Tabulate_tensor_integral becomes a performance hotspot when simulation moves from 2D to 3D

[dokken]

@chenyongxin

Why this happens? It is not the solving linear system but integral step (assemble) takes the most amount of time in 3D.

Two things change in 3D, you get more degrees of freedom per element (larger local matrix) and you get another quadrature rule (more points required to do the numerical integral).

You can control the latter, see for instance

Extremely slow solver when using coordinate transform

The problem is the automatic estimation of the quadrature degree for your integrals. Setting: dx = ufl.Measure( "dx", domain=mesh, subdomain_data=ct, metadata={"quadrature_degree": 8}, ) you get: Solved for 16433 dofs. Min, max of the solved potential is -0.11544615271350633, 0.1157284028550102 Solve time without spatial transform: 1.4832050800323486 Solved for 16433 dofs. Min, max of the solved potential is -0.11654400959639583, 0.11686836195473972 S…