# Error when implementing Subdomain Tutorial on CoLab **URL:** \ **Category:** dolfinx\ **Tags:** dolfinx\ **Created:** [April 23, 2024, 1:09am UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389 "2024-04-23T01:09:33Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 23, 2024, 1:09am UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/1 "2024-04-23T01:09:33Z")
Hi, When I tried to implement the **Subdomain on built-in meshes Tutorial** demo on CoLab following [Defining subdomains for different materials — FEniCSx tutorial](https://jsdokken.com/dolfinx-tutorial/chapter3/subdomains.html), the following error occurs becasue of the failure of kappa \* grad(u). kappa is a vector and grad(u) is a matrix here. Any idea here how to solve this problem? Thanks! ```auto from dolfinx import default_scalar_type from dolfinx.fem import (Constant, dirichletbc, Function, FunctionSpace, assemble_scalar, form, locate_dofs_geometrical, locate_dofs_topological) from dolfinx.fem.petsc import LinearProblem from dolfinx.io import XDMFFile, gmshio from dolfinx.mesh import create_unit_square, locate_entities from dolfinx.plot import vtk_mesh from ufl import (SpatialCoordinate, TestFunction, TrialFunction, dx, grad, inner) from mpi4py import MPI import meshio import gmsh import numpy as np import pyvista pyvista.start_xvfb() mesh = create_unit_square(MPI.COMM_WORLD, 10, 10) Q = dolfinx.fem.functionspace(mesh, ("DG", 0, (mesh.geometry.dim,))) def Omega_0(x): return x[1] <= 0.5 def Omega_1(x): return x[1] >= 0.5 kappa = Function(Q) cells_0 = locate_entities(mesh, mesh.topology.dim, Omega_0) cells_1 = locate_entities(mesh, mesh.topology.dim, Omega_1) kappa.x.array[cells_0] = np.full_like(cells_0, 1, dtype=default_scalar_type) kappa.x.array[cells_1] = np.full_like(cells_1, 0.1, dtype=default_scalar_type) V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,))) u, v = TrialFunction(V), TestFunction(V) a = inner(kappa * grad(u), grad(v)) * dx # x = SpatialCoordinate(mesh) # L = Constant(mesh, default_scalar_type(1)) * v * dx # dofs = locate_dofs_geometrical(V, lambda x: np.isclose(x[0], 0)) # bcs = [dirichletbc(default_scalar_type(1), dofs, V)] ``` The error information is ```auto --------------------------------------------------------------------------- ValueError Traceback (most recent call last) in () 38 V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,))) 39 u, v = TrialFunction(V), TestFunction(V) ---> 40 a = inner(kappa * grad(u), grad(v)) * dx 41 # x = SpatialCoordinate(mesh) 42 # L = Constant(mesh, default_scalar_type(1)) * v * dx 1 frames /usr/local/lib/python3.10/dist-packages/ufl/exproperators.py in _mult(a, b) 157 158 else: --> 159 raise ValueError(f"Invalid ranks {r1} and {r2} in product.") 160 161 # TODO: I think applying as_tensor after index sums results in ValueError: Invalid ranks 1 and 2 in product. ``` ---
**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:** [April 23, 2024, 5:51am UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/2 "2024-04-23T05:51:45Z")
> [@BoheT](#): > > ```auto > Q = dolfinx.fem.functionspace(mesh, ("DG", 0, (mesh.geometry.dim,))) > > def Omega_0(x): > > ``` Here you define Q as a vector space, then > [@BoheT](#): > > `kappa = Function(Q)` and > [@BoheT](#): > > `a = inner(kappa * grad(u), grad(v))` Does not make sende as the first product is a vector, while the second is matrix ---
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 23, 2024, 8:12pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/3 "2024-04-23T20:12:26Z")
Thank you for replying! I am trying to learn how to set up subdomains with different kappa, so I followed the Subdomain Demo [Defining subdomains for different materials — FEniCSx tutorial](https://jsdokken.com/dolfinx-tutorial/chapter3/subdomains.html), and want to set up different kappa for different domains. Every code is the same with the Demo, except for ```auto Q = dolfinx.fem.functionspace(mesh, ("DG", 0, (mesh.geometry.dim,))) ``` and ```auto V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,))) ``` In the Demo, they are ```auto Q = FunctionSpace(mesh, ("DG", 0)) ``` and ```auto V = FunctionSpace(mesh, ("Lagrange", 1)) ``` But another error would occur if I used the code shown in the Demo. I thought it was becasue of the update of FuncationSpace. Anything else is the same. Then I was not sure how to set up different kappa for different domains. I saw another way [https://fenicsproject.org/pub/tutorial/sphinx1/.\_ftut1005.html](https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1005.html) in FeniCs instead of FeniCSx is through Expression. ```auto class K(Expression): def __init__ (self, materials, k_0, k_1, **kwargs): self.materials = materials self.k_0 = k_0 self.k_1 = k_1 def eval_cell(self, values, x, cell): if self.materials[cell.index] == 0: values[0] = self.k_0 else: values[0] = self.k_1 kappa = K(materials, k_0, k_1, degree=0) ``` I can try this to see if this will work. But it would be great if you may have other suggestions. Thank you! ---
**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:** [April 23, 2024, 8:33pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/4 "2024-04-23T20:33:47Z")
> [@BoheT](#): > > [Defining subdomains for different materials — FEniCSx tutorial](https://jsdokken.com/dolfinx-tutorial/chapter3/subdomains.html), and want to set up different kappa for different domains. Every code is the same with the Demo, except for > > ```auto > Q = dolfinx.fem.functionspace(mesh, ("DG", 0, (mesh.geometry.dim,))) > > ``` > > and > > ```auto > V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,))) > > ``` > > In the Demo, they are > > ```auto > Q = FunctionSpace(mesh, ("DG", 0)) > > ``` Should kappa still be a constant per cell (But unique per cell) Or what does kappa signify in your code? ---
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 23, 2024, 9:07pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/5 "2024-04-23T21:07:45Z")
Thank you for your quick reply! kappa is a constant per cell, i.e. for one domain kappa is value\_1 and for another domain kappa is value\_2. Let’s say the conductivity is different within different domains. So for one domain, the governing equation is \partial T / \partial t = kappa\_1 \* diffusion term, For another subdomain, the governing equation is \partial T / \partial t = kappa\_2 \* diffusion term. And FYI, the interfaces between two subdomains will have a Neumann boundary condition. But this will be implemented later, it is not related to the question here. Thanks! ---
**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:** [April 23, 2024, 9:36pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/6 "2024-04-23T21:36:19Z")
> [@BoheT](#): > > Thank you for your quick reply! kappa is a constant per cell, i.e. for one domain kappa is value\_1 and for another domain kappa is value\_2. Then just use kappa as done in the tutorial. ---
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 23, 2024, 11:43pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/7 "2024-04-23T23:43:04Z")
That was what I did before. If I copied and pasted the tutorial code, then I will get the error shown below, ```auto --------------------------------------------------------------------------- TypeError Traceback (most recent call last) in () 20 21 mesh = create_unit_square(MPI.COMM_WORLD, 10, 10) ---> 22 Q = FunctionSpace(mesh, ("DG", 0)) 23 24 def Omega_0(x): TypeError: FunctionSpace. __init__ () missing 1 required positional argument: 'cppV' ``` If I copied and pasted the tutorial code but used “Q = dolfinx.fem.functionspace(mesh, (“DG”, 0, (mesh.geometry.dim,)))” instead, then I will get the error shown in my first message, ```auto --------------------------------------------------------------------------- ValueError Traceback (most recent call last) in () 44 V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,))) 45 u, v = TrialFunction(V), TestFunction(V) ---> 46 kappa * grad(u) 47 a = inner(kappa * grad(u), grad(v)) * dx 48 # x = SpatialCoordinate(mesh) 1 frames /usr/local/lib/python3.10/dist-packages/ufl/exproperators.py in _mult(a, b) 157 158 else: --> 159 raise ValueError(f"Invalid ranks {r1} and {r2} in product.") 160 161 # TODO: I think applying as_tensor after index sums results in ValueError: Invalid ranks 1 and 2 in product. ``` I guess my question is I cannot run the tutorial demo, but I thought it should work because I copied and pasted the tutorial demo. Is it possible it is because I am using FeniCSx on Colab? I copied and pasted the demo in this one [Defining subdomains for different materials — FEniCSx tutorial](https://jsdokken.com/dolfinx-tutorial/chapter3/subdomains.html). ---
**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:** [April 24, 2024, 4:57am UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/8 "2024-04-24T04:57:04Z")
You are using the main branch of DOLFINx, that has some API changes. The tutorial reflects the latest stable release (0.7.x). You should use ```auto import dolfinx.fem Q = fem.functionspace(mesh, ("DG", 0)) ``` Most changes relating to API changes are listed at > ---
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 24, 2024, 11:22pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/9 "2024-04-24T23:22:33Z")
I see. Thank you so much for this! ---
**Author:** ![BoheT](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@BoheT](https://fenicsproject.discourse.group/u/BoheT)\ **Post date:** [April 24, 2024, 11:37pm UTC](https://fenicsproject.discourse.group/t/error-when-implementing-subdomain-tutorial-on-colab/14389/10 "2024-04-24T23:37:13Z")
It works now on Colab! Thank you!