The solution speed is very slow

[dokken]

@ss780060872

for n in range(num_steps):
    
    t += dt
    
    solve(F == 0, T, bcs)

Avoid calling solve F==0 inside the loop, as it recreate a lot of structures (sparse matrices, vector for thr RHS, ksp solver etc.

This is covered in various other posts on the forum. In the context of DOLFINx at:

Out of memory error in frequency for loop

dolfinx.fem.Constant wraps constant quantities which can change between assemblies of the underlying matrix. dolfinx.fem.petsc.LinearProblem has a PETSc Mat and Vec. Creating one every time step is extremely expensive, and not their intended use. ... # Problem setup k = dolfinx.fem.Constant(mesh, 0.0) k.value = some_important_value ... # Weak form definition problem = LinearProblem(a, L, u=uh, petsc_options={"ksp_type": "preonly", "pc_type": "lu"}) ... # Other code for nf in range(0,len(f_a…

and for legacy dolfin and linear problems in

Simula-SSCP/SSCP_2023_lectures/blob/main/L12 (FEniCS Intro)/L02_FEniCS_Diffusion.ipynb

@ss780060872

1.When I change the total solving time, it always doesn’t converge, I usually refine the grid and reduce the time step to make it converge, but this tends to increase the time cost, how do I optimize my code?

You are not customizing your solver. See for instance:

Default absolute tolerance and relative tolerance

I write the following in the context of FE modelling rather than numerical analysis. I.e. this should be interpreted as tips and tricks. Perhaps someone else can contribute something more rigorous, or their own experience. Do you know what to expect the residual of your system to be to machine precision? Adjust your absolute tolerance accordingly. E.g: A Poisson problem with a diffusion coefficient of 1 may yield a residual to machine precision around 10^{-12}. Linear elasticity with a Young’…

@ss780060872

3.How can I detect iterations or progress more closely?
here is my code:

You can write a custom newton solver, see for instance Set krylov linear solver paramters in newton solver - #3 by nate