# Difference in performance between FEniCS and FEniCSX for higher order

**URL:** <https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522>\
**Category:** General\
**Created:** [October 18, 2022, 4:25pm UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522 "2022-10-18T16:25:56Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![nabarnaf](https://avatars.discourse-cdn.com/v4/letter/n/dec6dc/32.png) [@nabarnaf](https://fenicsproject.discourse.group/u/nabarnaf)\
**Post date:** [October 18, 2022, 4:25pm UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522/1 "2022-10-18T16:25:56Z")

</div>

Hi community, I am comparing some libraries, and FEniCSX seems to have issues for higher order. The test is solving

-\Delta u + u = 1, \quad \in (0,1)^3

with homogeneous Neumann BCs. The number of iterations using CG+Jacobi for P1 and P2 are equal between FEniCS and FEniCSX, but for P3 they do 227 and 247 resp. To confim, I have checked with FreeFEM and Firedrake, and they all do 227, so it is probably a problem with FEniCSX. I have checked, and varying the quadrature degree from 4 to 12 gives the same result (less than that results in divergence).

If you have another idea please let me know, if not I will report a bug.

Best!

---

<div class="post-metadata">

**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [October 18, 2022, 5:39pm UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522/2 "2022-10-18T17:39:50Z")

</div>

Without the code corresponding to the results you are seeing, it is hard to give you any pointers.

---

<div class="post-metadata">

**Author:** ![nabarnaf](https://avatars.discourse-cdn.com/v4/letter/n/dec6dc/32.png) [@nabarnaf](https://fenicsproject.discourse.group/u/nabarnaf)\
**Post date:** [October 19, 2022, 9:45am UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522/3 "2022-10-19T09:45:30Z")

</div>

Sorry, dumb mistake. Here they are:

FEniCS:

```auto
from petsc4py.PETSc import Options
from dolfin import *
N = 20
P = 3
mesh = UnitCubeMesh(N, N, N)
V = FunctionSpace(mesh, "Lagrange", P)
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v))*dx + u*v*dx
F = v*dx
u_sol = Function(V)
A = assemble(a)
FF = assemble(F)
solver_ops = Options()
solver_ops.setValue('ksp_type', 'cg')
solver_ops.setValue('pc_type', 'jacobi')
solver_ops.setValue('ksp_monitor', None)
solver_ops.setValue('ksp_atol', 1e-14)
solver_ops.setValue('ksp_rtol', 1e-6)
solver = PETScKrylovSolver()
solver.set_from_options()
solver.solve(A, u_sol.vector(), FF)

```

FEniCSX

```auto
from dolfinx import fem, io, mesh, plot
import ufl
from ufl import ds, dx, grad, inner
from mpi4py import MPI
N = 20
P = 3
msh = mesh.create_unit_cube(comm=MPI.COMM_WORLD, nx=N, ny=N, nz=N)
V = fem.FunctionSpace(msh, ("Lagrange", P))
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = inner(grad(u), grad(v)) + u*v
a = a * dx
L = v * dx
problem = fem.petsc.LinearProblem(a, L, petsc_options={"ksp_type": "cg", "pc_type": "jacobi", "ksp_monitor": None, "ksp_atol": 1e-14, "ksp_rtol": 1e-6})
uh = problem.solve()

```

---

<div class="post-metadata">

**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [October 19, 2022, 10:48am UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522/4 "2022-10-19T10:48:48Z")

</div>

This is because DOLFINx uses GLL dof placement of higher order Lagrange dofs, see:  
[https://docs.fenicsproject.org/dolfinx/v0.5.1/python/demos/demo\_lagrange\_variants.html#equispaced-points-vs-gll-points](https://docs.fenicsproject.org/dolfinx/v0.5.1/python/demos/demo_lagrange_variants.html#equispaced-points-vs-gll-points)

Thus, you would get different matrices, and different results, as your underlying polynomials and definitions of degrees of freedom would differ.

MWE. to produce the same iteration count as with DOLFIN

```python
from dolfinx import fem, io, mesh, plot
import ufl
from ufl import ds, dx, grad, inner
from mpi4py import MPI
from basix import ufl_wrapper
import basix

N = 20
P = 3
msh = mesh.create_unit_cube(comm=MPI.COMM_WORLD, nx=N, ny=N, nz=N)
element = ufl_wrapper.create_element(
    "Lagrange", msh.topology.cell_type.name, P,
    lagrange_variant=basix.LagrangeVariant.equispaced)
V = fem.FunctionSpace(msh, element)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = inner(grad(u), grad(v)) + u*v
a = a * dx
L = v * dx
options = {"ksp_type": "cg",
           "pc_type": "jacobi",
           "ksp_monitor": None,
           "ksp_atol": 1e-14,
           "ksp_rtol": 1e-6}
problem = fem.petsc.LinearProblem(a, L, petsc_options=options)
uh = problem.solve()

```

---

<div class="post-metadata">

**Author:** ![nabarnaf](https://avatars.discourse-cdn.com/v4/letter/n/dec6dc/32.png) [@nabarnaf](https://fenicsproject.discourse.group/u/nabarnaf)\
**Post date:** [October 19, 2022, 11:08am UTC](https://fenicsproject.discourse.group/t/difference-in-performance-between-fenics-and-fenicsx-for-higher-order/9522/5 "2022-10-19T11:08:57Z")

</div>

Amazing, thank you very much!