Numerical Solution of 2D Laplace equation using FDM and Inverse Matrix Technique

[@maryammohammadpour1966]

Great videos on these topics I have ever found on youtube. Keep updating new videos please and you did a really good job.

[@hekarluzir7955]

The two methods that you presented in step-by-step manner were easy to understand. Excellent videos indeed. Hope to see more great videos on numerical simulations using MATLAB. All the best in your thesis bro and good luck.

[@abolfazlmahmoodpoor_]

Thanks, will do!

[@AJ-et3vf]

Great video sir. Thank you!

[@ghufranullahkhan7479]

I am working on phase field model for concrete. My professor has done all the coding for implementing it. I will be greatful if you make a video on finite element implementation of phase field model using iterative technique.

[@priyeshpandey100]

its not just laplace ..its u that help me to do it ..

[@abolfazlmahmoodpoor_]

Glad it helped

[@cheikhbrahimabed4319]

Thank your for this course. Very helpful. In order to speed up the solution of 2D Laplace equation, is there any other faster method than FDM? Can we use POD-Galerkin method to Laplace equation?

[@abolfazlmahmoodpoor_]

Glad it was helpful. It is possible to use finite element method for solution of Laplace equation but honestly I don't know is it faster than FDM (inverse matrix) or not. About POD Galerkin method it is usually used for convection-diffusion equation I didn't use this method at all!

[@cheikhbrahimabed4319]

@@abolfazlmahmoodpoor_ I think POD-Galerkin is for all PDE's? but i don't know if we can use it for steady PDE's There is another one called "Reduced Basis Methods'' but i didn't use it at all

[@shadowmonarch3155]

@@abolfazlmahmoodpoor_ how can i right in code if my right boundary condition is if x tends to infinity then V=0?

[@weibinchen4807]

Which one is better? Iterative or inverse matrix ? I guess depending on the stability and the problem of interest? Thanks!

[@abolfazlmahmoodpoor_]

iterative method is simple in coding but it's slow in comparison to inverse matrix method, on the other hand inverse matrix is faster and harder in coding. Moreover you can adjust the error in iterative method and stop calculation at desired error (number of iteration) but inverse matrix method's error is fixed.

[@weibinchen4807]

@@abolfazlmahmoodpoor_ thank you very much for the explanation! Very helpful!

[@fatihbaykal5147]

Excellent explanations ! Thank you.

[@abolfazlmahmoodpoor_]

Glad it was helpful!

[@muhammadaslanimoghanloo5014]

Many thanks, Abolfazl for your great video, I just have a short question, in the Neumann BC how do we define the corners?

[@abolfazlmahmoodpoor_]

Corners are defined by either vertical or horizontal boundary.

[@muhammadaslanimoghanloo5014]

@@abolfazlmahmoodpoor_ you mean we can consider an imaginary point beyond the scheme and use it's value to calculate the corner value?

[@abolfazlmahmoodpoor_]

@@muhammadaslanimoghanloo5014 No, I mean that the value of the function at the boundaries are known, the corners are the cross section of two boundaries, vertical and horizontal, therefore you can easily consider them by either vertical or horizontal boundary.

[@nihedtsouli2619]

Excellent video Please I need help to result a diffusion-convection equation using a 2D grid with FORTRAN

[@throine]

What if our boundary conditions are inside the mesh grid? Do we have to modify the code?

[@abolfazlmahmoodpoor_]

definitely, the code and analytical solution is for boundary condition in the sides of mesh, any other boundary inside geometry changes the results.

[@ndukamoses8475]

Thanks so much sir for this great video. But my problem is; how do I implement the Neumann boundary conditions on one, two or three sides of the Laplace equation using finite difference method?

[@abolfazlmahmoodpoor_]

I received your email. If following explanation is not enough let me know using the email, it is easy, just using the definition of first order derivative. We used it a lot in the videos, If you use it you will see that one node after boundary the value of function at that point is given by the condition that imposed by derivate (an example: df/dx = a -> f(1) - f(0)= a*dx --> f(1)=a*dx + f(0) so the value of function is known in either node number 0 and node number 1 and you should just start calculation from node number 2 )

[@ndukamoses8475]

@@abolfazlmahmoodpoor_ Thank you so much Sir. God bless you Dr.

[@SashaPrival]

Neumann conditions?

[@shadowmonarch3155]

how can i right in code if my right boundary condition is if x tends to infinity then V=0?

[@weibinchen4807]

Thanks so much!

[@ahmedzaki3119]

hey dear abo fazl I am waiting for new videos

[@abolfazlmahmoodpoor_]

Hi Ahmed, Sorry for such a silence in my channel, I am busy with my thesis these days. I hope I can upload another video soon

[@ahmedzaki3119]

Good luck

[@abolfazlmahmoodpoor_]

Thank you so much

[@harshitsharma7963]

thank you so much sir

[@vishalchhabra7016]

sir for working on matlab which laptop should be good..?

[@abolfazlmahmoodpoor_]

My laptop is Core i5 with 6 GB RAM, it works well and more than enough for Matlab program.

[@vishalchhabra7016]

@@abolfazlmahmoodpoor_ thankyou so much sir.

[@vishalchhabra7016]

@@abolfazlmahmoodpoor_ sir how to apply finite differential method on mixed condition with Laplace equation. means after plotting grid points and making equations what is the approach

[@abolfazlmahmoodpoor_]

@@vishalchhabra7016 What do you mean by mixed condition?

[@vishalchhabra7016]

@@abolfazlmahmoodpoor_condition of Drichlet problem and neumann problem are present together in which

[@fatitraka3722]

Merci monsieur pour toutes ces informations. je suis à la recherche la résolution équation de chaleur par méthode éléments finis et différence finie. De la même manière d'explication.😊

[@abolfazlmahmoodpoor_]

Here you can find solution of 1D heat equation using finite difference method kzbin.info/www/bejne/aGOlkpuCqa5mfLM

[@alisoleimani5533]

Grazie mille