# Solve time dependent problem with Error :Integral is missing an integral domain **URL:** \ **Category:** General\ **Created:** [March 22, 2023, 8:06am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737 "2023-03-22T08:06:02Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Discoverer](https://avatars.discourse-cdn.com/v4/letter/d/b2d939/32.png) [@Discoverer](https://fenicsproject.discourse.group/u/Discoverer)\ **Post date:** [March 22, 2023, 8:06am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/1 "2023-03-22T08:06:02Z")
I try to solve a time dependent problem of this kind : `u_t -\epsilon div(grad(u))+dot(b,grad(u))+cu=f` with u=0 on the boundary.I use the SUPG and Euler Backwards scheme to solve this problem. I use grids with 20,40,80,160 on each direction for space discretization while I choose number of time steps as 5 from t=0 to 1. With this number of time steps, I encounter the following error `This integral is missing an integration domain. ERROR:UFL:This integral is missing an integration domain. Traceback (most recent call last): File "/home/fenics/FSI_Solver/SUPG_TEST.py", line 56, in a=fem.form(u*v*dx+dt*epsilon*inner(grad(u),grad(v))*dx+dt*dot(b,grad(u))*v*dx+dt*c*u*v*dx+dt*delta*(-epsilon*div(grad(u))+dot(b,grad(u))+c*u)*(dot(b,grad(v)))*dx+(u*delta*dot(b,grad(v))*dx)) File "/usr/local/lib/python3.10/dist-packages/ufl/measure.py", line 413, in __rmul__ error("This integral is missing an integration domain.") File "/usr/local/lib/python3.10/dist-packages/ufl/log.py", line 135, in error raise self._exception_type(self._format_raw(*message)) ufl.log.UFLException: This integral is missing an integration domain.` Is this because the time step is so small?Since when I use 10 as number of time steps, it works well but it breaks down with 5,6,7,8. The complete code is as follows: ```auto from dolfinx import mesh,fem import numpy as np from ufl import div,grad,diff,dot,inner,dx,ds,CellDiameter,TrialFunction,TestFunction,sin,pi,exp import ufl from mpi4py import MPI from petsc4py import PETSc t=0 T=1 for nx in [20, 40, 80, 160,320]: ny=nx num_steps=8 dt=(T-t)/num_steps domain=mesh.create_unit_square(MPI.COMM_WORLD,nx,ny,mesh.CellType.triangle) V=fem.FunctionSpace(domain,("CG",1)) epsilon=fem.Constant(domain,PETSc.ScalarType(1e-8)) b=fem.Constant(domain,np.array([1,-1],dtype=PETSc.ScalarType)) c=fem.Constant(domain,PETSc.ScalarType(1)) #define exact solution def u_exact(mod, t): return lambda x: mod.exp(mod.sin(2*mod.pi*t))*mod.sin(2*mod.pi*x[0])*mod.sin(2*mod.pi*x[1]) x=ufl.SpatialCoordinate(domain) t_var=ufl.variable(t) exact_soln_ufl=u_exact(ufl,t_var) #used for linear form exact_soln_np=u_exact(np,t) #used for interpolation #Apply homogeneous Dirichlet boundary condition boundary_fun=fem.Function(V) boundary_fun.interpolate(exact_soln_np) tdim=domain.topology.dim fdim=tdim-1 domain.topology.create_connectivity(fdim,tdim) boundary_facets=mesh.exterior_facet_indices(domain.topology) bc=fem.dirichletbc(boundary_fun,fem.locate_dofs_topological(V,fdim,boundary_facets)) #Initial condition u_old=fem.Function(V) u_old.interpolate(exact_soln_np) #Define right hand side f f=diff(exact_soln_ufl(x),t_var)-epsilon*div(grad(exact_soln_ufl(x)))+dot(b,grad(exact_soln_ufl(x)))+c*exact_soln_ufl(x) u,v=TrialFunction(V),TestFunction(V) h=CellDiameter(domain) delta=h/4 a=fem.form(u*v*dx+dt*epsilon*inner(grad(u),grad(v))*dx+dt*dot(b,grad(u))*v*dx+dt*c*u*v*dx+dt*delta*(-epsilon*div(grad(u))+dot(b,grad(u))+c*u)*(dot(b,grad(v)))*dx+(u*delta*dot(b,grad(v))*dx)) L=fem.form(u_old*v*dx+dt*f*(v+delta*dot(b,grad(v)))*dx+u_old*delta*dot(b,grad(v))*dx) A=fem.petsc.assemble_matrix(a,bcs=[bc]) A.assemble() b=fem.petsc.create_vector(L) uh=fem.Function(V) solver=PETSc.KSP().create(domain.comm) solver.setOperators(A) solver.setType(PETSc.KSP.Type.PREONLY) solver.getPC().setType(PETSc.PC.Type.LU) V_ex = fem.FunctionSpace(domain, ("CG", 2)) u_ex = fem.Function(V_ex) #Use Euler Backwards for time discretization for n in range(num_steps): t+=dt exact_soln_np=u_exact(np,t) boundary_fun.interpolate(exact_soln_np) with b.localForm() as loc_b: loc_b.set(0) fem.petsc.assemble_vector(b,L) fem.petsc.apply_lifting(b,[a],[[bc]]) b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,mode=PETSc.ScatterMode.REVERSE) fem.petsc.set_bc(b,[bc]) solver.solve(b,uh.vector) uh.x.scatter_forward() u_old.x.array[:] = uh.x.array # Compute L2 norm of the discrete solution at final time L2 = np.sqrt(domain.comm.allreduce(fem.assemble_scalar(fem.form((uh)**2 * dx)),op=MPI.SUM)) if domain.comm.rank == 0: print(f"L2: {L2:.2e}") ``` Thanks in advance! ---
**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:** [March 22, 2023, 9:14am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/2 "2023-03-22T09:14:41Z")
I would start by trying: ```python from ufl import Measure dx = ufl.Measure("dx", domain=domain) ``` and see if that works. Note that if you wrap `dt` as a `k = dolfinx.fem.Constant(mesh, dt)` and use `k` in your variational form, it should give you some performance benefit, as the form does not have to be recompiled if you ever need to change `T, t, or num_steps` ---
**Author:** ![Discoverer](https://avatars.discourse-cdn.com/v4/letter/d/b2d939/32.png) [@Discoverer](https://fenicsproject.discourse.group/u/Discoverer)\ **Post date:** [March 22, 2023, 9:40am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/4 "2023-03-22T09:40:59Z")
Thank you very much. Sorry for another question. Since I define f as ` f=diff(exact_soln_ufl(x),t_var)-epsilon*div(grad(exact_soln_ufl(x)))+dot(b,grad(exact_soln_ufl(x)))+c*exact_soln_ufl(x)` it depends on time t . So when I solve the linear system at every time step, I need to update the time.If I try to use ```auto for n in range(num_steps): t+=dt ``` to update the time, will the `f(t)` be automatically updated to f(t+dt)? Further, I use t\_var=ufl.variable(t) to define the time t as a variable for differentiating with time.So if t is a variable now or we create a new variable t\_var which has the value of t?I dont know how this works when defining bilinear form and when I compute the right hand side. ---
**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:** [March 22, 2023, 10:02am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/5 "2023-03-22T10:02:37Z")
You should wrap `t` as a `dolfinx.fem.Constant` to make sure that it is automatically update when you call `t.value += dt` When you call `dolfinx.fem.form` you generate `C` code for assembly, and the only parameters that are modifiable after this are `dolfinx.fem.Constant`, `dolfinx.fem.Function` and the mesh geometry. ---
**Author:** ![Discoverer](https://avatars.discourse-cdn.com/v4/letter/d/b2d939/32.png) [@Discoverer](https://fenicsproject.discourse.group/u/Discoverer)\ **Post date:** [March 22, 2023, 10:37am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/6 "2023-03-22T10:37:27Z")
Thank you. Now I define the paarameters and function f as follows ```auto domain=mesh.create_unit_square(MPI.COMM_WORLD,nx,ny,mesh.CellType.triangle) V=fem.FunctionSpace(domain,("CG",1)) k=T/num_steps t=fem.Constant(domain,PETSc.ScalarType(0)) dt=fem.Constant(domain,PETSc.ScalarType(k)) def u_exact(mod, t): return lambda x: mod.exp(mod.sin(2*mod.pi*t))*mod.sin(2*mod.pi*x[0])*mod.sin(2*mod.pi*x[1]) x=ufl.SpatialCoordinate(domain) t_var=ufl.variable(t) exact_soln_ufl=u_exact(ufl,t_var) #used for linear form exact_soln_np=u_exact(np,t) #used for interpolation f=diff(exact_soln_ufl(x),t_var)-epsilon*div(grad(exact_soln_ufl(x)))+dot(b,grad(exact_soln_ufl(x)))+c*exact_soln_ufl(x) ``` and in iteration I use ```auto for n in range(num_steps): t.value+=k ``` Will it automatically update the function `f`? And t\_var is related with t so they change values in the same time as t changes? ---
**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:** [March 22, 2023, 12:43pm UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/7 "2023-03-22T12:43:56Z")
> [@Discoverer](#): > > Will it automatically update the function `f`? And t\_var is related with t so they change values in the same time as t changes? Yes, as you are not changing the object `t`, but the internal value it represents, `t_var` is keeping track of the change. ---
**Author:** ![Discoverer](https://avatars.discourse-cdn.com/v4/letter/d/b2d939/32.png) [@Discoverer](https://fenicsproject.discourse.group/u/Discoverer)\ **Post date:** [March 22, 2023, 12:47pm UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/8 "2023-03-22T12:47:47Z")
Very helpful!Thank you very much. ---
**Author:** ![dparsons](https://avatars.discourse-cdn.com/v4/letter/d/5e9695/32.png) [@dparsons](https://fenicsproject.discourse.group/u/dparsons)\ **Post date:** [September 27, 2023, 2:54am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/9 "2023-09-27T02:54:14Z")
> [@dokken](#): > > I would start by trying: > > ```auto > from ufl import Measure > dx = ufl.Measure("dx", domain=domain) > > ``` > > and see if that works. Hi @dokken, I’ve just hit the error reported here, “Integral is missing an integral domain”. Your suggestion to explicitly define the dx measure resolves the problem. What is strange is that my script runs fine with exactly the same code (without Measure), only with a different value for one of my parameters. Not sure I can reduce to a short MWE to demonstrate, but on the face of it the parameter that is different should be completely unrelated to the domain or the dx Measure. Is it possible to provide some background on the solution given here? Why would the default ufl.dx object work fine with one value of the parameter, but fail, requiring an explicit Measure, for another value of the parameter, where the code is otherwise the same? ---
**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:** [September 27, 2023, 6:29am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/10 "2023-09-27T06:29:31Z")
> [@dparsons](#): > > What is strange is that my script runs fine with exactly the same code (without Measure), only with a different value for one of my parameters. Not sure I can reduce to a short MWE to demonstrate, but on the face of it the parameter that is different should be completely unrelated to the domain or the dx Measure. UFL consists several important classes, here I’ll refer to two of them, namely `ufl.core.expr.Expr` and `ufl.form.Form`. A `ufl.core.expr.Expr` is anything that can be an integrand in ufl. This means it could be `1`, `u*v`, `ufl.inner(ufl.div(ufl.grad(u)), v)` etc. These expressions are usually associated with a mesh through its test or trial functions, coefficients or constants. A form is whenever you want to integrate this expression over a domain, i.e. right multiply by `ufl.dx` or `ufl.Measure("dx")`. For this right multiplication to work (and create a `ufl.integral.Integral`, it requires an integration domain (a mesh, or `ufl_domain` in ufl-speak): [https://github.com/FEniCS/ufl/blob/77ae57c4b9594851f6bff4a63b7eecb81477c486/ufl/measure.py#L380-L388](https://github.com/FEniCS/ufl/blob/77ae57c4b9594851f6bff4a63b7eecb81477c486/ufl/measure.py#L380-L388) Some forms do not have this property, for instance `1*ufl.dx` This can be solved by either making `1` a `dolfinx.fem.Constant(mesh, 1)` (which is also good for other reasons), or attaching the `ufl_domain` to the measure. However, `ufl` does some clever graph simplification and matching of terms, so that whenever you multiply by `0`, it reduced the ufl-form: i.e. ```python v = ufl.TestFunction(V) L = v * ufl.dx ``` is fine, while ```python 0*v*ufl.dx ``` produces the error with missing integration domain, as ```python 0 * v ``` produces ```bash Zero((), (), ()) ``` which does not have a ufl domain. I guess this is what is happening for on of the terms of your variational form. The best way to counteract this is to wrap material parameters as `dolfinx.fem.Constant` (which is also beneficial for code generation), or simply always define the integration domain in the `ufl.Measure`, as it is the first place it looks: 77ae57c4b9594851f6bff4a63b7eecb81477c486/ufl/measure.py#L380-L388 without an example I cannot really pinpoint what goes wrong in your code. This is just my best guess from my understanding of UFL (which might not be 100 % correct, so anyone feel free to jump in and add more context or corrections). ---
**Author:** ![dparsons](https://avatars.discourse-cdn.com/v4/letter/d/5e9695/32.png) [@dparsons](https://fenicsproject.discourse.group/u/dparsons)\ **Post date:** [September 27, 2023, 8:28am UTC](https://fenicsproject.discourse.group/t/solve-time-dependent-problem-with-error-integral-is-missing-an-integral-domain/10737/11 "2023-09-27T08:28:45Z")
That makes sense about how `const*ufl.dx` is handled, it’s it’s certainly true I need to do through my code and replace some with `dolfinx.fem.Constant`. It’s strange though, in my instance the parameter that triggers the error is not a constant (not even 0), it’s a python function used as an argument inside other ufl maths functions (counterpart to the old Expression from legacy dolfin). In lieu of an available MWE maybe I should send you the code and make you a coauthor 🙂 Setting an explicit Measure is easy enough to do in any case.