any suggestions to speed up explicit DG updates?

1 week 6 days ago #2909 by Guosheng Fu
Dear all,

I have attached a demo code for incompressible two phase flow using hybrid-mixed FEM (RT0) for pressure and DG-P0 for saturation.
Currently, I use the standard DG updates for the saturation conservation law equation.
I believe this default version could be significantly improved, but I don't know what's the best option available now in ngsolve. I would like to get ideas about speeding up this code. Many thanks as always!


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1 week 3 days ago #2923 by mneunteufel
Hi Guosheng,

I tried to modify your ForwardEuler by replacing the Matrix-Vector multiplication, but this did not really help.
def ForwardEuler(sh, dt): = aS.mat * sh = invm*rhsS
        return sh-dt*rhsS
Also to "inline" it did not bring a lot = ForwardEuler(gfuS.vec, dt)
aS.Apply(gfuS.vec,rhsS) -= dt*invm*rhsS

However, the Compile flag made a huge difference! It is important to compile everything, not only a part of it
if kdg>0:
    aS += (-uh*fw(ss)*grad(tt)).Compile(true_compile, wait=True)*dx
aS += (uh*n*Fhat*tt).Compile(true_compile, wait=True)*dx(element_boundary=True)
With this I got a speed up of a factor 3!

It is also possible to speed up your "fast" part even more. Instead of calling mat.Invert every time you can "update" the inverse:
inv = a.mat.Inverse(fesP.FreeDofs(True),inverse="sparsecholesky")

while  time < tend-dt/2 :
            if stepS%nsubcycles == 0:
       = inv * rhsP

Then the symbolic factorization is done only once and not every step. This improved the "fast" part from 2.4 to 1.5 seconds on my machine.


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1 week 2 days ago #2925 by Guosheng Fu
Hi Michael,

Thanks about the two tricks, they are helpful.
I also get roughly a factor of 3 speedup with the correct use of the Compile flag, and a factor of 2 for the sparse Cholesky inverse update.

Changing element_boundary formulation to skeleton-based formulation further helps to speed-up the explicit DG solver slightly.

I am now thinking about using implicit DG solver for saturation. But Newton solver fails since .Other() only works for proxyfunctions, not gridfunctions. Do you have any suggestions on this issue?


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