What block preconditioners really do

jan@papez.org
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4 years 6 months ago #2676 by jan@papez.org

What block preconditioners really do was created by jan@papez.org

Hello,

I wonder what block preconditioners build using

Code:

CreateBlockSmoother

really do.

In my code, I want to use block Jacobi smoother and I observed that

Code:

rho.data = smoother * b
rho.data *= weight

gives different results than

Code:

b *= weight
rho.data = smoother * b

Do I miss something? I use quite particular construction of blocks for block smoother (I consider the dofs corresponding to each patch but those on the boundary.). Nevertheless, I would not expect such behavior for any block smoother.

Many thanks for any help,
Jan Papez

lkogler
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4 years 6 months ago - 4 years 6 months ago #2677 by lkogler

Replied by lkogler on topic What block preconditioners really do

BlockSmoother used with the matrix-vector multiplication is Block-Jacobi, so linear.

BlockSmoother used multiplicatively is Block-Gauss-Seidel.

If rho is 0,

Code:

smoother.Smooth(rho, b)

and also the symmtric version

Code:

smoother.Smooth(rho, b)
smoother.SmoothBack(rho, b)

are linear operations.

Best,
Lukas

Last edit: 4 years 6 months ago by lkogler.

jan@papez.org
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4 years 6 months ago #2678 by jan@papez.org

Replied by jan@papez.org on topic What block preconditioners really do

Thank you , Lukas. This is exactly what I learnt from the tutorials. However, then I would expect to have the same results (for the codes given in my initial post), which is not the case.

lkogler
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4 years 6 months ago #2679 by lkogler

Replied by lkogler on topic What block preconditioners really do

You should get the same result.

Could you upload a failing minimal example?

jan@papez.org
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4 years 6 months ago - 4 years 6 months ago #2682 by jan@papez.org

Replied by jan@papez.org on topic What block preconditioners really do

I enclose an example, which is not very minimal but provides different results for two variants (switch on the line 8 ) of computations on lines 101-106.

( I use a multigrid solver with adaptive stepsize computed on lines 157-160. )

Many thanks for your help!
Jan

File Attachment:

File Name: minimal_example.py
File Size:5 KB

Attachments:

minimal_example.py

Last edit: 4 years 6 months ago by jan@papez.org.

lkogler
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4 years 6 months ago - 4 years 6 months ago #2683 by lkogler

Replied by lkogler on topic What block preconditioners really do

In variant 2 you modify b, which you seem to use again at another point:

Code:

            if variant == 1:
                rho.data = self.smoothers[level] * b
                rho.data *= (1./self.w1)  #weightening
            else:
                b.data *= (1./self.w1)
                rho.data = self.smoothers[level] * b

Changing this to:

Code:

            if variant == 1:
                rho.data = self.smoothers[level] * b
                rho.data *= (1./self.w1)  #weightening
            else:
                b.data *= (1./self.w1)
                rho.data = self.smoothers[level] * b
                b.data *= self.w1

solves the problem.

Another thing: It seems that you are only using blocks consisting of one DOF each. Using ".CreateSmoother()" instead of ".CreateBlockSmoother()" might be cheaper.

Last edit: 4 years 6 months ago by lkogler.

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