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Meshfree Methods: Frequently Asked Questions

Questions about meshfree methods are now addressed in the forum, under the Computational Mechanics subheading.

If you click on a question below, you will be redirected to the forum. I will update this post as more questions are added. Other experts are encouraged to augment my response there.

1. If I have meshfree shape functions that satisfy Kronecker-Delta, can I satisfy essential boundary conditions?

2. Is a mesh required in meshfree methods?


Hello mechanicians,

Please help me with some following questions.

Which are the benchmark problems must be tested for a new numerical method in 1D, 2D, and 3D ?

If there are two methods, with what criterions we can say one is better than other in such a particular problem? in all problems ?

And who supposed above rules ?

I look forward to your replies.

Happy new year to all !



I think this is very hard to tell which method is better.

But for a routh comparison we can analyze a benchmark and obtain parameters such energy norm, displacements on the boundary and in the domain.

But instead of telling which is better we must try to find "which method is better for this kind of problem".

with regards

mahdi rezaei

MS. mechanical eng

University of ferdowsi-Iran-mashhad

Thank you for your reply, Mahdi Rezaei !

In my case, the Kriging shape functions of EFG method satisfy the Kronecker properties, i.e., equal 1 at a given node and zero at others. However, its gradient does not  vanish at given node. Hence, it seems that the more Gauss points are used in numerical integration the worse results I obtain .

So, in comparison with Moving least square EFG method, it is difficult to say which method is better.

I hope to get more comments on this problem.

Best regards,


abshaw's picture

The original form of Kriging shape functions (used in geostatistics) are based on best linear unbaised estimation (BLUE). However, one may also construct Kriging with higher order consistency. From my personal experience I can say that Kriging shape functions with higher order consistency do not suffer any gradient problem that you have mentioned.

Please correct me if I am wrong.


I want program thin plate for natural frequencies with EFG with penelty method.I have some questions:

1-Is four gauss point enough for programming?

2-I want to find natural frequencies for Fully free thin plate.(ffff)I think for this boundary conditions i dont need use penalty factor.Is it true?(because we dont have to impose b.c there fore we dont need penalty factor)

3-I can not write program for finding gauss point for 10 gauss point.but i saw a program for 4 gauss can i write program for more than 4 gauss point?

Has any one program for thin plate?(with EFG or other methods)

(excuse me for my writing!)

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