Why does this direct solver appear to call a Krylov solver?


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9 months ago by

In the following MWE (which I ran with a Docker container from quay.io/fenicsproject/stable), I intend to solve the Poisson problem with a direct solver:

import fenics


def boundary(x, on_boundary):

    return on_boundary
    
    
mesh = fenics.UnitSquareMesh(8, 8)

x = fenics.SpatialCoordinate(mesh)

exact_solution = 1. + x[0]**2 + 2.*x[1]**2

f = -6.

V = fenics.FunctionSpace(mesh, 'P', 2)
    
bc = fenics.DirichletBC(V, exact_solution, boundary)

u = fenics.TrialFunction(V)

v = fenics.TestFunction(V)

dot, grad = fenics.dot, fenics.grad

a = dot(grad(v), grad(u))*fenics.dx

L = v*f*fenics.dx

solution = fenics.Function(V)

fenics.set_log_level(fenics.DEBUG)

fenics.solve(a == L, solution, bc)

This outputs

Solving linear variational problem.
Matrix of size 289 x 289 has 3073 (3.67931%) nonzero entries.
Elapsed wall, usr, sys time: 0.0001026, 0, 0 (Build sparsity)
Elapsed wall, usr, sys time: 4.08e-05, 0, 0 (Init tensor)
Elapsed wall, usr, sys time: 8e-07, 0, 0 (Delete sparsity)
Elapsed wall, usr, sys time: 6.79e-05, 0, 0 (Assemble cells)
Elapsed wall, usr, sys time: 1.02e-05, 0, 0 (Apply (PETScMatrix))
Elapsed wall, usr, sys time: 1.8e-06, 0, 0 (Build sparsity)
Elapsed wall, usr, sys time: 2e-06, 0, 0 (Apply (PETScVector))
Elapsed wall, usr, sys time: 2.16e-05, 0, 0 (Init tensor)
Elapsed wall, usr, sys time: 8e-07, 0, 0 (Delete sparsity)
Elapsed wall, usr, sys time: 1.4e-06, 0, 0 (Apply (PETScVector))
Elapsed wall, usr, sys time: 4.43e-05, 0, 0 (Assemble cells)
Elapsed wall, usr, sys time: 1.8e-06, 0, 0 (Apply (PETScVector))
Computing sub domain markers for sub domain 0.
Elapsed wall, usr, sys time: 0.0002229, 0, 0 (DirichletBC init facets)
Elapsed wall, usr, sys time: 0.0002584, 0, 0 (DirichletBC compute bc)
Applying boundary conditions to linear system.
Elapsed wall, usr, sys time: 2.5e-06, 0, 0 (Apply (PETScVector))
Elapsed wall, usr, sys time: 4.2e-06, 0, 0 (Apply (PETScMatrix))
Elapsed wall, usr, sys time: 0.0003256, 0, 0 (DirichletBC apply)
Solving linear system of size 289 x 289 (PETSc LU solver, umfpack).
PETSc Krylov solver starting to solve 289 x 289 system.
Elapsed wall, usr, sys time: 0.0010557, 0, 0 (PETSc Krylov solver)
Elapsed wall, usr, sys time: 0.0011284, 0, 0 (LU solver)


Why is a Krylov solver being called?

Here's what I've looked at so far:

  • I only know the term "Krylov" in regards to Krylov subspace methods, which are iterative (not direct) methods.
  • I have spent some time reading up on UMFPACK and PETSc, and I'm not seeing anything that could explain this.
  • I also made a short attempt to catch with PDB where a Krylov solver is being called, so far with no success.
  • I am guessing that the actual log output comes from this source , which sure does look like a collection of Krylov subspace iterative (not direct) methods.
Community: FEniCS Project
1
If an iterative solver was being used, it would have shown some info of the iterations, which does not appear in your logs, so it is just using direct solver.
written 9 months ago by Praveen C  

1 Answer


5
9 months ago by
In PETSc, all linear solvers are Krylov solvers, with a direct solver being a 'pre-only' solver with a LU factorisation for the preconditioner. PETScLUSolver configures a PETScKrylovSolver to act as a direct solver.

Thanks!

I have a follow up question which may be most easily addressed here:


Is there a way to suppress that message and still invoke

fenics.set_log_level(fenics.PROGRESS)​

? (this log level indeed reproduces the message "PETSc Krylov solver starting to solve...")

Personally I find it misleading to print messages about a Krylov solver. I have been using that log level to report time progress in time-dependent problems per a tutorial I saw a while ago.

written 9 months ago by Alexander G. Zimmerman  
Could you register an issue of the last point on Bitbucket?
written 9 months ago by Garth Wells  
Done: https://bitbucket.org/fenics-project/dolfin/issues/960/log-mentions-krylov-solver-when-using
written 9 months ago by Alexander G. Zimmerman  
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