[aerosayan]

Hello everyone,

I'm realizing that developing GMG methods for explicit solvers on unstructured grids might be a lot of work. I'm wondering if it's possible to use AMG methods instead.

Converting the equations to a sparse Ax=b form, then applying AMG to solve this, just might be possible.

Since explicit equations are easy to parallelize, I'm wondering if it's possible to do the same to the matrix A i.e domain decompose across all processors, and apply AMG on the matrix's "block" locally on each processor.

Benefit of the method, if possible, would be that it might work for explicit solvers on all kinds of grids. Tri, Quad, Hex, Prism, Tetra, i.e in both 2D and 3D, and we save time on development.

[LuckyTran]

The AMG approach is used in just about every commercial cfd software unless I missed something about why AMG can't be done for your case.

[arjun]

Originally Posted by aerosayan

Hello everyone,

I'm realizing that developing GMG methods for explicit solvers on unstructured grids might be a lot of work. I'm wondering if it's possible to use AMG methods instead.

Converting the equations to a sparse Ax=b form, then applying AMG to solve this, just might be possible.

Since explicit equations are easy to parallelize, I'm wondering if it's possible to do the same to the matrix A i.e domain decompose across all processors, and apply AMG on the matrix's "block" locally on each processor.

Benefit of the method, if possible, would be that it might work for explicit solvers on all kinds of grids. Tri, Quad, Hex, Prism, Tetra, i.e in both 2D and 3D, and we save time on development.

As it is mentioned AMG methods are pretty much default in all commercial softwares. Writing a good parallel AMG could be time consuming so you can try libs like hypre etc.

[sbaffini]

If I understand you correctly, you mean something like an algebraic FAS.

This, or a similar question, already popped up here some time ago. I now miss the several reasons against this, but for sure there is one, the highest difficulty in AMG (at least in its common FV implementation as additive correction) is building the matrix in parallel at the coarse levels (the serial version is pretty much trivial). Once you have that, using it explicitly makes no sense.

Which recalls me of another fundamental reason, the fact that the power of AMG is indeed in the implicit realm. In the explicit case FAS is much less effective in accelerating the solution, whose advancement speed is mostly governed by the time step.

[aerosayan]

Originally Posted by sbaffini

If I understand you correctly, you mean something like an algebraic FAS.

This, or a similar question, already popped up here some time ago. I now miss the several reasons against this, but for sure there is one, the highest difficulty in AMG (at least in its common FV implementation as additive correction) is building the matrix in parallel at the coarse levels (the serial version is pretty much trivial). Once you have that, using it explicitly makes no sense.

Which recalls me of another fundamental reason, the fact that the power of AMG is indeed in the implicit realm. In the explicit case FAS is much less effective in accelerating the solution, whose advancement speed is mostly governed by the time step.

Yeah, true. Implicit is better.

If my code is explicit, it will be far too slow for most people's use.

Luckily, I now have enough brain cells to understand implicit codes and am slowly moving away from explicit ones.

[sbaffini]

Originally Posted by aerosayan

Yeah, true. Implicit is better.

If my code is explicit, it will be far too slow for most people's use.

Luckily, I now have enough brain cells to understand implicit codes and am slowly moving away from explicit ones.

Ok, now that I read again your post, I might have misunderstood, at least partially ,what you meant.

In this case, what Luckytran and Arjun wrote applies, using AMG for linearized systems of equations arising from implicit discretizations is, indeed, the norm in most commercial solvers out there.

As I already wrote, doing it in serial is trivial, at least for the common additive correction multigrid in use in most FV solvers.

The difficult part is the parallel, it has costs at each iteration and there is no definitive guide out there on how to implement it, nor the matter is such that some specific way would appear obvious from the context. There are some papers out there, from Maximillian Emans, former AVL developer, that give some context and clue. Some others from the Moukalled
and Darwish group, but that's it. Most of the remaining stuff is focused on more complex AMG flavors, mostly for math oriented people (who like a lot to complicate stuff).

Note, however, that the system solver is not a difficult part, in general, for the implicit approach. A LU-SGS is just a couple of loops on the cells, where you update the system unknowns. Most Krylov methods add some matrix-vector products, which again are the same kind of loop. AMG is the kind of the exception here, because you need to update the matrix at each level in parallel. For tall the others, you just need a sparse-matrix data structure and you're done, the parallel exchange is not different fromother variables. The difficult part is the book-keeping one, which sign does this element have, which matrix element does this term goes, etc.

Explicit has his use cases, but that is in the unsteady realm with no doubt.

[arjun]

Why not just use BiCGStab or GMRES etc. They are not tough to write and in compressible solver the linear system is easier to solve compared to incompressible case (hyperbolic vs elliptic system).

[aerosayan]

Originally Posted by arjun

Why not just use BiCGStab or GMRES etc. They are not tough to write and in compressible solver the linear system is easier to solve compared to incompressible case (hyperbolic vs elliptic system).

Thanks Arjun! I will most likely use LU-SGS or BiCGStab or GMRES. Which one is the easiest?

[arjun]

Originally Posted by aerosayan

Thanks Arjun! I will most likely use LU-SGS or BiCGStab or GMRES. Which one is the easiest?

Try BiCGStab even though the LU-SGS will be faster but BiCG will be more robust. If you want parallel consistency then use polynomial methods are preconditioner for BiCGStab.

[aerosayan]

Originally Posted by arjun

Try BiCGStab even though the LU-SGS will be faster but BiCG will be more robust. If you want parallel consistency then use polynomial methods are preconditioner for BiCGStab.

BiCGStab seems to be the combination of BiCG, and GMRES. Su2 uses FGMRES by default. I think it might be easier for me to implement and use FGMRES first, then move on to BiCGStab.

[arjun]

Originally Posted by aerosayan

BiCGStab seems to be the combination of BiCG, and GMRES. Su2 uses FGMRES by default. I think it might be easier for me to implement and use FGMRES first, then move on to BiCGStab.

I believe the F in FGMRES here stands for Flex and it stands for Flexible preconditioners in same GMRES. This I believe could be more efficient but not neccessarily easier to implement compared to BiCGStab.


However please check out PyAMG library. There you can learn how to implement BiCGStab or GMRES or even FGMRES if I remember correctly . They are at github too.

[aerosayan]

Originally Posted by arjun

I believe the F in FGMRES here stands for Flex and it stands for Flexible preconditioners in same GMRES. This I believe could be more efficient but not neccessarily easier to implement compared to BiCGStab.


However please check out PyAMG library. There you can learn how to implement BiCGStab or GMRES or even FGMRES if I remember correctly . They are at github too.

Oh okay thanks. GMRES looked easy, and if FGMRES is more difficult, I'll see GMRES first. I want to use BiCGStab, but have reliable but slow fallback code too. GMRES seemed like the best option since it's required in BiCGStab, and I'll have to understand and develop it anyway.

[arjun]

Originally Posted by aerosayan

Oh okay thanks. GMRES looked easy, and if FGMRES is more difficult, I'll see GMRES first. I want to use BiCGStab, but have reliable but slow fallback code too. GMRES seemed like the best option since it's required in BiCGStab, and I'll have to understand and develop it anyway.

Thats why suggested PyAMG. You can see the python code for them and it makes it easier to learn.

[luckyXing]

Originally Posted by arjun

Thats why suggested PyAMG. You can see the python code for them and it makes it easier to learn.

I have a qustion, is the GMERS,LU-SGS,BiCG methods used as smoother in AMG? as i know, AMG has Pre-smoothing, Coarse-grid correction and Post-smoothing; all the methods before used as Coarse-grid correction?

[arjun]

Originally Posted by luckyXing

I have a qustion, is the GMERS,LU-SGS,BiCG methods used as smoother in AMG? as i know, AMG has Pre-smoothing, Coarse-grid correction and Post-smoothing; all the methods before used as Coarse-grid correction?

even though the post is bot generated. I think (need to double check) only CFX has AMG that uses BiCG as smoother.

[luckyXing]

Originally Posted by arjun

even though the post is bot generated. I think (need to double check) only CFX has AMG that uses BiCG as smoother.

Yeah, but in fluent, there are G-S/ILU used as smoother, so the BiCGSTAB/RPM/GMERS which can choose at Stabilization Method means iteration for Coarse-grid?

[arjun]

Originally Posted by luckyXing

Yeah, but in fluent, there are G-S/ILU used as smoother, so the BiCGSTAB/RPM/GMERS which can choose at Stabilization Method means iteration for Coarse-grid?

?????????

I mean what??????

[luckyXing]

Originally Posted by arjun

?????????

I mean what??????

sorry, maybe i didn't get you, i wonder just like in the Fluent, i can use G-S/ILU as pre/post-smoothing, but what is the iterarion method for coarse-mesh? direct iteration or use these methods 'GMERS'/'BiCGSTAB'; I just learn AMG method recently and i confused is the 'GMERS'/'BiCGSTAB' methods used as iteration in solve Coarse-grid or AMG is a preconditioner before we use the'GMERS'.

anyway, thank you for your response.

[arjun]

Originally Posted by luckyXing

sorry, maybe i didn't get you, i wonder just like in the Fluent, i can use G-S/ILU as pre/post-smoothing, but what is the iterarion method for coarse-mesh? direct iteration or use these methods 'GMERS'/'BiCGSTAB'; I just learn AMG method recently and i confused is the 'GMERS'/'BiCGSTAB' methods used as iteration in solve Coarse-grid or AMG is a preconditioner before we use the'GMERS'.

anyway, thank you for your response.

Yes you can use G-S and ILU as smoother. These are the most popular options.

AMG can be used as stand alone linear system solver.

AMG can also be used as precoditioner to GMRES, BiCongujate etc solvers.


Rarely BiConjugate and GMRES are used as smoothers because they are expensive or they take more time.