Professor
Glad to hear!
Dear Professor. I have some questions for your lecture. In slide 24, how do we know that solution is the exact solution if we do not solve the problem before? In another word, how do we know when the result converge or not? In slide 39, how do we get the value of components of global matrix K? Thank you very much.
@@camlainguyen3545 In this case, if we kept adding terms the solution would stay the same. In this sense, the answer converges and that is how we know it is the final answer.
Deriving the components of the element matrix is a lot more involved and depends heavily on the element and order of the element chosen. That is a bit outside the simple purpose of this set of notes. The short answer is that it is derived using the Galerkin method (or many other approaches). Given this matrix, the global matrix is really just an assembly of all the element matrices. I hope some day I can make a series of videos on this topic.
@@empossible1577 Thank you very much for your answer! I hope we will see your new series on that topic soon.
Really helpful lectures ,which is used to gain a lot of knowledge about variational methods.
Really good lecture, thanks for this. Very clear and practical explanations.
Great lecture ! Thank you Professor
This clarified some ambiguities that I was dealing with for two years ! nice
That is great to hear!! Thank you!!!
thanks Professor, you made the whole image more clear!
Great to hear!
You are god mate, cant figured out this for two years and finally i can do , thanks a lot. Cheers from VŠCHT Prague.
Great! Thank you!!
This is pure gold, thank you!
Great lecture!
Thanks a lot Prof. great lectures....
I hope it is not too late to thank you for the great job.
Ha ha. Never to late!! Thank you!
This explanation is the best I have seen on RUclips 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?
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.
@@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?
Saved my course, finally variational method is making sense to me, thank you!!!
+Samson Victor You are welcome!
great thanks for this lecture
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?
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.
You are welcome!!
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
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/
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?
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
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
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
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?
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.
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.
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!!!
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
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.
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
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!
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.
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!
@@empossible1577
All right
Sure no problem.
Thanks
@@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!
instructive, a small correction at 45:31, fast multipole not multiple
Thank you! I have fixed the notes but not the video.
Really helpful, thanks! Any chance u could recommend some literature about the math u skipped? Interested in FEM, Ritz - Galerkin.
+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
+CEM Lectures Thanks!
Thats a good lecture. The problem is that FEM was presented wrong and it isn't about Variational Methods at all
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!
GREEEEAAAAATTTT!!!
Sir
i got to say this
But i will
that is
YEEEAAAAAAH.