Green Lagrange tensor

[nicolas-tardieu]

Dear firedrakers,

I am trying to use a simple finite strain model based on the use of the Green-Lagrange tensor. Unfortunately, I get a strange error :
KeyError: 'Object with key a9198fc8d1d6100862060f0212858a83 not found'
Am I missing something? Everything is OK when using the linear strain tensor.

The script is attached to this email.

Thanks for your help,
Nicolas
test.py.gz

[connorjward]

We really need to see the full error traceback as KeyError happens whenever a cache is missed (which is perfectly normal). Please also share the code directly in the post using backticks as it's easier to review.

[nicolas-tardieu]

OK. Here is the code :

from firedrake import *
from mpi4py import MPI

mesh = RectangleMesh(
        2, 2, 2, 2, comm=MPI.COMM_WORLD, quadrilateral=True
    )

V = VectorFunctionSpace(mesh, "Lagrange", 1)

u = Function(V)
v = TestFunction(V)

E = 1
nu = 0.0
lambda_ = Constant(E * nu / (1 + nu) / (1 - 2 * nu))
mu = Constant(E / 2.0 / (1 + nu))
Id = Identity(2)  # 2x2 Identity tensor

def epsilon(u):
    # return 0.5 * (grad(u) + grad(u).T)  # <- This works!
    return 0.5 * (grad(u) + grad(u).T + grad(u) * grad(u).T)

def sigma(u):
    return lambda_ * div(u) * Id + 2 * mu * epsilon(u)

Jr = assemble(derivative(inner(sigma(u), epsilon(v)) * dx, u)).petscmat 

And the traceback error :

Traceback (most recent call last):
  File "/home/nick/dev/firedrake/src/PyOP2/pyop2/caching.py", line 205, in __new__
    return cls._cache_lookup(key)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 73, in _cache_lookup
    return cls._cache.get((key, commkey)) or cls._read_from_disk(key, comm)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 94, in _read_from_disk
    raise KeyError(f"Object with key {key} not found")
KeyError: 'Object with key caf8b6e1668e5d5c971ed7e462da2ce0 not found'

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/tmp/test.py", line 37, in <module>
    Jr = assemble(derivative(inner(sigma(u), epsilon(v)) * dx, u),form_compiler_parameters={"slate_compiler": {"optimise": False}}).petscmat
  File "petsc4py/PETSc/Log.pyx", line 188, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 189, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/adjoint_utils/assembly.py", line 19, in wrapper
    output = assemble(*args, **kwargs)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 104, in assemble
    return assemble_base_form(expr, *args, **kwargs)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 191, in assemble_base_form
    visited[e] = base_form_assembly_visitor(e, tensor, bcs, diagonal,
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 276, in base_form_assembly_visitor
    return _assemble_form(expr, tensor=tensor, bcs=bcs,
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 545, in _assemble_form
    return assembler.assemble()
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 682, in assemble
    self.execute_parloops()
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 702, in execute_parloops
    for parloop in self.parloops:
  File "/home/nick/dev/firedrake/src/PyOP2/pyop2/utils.py", line 62, in __get__
    obj.__dict__[self.__name__] = result = self.fget(obj)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 761, in parloops
    self.local_kernels, self.global_kernels
  File "/home/nick/dev/firedrake/src/PyOP2/pyop2/utils.py", line 62, in __get__
    obj.__dict__[self.__name__] = result = self.fget(obj)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/assemble.py", line 726, in local_kernels
    kernels = tsfc_interface.compile_form(
  File "petsc4py/PETSc/Log.pyx", line 188, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 189, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 261, in compile_form
    kinfos = TSFCKernel(f, prefix, parameters,
  File "/home/nick/dev/firedrake/src/PyOP2/pyop2/caching.py", line 207, in __new__
    obj = make_obj()
  File "/home/nick/dev/firedrake/src/PyOP2/pyop2/caching.py", line 197, in make_obj
    obj.__init__(*args, **kwargs)
  File "/home/nick/dev/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 146, in __init__
    tree = tsfc_compile_form(form, prefix=name, parameters=parameters,
  File "/home/nick/dev/firedrake/src/tsfc/tsfc/driver.py", line 80, in compile_form
    fd = ufl_utils.compute_form_data(form, complex_mode=complex_mode)
  File "/home/nick/dev/firedrake/src/tsfc/tsfc/ufl_utils.py", line 56, in compute_form_data
    fd = ufl_compute_form_data(
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/compute_form_data.py", line 413, in compute_form_data
    check_form_arity(preprocessed_form, self.original_form.arguments(), complex_mode)
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/check_arities.py", line 198, in check_form_arity
    check_integrand_arity(itg.integrand(), arguments, complex_mode)
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/check_arities.py", line 179, in check_integrand_arity
    arg_tuples = map_expr_dag(rules, expr, compress=False)
  File "/home/nick/dev/firedrake/src/ufl/ufl/corealg/map_dag.py", line 34, in map_expr_dag
    result, = map_expr_dags(function, [expression], compress=compress,
  File "/home/nick/dev/firedrake/src/ufl/ufl/corealg/map_dag.py", line 100, in map_expr_dags
    r = handlers[v._ufl_typecode_](v, *[vcache[u] for u in v.ufl_operands])
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/check_arities.py", line 71, in product
    f"{x[0].number()}, argument is {_afmt(x)}.")
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/check_arities.py", line 17, in _afmt
    return tuple(f"conj({arg})" if conj else str(arg) for arg, conj in atuple)
  File "/home/nick/dev/firedrake/src/ufl/ufl/algorithms/check_arities.py", line 17, in <genexpr>
    return tuple(f"conj({arg})" if conj else str(arg) for arg, conj in atuple)
TypeError: cannot unpack non-iterable bool object

[connorjward]

So the error is misleading because it is failing for one reason and printing the error message is then failing. From inspecting your traceback it seems your are hitting this code.

Inside epsilon you are multiplying the test function with itself which is not allowed as the form must be linear w.r.t. the test and trial functions.

It would be helpful to see the maths you are trying to reproduce in Firedrake to compare.

[nicolas-tardieu]

Thanks for pointing this error. I revisited the form and things are OK now.