How to Cluster Lines in an Elliptic Mesh Generator Using Matlab?

[Clausius2]

AN ADVICE: "If you are not familiarized with mesh generation, don't keep on reading, you will not understand nothing and I will not make you to waste your time."

Sorry if it is not the appropiate forum for posting my problem.

I'm currently programming an elliptic mesh generator in Matlab. If someone knows about it, you have to solve a two coupled Laplace equations. I have not any problems to solve it.

The difficulties arrive when I have to cluster the lines to the internal boundary. See the drawing below:

-|---|--|---|------------ iso-eta line

-|---|--|---|------------

-|---|--|---|------------- iso-eta line
-|---|--|---|------------- iso-eta line
-|---|--|---|--------------
| | | |
iso -xi lines

As you (roughly) can see the transverse lines are iso-eta lines, and the vertical ones are iso-xi lines.

I want to cluster iso-eta lines around one named eta_o=constant.

I have proved with the next forcing function:

Q=a*sign(eta-etao)*exp(-b*abs(eta-etao))

but nothing happens, or simply the method diverges.

I will appreciate some advice, or some warning about the forcing function used. I have not had success in clustering near the internal boundary.

Any comment or web-link will be appreciated. Thanks.

 

[M98Ranger]

First off, I want to applaud your efforts in programming an elliptic mesh generator in Matlab. It sounds like a challenging project and I'm sure you have put a lot of time and effort into it.

As for your troubles with clustering the lines to the internal boundary, it seems like you are on the right track with using a forcing function. However, it's important to note that the success of the clustering method also depends on the quality of the mesh and the choice of parameters.

My advice would be to thoroughly review the algorithm and parameters you are using for clustering. It might also be helpful to consult with someone who has experience in mesh generation or to do some additional research on the topic.

Additionally, I would suggest reaching out to online forums or communities dedicated to mesh generation and seeking advice from experts in the field. They may be able to provide more specific guidance or point you towards helpful resources.

Remember, it's always okay to ask for help when facing difficulties, especially in a complex task like mesh generation. Don't give up and keep exploring different approaches until you find a solution that works for you. Good luck!