How to set the PETSc block size for GAMG when using enriched_element in DOLFINx

TL;DR

A PETSc block size of 1 on a matrix assembled from a basix enriched_element (for example the MINI element, P1 Lagrange plus bubble) is expected, not a bug in your code. Plain vector Lagrange elements are blocked, so the block size equals gdim (2 in 2D), but an enriched element concatenates sub-element dofmaps and reports block size 1. PETSc GAMG reads the matrix block size to find the degrees of freedom per grid point, so set it yourself with A.setBlockSize(gdim) right after building the problem and before the first solve().

The PETSc PCGAMG docs state the requirement this way:

To obtain good performance for PCGAMG for vector valued problems you must call MatSetBlockSize() to indicate the number of degrees of freedom per grid point

Step 1 - confirm where the block size comes from

print("dofmap block size:", V.dofmap.bs)
print("matrix block size:", problem.A.getBlockSize())

Expected output: dofmap bs is 1 and matrix block size is 1 for the enriched element; for the plain vector P2 element both report 2.

Step 2 - set the block size before the solve

from dolfinx.fem.petsc import LinearProblem
problem = LinearProblem(a_ufl, L_ufl, petsc_options={"ksp_type": "gmres", "pc_type": "gamg"})
problem.A.setBlockSize(gdim)
problem.solve()

Success check: problem.A.getBlockSize() now returns gdim, and GAMG needs fewer iterations than the block size 1 run (compare with the kspconvergedreason option).

Step 3 - nested Stokes matrices: set it on the velocity block

A00 = A_nest.getLocalSubMatrix(0, 0)
A00.setBlockSize(gdim)

Do this for each vector-valued diagonal block before the KSP is set up.

When this applies

• Matrix assembled from basix.ufl.enriched_element in DOLFINx (MINI element or any enriched combination)
• Using PETSc GAMG (or hypre BoomerAMG nodal coarsening) on the vector block
• A.getBlockSize() returns 1 where you expected gdim

When this does not apply

• Plain vector Lagrange, Nedelec, or Raviart-Thomas elements already report the right block size; leave them alone
• Scalar problems, where block size 1 is correct
• Matrices you built explicitly as BAIJ, where the block size is fixed at creation

Compatibility

DOLFINx 0.10 and 0.11, petsc4py 3.2x, PETSc 3.2x, basix enriched_element. The setBlockSize workaround applies to any version where the dofmap reports bs 1.

Variant phrasings

• MINI element PETSc block size 1
• GAMG slow on enriched element in dolfinx
• MatGetBlockSize returns 1 for a vector function space

Root cause

basix reports block size 1 for enriched elements because the element is a concatenation of sub-elements rather than a single blocked element. DOLFINx builds the dofmap from that (V.dofmap.bs is 1), and the assembled PETSc matrix inherits block size 1. GAMG then treats every degree of freedom as scalar, which usually still converges but builds a weaker multigrid hierarchy on the velocity block.

Edge cases

• Set the block size before the KSP is set up (before the first solve()); changing it later may have no effect.
• Inside each sub-element block the dofs are still grouped gdim-per-entity (vertices for the P1 part, cell interiors for the bubble part), so gdim is the right value, but it remains a heuristic grouping for GAMG rather than a true nodal layout.
• For even better GAMG performance, also provide the near null space (one constant vector per component) via MatSetNearNullSpace; the PCGAMG docs page describes both requirements.

Provenance: drafted from public thread https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805

Provenance

Resolved from the public thread: https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805

In FEniCS Project Discourse: Incorrect PETSc.Mat block size when using enriched_element (https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805): a MINI-element (P1 enriched with bubble) velocity matrix reports block size 1 while the equivalent P2 vector element reports 2, and the PETSc PCGAMG docs require MatSetBlockSize to indicate dofs per grid point for vector problems. Source: https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805