Even though I use the approach similar to the mixed formulation in the online tutorial (Mixed formulation for the Poisson equation):

BDM = VectorFunctionSpace(mesh, "BDM", 1)
DGv = VectorFunctionSpace(mesh, "DG", 0)
DGs = FunctionSpace(mesh, "DG", 0)

Vh = BDM * DGv * DGs

I have the same error as before:

Traceback (most recent call last):
File "/home/simone/firedrake/src/PyOP2/pyop2/caching.py", line 197, in __new__
return cls._cache_lookup(key)
File "/home/simone/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 53, in _cache_lookup
return cls._cache.get(key) or cls._read_from_disk(key, comm)
File "/home/simone/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 74, in _read_from_disk
raise KeyError("Object with key %s not found" % key)
KeyError: 'Object with key aec71f5f7a30a3d0b4db90beac07de85 not found'

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
File "Elasticity2D_Firedrake.py", line 163, in <module>
solve(lhs_varf == rhs_varf, sol, bcs=[bc1,bc2])
File "/home/simone/firedrake/src/firedrake/firedrake/solving.py", line 125, in solve
_solve_varproblem(*args, **kwargs)
File "/home/simone/firedrake/src/firedrake/firedrake/solving.py", line 152, in _solve_varproblem
appctx=appctx)
File "/home/simone/firedrake/src/firedrake/firedrake/variational_solver.py", line 335, in __init__
super(LinearVariationalSolver, self).__init__(*args, **kwargs)
File "/home/simone/firedrake/src/firedrake/firedrake/variational_solver.py", line 182, in __init__
options_prefix=self.options_prefix)
File "/home/simone/firedrake/src/firedrake/firedrake/solving_utils.py", line 131, in __init__
form_compiler_parameters=self.fcp)
File "/home/simone/firedrake/src/firedrake/firedrake/assemble.py", line 158, in create_assembly_callable
loops = tuple(loops)
File "/home/simone/firedrake/src/firedrake/firedrake/assemble.py", line 228, in _assemble
kernels = tsfc_interface.compile_form(f, "form", parameters=form_compiler_parameters, inverse=inverse)
File "/home/simone/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 212, in compile_form
number_map, interface, coffee).kernels
File "/home/simone/firedrake/src/PyOP2/pyop2/caching.py", line 199, in __new__
obj = make_obj()
File "/home/simone/firedrake/src/PyOP2/pyop2/caching.py", line 189, in make_obj
obj.__init__(*args, **kwargs)
File "/home/simone/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 121, in __init__
tree = tsfc_compile_form(form, prefix=name, parameters=parameters, interface=interface, coffee=coffee)
File "/home/simone/firedrake/src/tsfc/tsfc/driver.py", line 57, in compile_form
fd = ufl_utils.compute_form_data(form, complex_mode=complex_mode)
File "/home/simone/firedrake/src/tsfc/tsfc/ufl_utils.py", line 59, in compute_form_data
complex_mode=complex_mode
File "/home/simone/firedrake/src/ufl/ufl/algorithms/compute_form_data.py", line 298, in compute_form_data
form = apply_function_pullbacks(form)
File "/home/simone/firedrake/src/ufl/ufl/algorithms/apply_function_pullbacks.py", line 267, in apply_function_pullbacks
return map_integrand_dags(FunctionPullbackApplier(), expr)
File "/home/simone/firedrake/src/ufl/ufl/algorithms/map_integrands.py", line 58, in map_integrand_dags
form, only_integral_type)
File "/home/simone/firedrake/src/ufl/ufl/algorithms/map_integrands.py", line 39, in map_integrands
for itg in form.integrals()]
File "/home/simone/firedrake/src/ufl/ufl/algorithms/map_integrands.py", line 39, in <listcomp>
for itg in form.integrals()]
File "/home/simone/firedrake/src/ufl/ufl/algorithms/map_integrands.py", line 46, in map_integrands
return itg.reconstruct(function(itg.integrand()))
File "/home/simone/firedrake/src/ufl/ufl/algorithms/map_integrands.py", line 57, in <lambda>
return map_integrands(lambda expr: map_expr_dag(function, expr, compress),
File "/home/simone/firedrake/src/ufl/ufl/corealg/map_dag.py", line 37, in map_expr_dag
result, = map_expr_dags(function, [expression], compress=compress)
File "/home/simone/firedrake/src/ufl/ufl/corealg/map_dag.py", line 84, in map_expr_dags
r = handlers[v._ufl_typecode_](v)
File "/home/simone/firedrake/src/ufl/ufl/corealg/multifunction.py", line 42, in _memoized_handler
r = handler(self, o)
File "/home/simone/firedrake/src/ufl/ufl/algorithms/apply_function_pullbacks.py", line 256, in form_argument
return apply_single_function_pullbacks(o)
File "/home/simone/firedrake/src/ufl/ufl/algorithms/apply_function_pullbacks.py", line 151, in apply_single_function_pullbacks
assert len(gsh) == 1
AssertionError

Thank you so much, have a wonderful day.

Best regards,

Simone

On Tue, Jun 25, 2019 at 8:03 AM Simone Puel <spuel@utexas.edu> wrote:

Dear Lawrence and Matt,

Thank you so much for your emails. I am not sure I understood correctly. In my case BDM is used for the stress (tensor), DGv for displacement (vector) and DGs for rotation (vector).
If I write something like this:

BDM = TensorFunctionSpace(mesh, "BDM", 1)
DGv = VectorFunctionSpace(mesh, "DG", 0)
DGs = VectorFunctionSpace(mesh, "DG", 0)

# Mixed function spaces
Vh_element = MixedElement([TensorElement(BDM), VectorElement(DGv), VectorElement(DGs)])
Vh = FunctionSpace(mesh, Vh_element)

I have the following error:

Traceback (most recent call last):
File "Elasticity2D_Firedrake.py", line 116, in <module>
BDM = TensorFunctionSpace(mesh, "BDM", 1)
File "/home/simone/firedrake/src/firedrake/firedrake/functionspace.py", line 213, in TensorFunctionSpace
assert sub_element.value_shape() == ()
AssertionError

Thank you so much, probably I am a little bit confused how to use these terms.
Thanks in advance, have a wonderful day.

Best regards,
Simone

On Tue, Jun 25, 2019 at 6:33 AM Matthew Knepley <knepley@gmail.com> wrote:
On Tue, Jun 25, 2019 at 7:22 AM Lawrence Mitchell <wence@gmx.li> wrote:
> On 25 Jun 2019, at 11:49, Matthew Knepley <knepley@gmail.com> wrote:
>
> On Tue, Jun 25, 2019 at 6:44 AM Ham, David A <david.ham@imperial.ac.uk> wrote:
> I *think* that the concept is that the physical cell is mapped to the reference cell, so you are pulling back reference values through that mapping to get physical values.
>
>
> Ah. I named them the opposite way :) This is a good window into how my mind works. I thought
> since the Jacobian maps reference to real (and phi for that matter) that the default direction of any
> mapping should be ref-to-real. It seems like this is the overwhelming convention in large deformations.

If you have a mapping

\phi : \hat{K} \to K

Then

\phi^* : Alt^k(K) \to Alt^k(\hat{K})

is the pullback defined by

\phi^* w(v_1, ..., v_k) = w(\phi v_1, ... \phi v_k), v_i \in \hat{K}, w \in Alt^k(K)

So at least differential geometry says the pullback goes in the opposite direction to the mapping.

Yes, exactly. So if the mapping is ref-to-real, then then pulllback should be real-to-ref, which is what I needed for
dual basis application. I needed ref-to-real for cell integration (since tabulations are in ref), which I called pushforward.

Thanks,

Matt

Lawrence

--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/
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--
Simone Puel
Ph.D. student in Geological Sciences at the University of Texas at Austin
Jackson School of Geosciences & Institute for Geophysics (UTIG)
JGB 5.332 & ROC 2.116L
spuel@utexas.edu
+1 (737)-230-6811