Hello David,

At the moment I am using UnitSquareMesh but at some point I would like to consider different geometries.

What I tried is using

    n = FacetNormal(mesh)

    x, y = SpatialCoordinate(mesh)
    g = (sin(pi*x)*sin(pi*y))*n[0] + cos(pi*x)*cos(pi*y)*n[1]
    g1 = g*n[0]
    g2 = g*n[1]

    bcs = DirichletBC(W.sub(0), as_vector([g1, g2]), "on_boundary")

but that failed miserably with the following,

(firedrake) fpoulin@fpoulin-Gazelle:~/software/poulinrhebergen/codes/firedrake/stokes$ python stokes.py UFL:ERROR Integral of type cell cannot contain a ReferenceNormal.
Traceback (most recent call last):
File "stokes.py", line 96, in <module>
    bcs = DirichletBC(W.sub(0), as_vector([g1, g2]), "on_boundary")
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/bcs.py", line 57, in __init__
    self.function_arg = g
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/bcs.py", line 125, in function_arg
    g = projection.project(g, self._function_space)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/projection.py", line 101, in project
    form_compiler_parameters=form_compiler_parameters)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/solving.py", line 124, in solve
    _solve_varproblem(*args, **kwargs)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/solving.py", line 153, in _solve_varproblem
    appctx=appctx)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/variational_solver.py", line 286, in __init__
    super(LinearVariationalSolver, self).__init__(*args, **kwargs)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/variational_solver.py", line 156, in __init__
    pre_function_callback=pre_f_callback)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/solving_utils.py", line 333, in __init__
    form_compiler_parameters=fcp)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/assemble.py", line 143, in create_assembly_callable
    collect_loops=True)
File "<decorator-gen-280>", line 2, in _assemble
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/utils.py", line 62, in wrapper
    return f(*args, **kwargs)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/assemble.py", line 192, in _assemble
    kernels = tsfc_interface.compile_form(f, "form", parameters=form_compiler_parameters, inverse=inverse)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 193, in compile_form
    number_map).kernels
File "/home/fpoulin/software/firedrake/src/PyOP2/pyop2/caching.py", line 200, in __new__
    obj = make_obj()
File "/home/fpoulin/software/firedrake/src/PyOP2/pyop2/caching.py", line 190, in make_obj
    obj.__init__(*args, **kwargs)
File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 112, in __init__
    tree = tsfc_compile_form(form, prefix=name, parameters=parameters)
File "/home/fpoulin/software/firedrake/src/tsfc/tsfc/driver.py", line 46, in compile_form
    fd = ufl_utils.compute_form_data(form)
File "/home/fpoulin/software/firedrake/src/tsfc/tsfc/ufl_utils.py", line 56, in compute_form_data
    do_estimate_degrees=do_estimate_degrees,
File "/home/fpoulin/software/firedrake/src/ufl/ufl/algorithms/compute_form_data.py", line 382, in compute_form_data
    _check_facet_geometry(self.integral_data)
File "/home/fpoulin/software/firedrake/src/ufl/ufl/algorithms/compute_form_data.py", line 168, in _check_facet_geometry
    error("Integral of type %s cannot contain a %s." % (it, cls.__name__))
File "/home/fpoulin/software/firedrake/src/ufl/ufl/log.py", line 172, in error
    raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Integral of type cell cannot contain a ReferenceNormal.

------------------
Francis Poulin
Associate Professor
Department of Applied Mathematics
University of Waterloo

email:           fpoulin@uwaterloo.ca
Web:            https://uwaterloo.ca/poulin-research-group/
Telephone: +1 519 888 4567 x32637

From: firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk] on behalf of David Ham [David.Ham@imperial.ac.uk]
Sent: Wednesday, May 10, 2017 10:41 AM
To: firedrake
Subject: Re: [firedrake] imposing Dirichlet BCS

Hi Francis,

Usually we use the boundary markers on the incoming mesh. Where are you getting your more general mesh from?

Regards,

David

On Wed, 10 May 2017 at 15:37 Francis Poulin <fpoulin@uwaterloo.ca> wrote:

Hello,

We are trying to translate part of the mixed-poisson Fenics demo into Firedrake. I know that there is already a Firedrake demo that does this but for the special case of a square. I am hoping we can do this more generally.

Below are the lines of code from Fenics. Can someone suggest how this could be implemented in Firedrake?
Cheers, Francis

https://fenics.readthedocs.io/projects/dolfin/en/latest/demos/mixed-poisson/python/demo_mixed-poisson.py.html
# Define function G such that G \cdot n = g
class BoundarySource(Expression):
    def __init__(self, mesh, **kwargs):
        self.mesh = mesh
    def eval_cell(self, values, x, ufc_cell):
        cell = Cell(self.mesh, ufc_cell.index)
        n = cell.normal(ufc_cell.local_facet)
        g = sin(5*x[0])
        values[0] = g*n[0]
        values[1] = g*n[1]
    def value_shape(self):
        return (2,)

G = BoundarySource(mesh, degree=2)

# Define essential boundary
def boundary(x):
    return x[1] < DOLFIN_EPS or x[1] > 1.0 - DOLFIN_EPS
bc = DirichletBC(W.sub(0), G, boundary)
------------------
Francis Poulin
Associate Professor
Department of Applied Mathematics
University of Waterloo

email:           fpoulin@uwaterloo.ca
Web:            https://uwaterloo.ca/poulin-research-group/
Telephone: +1 519 888 4567 x32637

Dr David Ham

Department of Mathematics

Imperial College London