Implicit versus Explicit FEA in parallel computing

[ahildershavn]

Hello,

I was wondering if anyone here could explain to me in a simple manner why implicit fea benefits less from parallel computing than explicit fea?

Hopefully awaiting intelligently elaborated replies easily understandable by a person whos mothertongue is not english.

-Andreas-

 

[IRstuff]

http://imechanica.org/node/5396

https://www.researchgate.net/post/W...licit_FEM_in_non-linear_quasi-static_problems

http://www.dynasupport.com/faq/general/what-are-the-differences-between-implicit-and-explicit

Presumably, it has to do with the stiffness matrix inversion.

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[ThomasH]

In both cases you have a stiffness matrix BUT for the explicit solution there are only diagonal terms in the matrix. So no traditional solution is required. You can solve each row in the system independant of all the others. Or, all of them at once if you have enough processors.

I think that is a short and a bit simplified explanation. Hopefully not to simplified.

Thomas

 

[Dave442]

just want to correct one point from Thomas's post.

In an explicit solution we initially solve for accelerations and only need to invert the mass matrix [M] as opposed to the stiffness matrix [K].

For lower order elements [M] is diagonal.

 

[ahildershavn]

So if I understand correctly:

1.) Implicit requires inversion of the stiffness matrix [K]. Implicit requires solving system of variables with more than two unknowns. Which is why the task cannot easily be split up and sent to different nodes/cpu cores.

2.) Explicit requires inversion of the mass matrix [M]. Mass matrix only has diagonal terms, which results in multiple equations each with only one unknown. These equations can easily be solved on different nodes/cpu cores.

Would you agree to above statements?

-Andreas-

 

[IRstuff]

I don't know if those are the specific issues. In general, matrix equations can be run in parallel, but stiffness matrix inversion cannot, and if the inversions are both complex and frequent, the overall calculation will be dominated by the stiffness matrix inversions.

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[ThomasH]

I think that matrix inversion in general can be run in parallel. But the complexity of a stiffness matrix inversion for the implicit solution does not scale (speed vs cpu cores) as well as the mass matrix inversion in the explicit solution. Especially if the mass matrix is diagonal.

But it gets better as the algorithms improve since the cpu's don't get faster to the same extent as they "grow" more cores .

Also, as Dave442, already mentioned. My description was based om lower order elements with diagonal mass matrix. My experience is based on that type of elements.

Thomas