I have been studying multi-phase materials with one diffusive system.
That mean my domain has two subdomains. The solution of the system is discontinuous.
I am tryng to use DG method. The equation of the system are discribe below:
$-\nabla \cdot \beta \nabla u =f \space in \space \space \Omega_1 \cup \Omega_2, $
$u=g \space on \space \partial \Omega $
$[u]= a \space on \space \Gamma_I$
$[\beta \partial_n u]= bn$
$ A(u,v)= \int_{\Omega }^{}{\beta \nabla u \cdot \nabla v \space dx} - \int_{\Gamma } \left( [u] \cdot \lbrace \beta \nabla v \rbrace + [v] \cdot \lbrace \beta \nabla u \rbrace \right)ds$
$+\sum\limits_{e\in \Gamma }{ \frac{\eta}{h_e} \int [u] \cdot [v] }dS $
$ L(v)= \int_{\Omega}{f\space v \space dx}+ \int_{\Gamma_I}{b \lbrace v \rbrace }ds -\int_{\Gamma_I} an \cdot \lbrace D \nabla u \rbrace ds $
$- \int_{\partial \Omega}{gn \cdot \lbrace \beta \nabla v \rbrace}ds +\sum\limits_{e\in \partial \Omega }{ \frac{\eta}{h_e} \int g \space [v] }dS $
$Domain = \Omega = \Omega_1 \cup \Omega_2$
$\Gamma_I = \text{Intern interface between }\space \Omega_1 and \space \Omega_2$
$\partial \Omega = \text{boundary for Dirichilet condition}$
$\Gamma = \text{all interfaces}$
The strong formulation and problem and figures was taken from this ddf in internet (Paper with similar problem
But i would like to use my formulation.
f = Expression('0.0', degree= 1)
u0 = Expression('100.0', degree= 1)
u02 = Expression('0.0', degree= 1)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
#Define normal vector and mesh size
n = FacetNormal(mesh)
h = CellSize(mesh)
h_avg = (h('+') + h('-'))/2.0
u = TrialFunction(DG)
v = TestFunction(DG)
a = dot(D*grad(v), grad(u))*dx\
- dot(jump(u, n), avg(D*grad(v)))*dS(0)\
- dot(jump(v, n), avg(D*grad(u)))*dS(0)\
+ alpha/h_avg*dot(jump(v, n), jump(u, n))*dS(0)\
- dot(jump(u, n), avg(D*grad(v)))*dS(3)\
- dot(jump(v, n), avg(D*grad(u)))*dS(3)\
- lamb/h_avg*dot(jump(v, n), jump(u, n))*dS(3)\
a+=- dot(D*grad(v), u*n)*ds(1) - dot(v*n, D*grad(u))*ds(1)\
- dot(D*grad(v), u*n)*ds(2) - dot(v*n, D*grad(u))*ds(2)\
+ (gamma/h)*v*u*ds(1) + (gamma/h)*v*u*ds(2)
L = v*f*dx- u0*dot(D*grad(v), n)*ds(1) + (gamma/h)*u0*v*ds(1) \
-u02*dot(D*grad(v), n)*ds(2) + (gamma/h)*u02*v*ds(2)\
+u0*avg(v)*dS(3)\
+dot(u0*n,avg(D*grad(v)))*dS(3)
Can someone helpme with this particle this integral?
+dot(u0n,avg(Dgrad(v)))*dS(3)
ir doesnt work
error:
Calling FFC just-in-time (JIT) compiler, this may take some time.
Discontinuous type FacetNormal must be restricted.
Traceback (most recent call last):
File "/media/leocosta/C863-4EBF/fotos/fick/test_disc.py", line 149, in
solve(a==L , C)
File "/usr/lib/python2.7/dist-packages/dolfin/fem/solving.py", line 300, in solve
_solve_varproblem(*args, **kwargs)
File "/usr/lib/python2.7/dist-packages/dolfin/fem/solving.py", line 325, in _solve_varproblem
form_compiler_parameters=form_compiler_parameters)
File "/usr/lib/python2.7/dist-packages/dolfin/fem/solving.py", line 81, in __init__
L = Form(L, form_compiler_parameters=form_compiler_parameters)
File "/usr/lib/python2.7/dist-packages/dolfin/fem/form.py", line 89, in __init__
mpi_comm=mesh.mpi_comm())
File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/jit.py", line 68, in mpi_jit
return local_jit(*args, **kwargs)
File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/jit.py", line 133, in jit
"ffc.jit failed with message:\n%s" % (tb_text,))
File "/usr/lib/python2.7/dist-packages/dolfin/cpp/common.py", line 2973, in dolfin_error
return _common.dolfin_error(location, task, reason)
RuntimeError:
*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
*** fenics-support@googlegroups.com
*** Remember to include the error message listed below and, if possible,
*** include a minimal running example to reproduce the error.
*** -------------------------------------------------------------------------
*** Error: Unable to perform just-in-time compilation of form.
*** Reason: ffc.jit failed with message:
Traceback (most recent call last):
File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/jit.py", line 128, in jit
result = ffc.jit(ufl_object, parameters=p)
File "/usr/lib/python2.7/dist-packages/ffc/jitcompiler.py", line 198, in jit
module = jit_build(ufl_object, module_name, parameters)
File "/usr/lib/python2.7/dist-packages/ffc/jitcompiler.py", line 120, in jit_build
generate=jit_generate)
File "/usr/lib/python2.7/dist-packages/dijitso/jit.py", line 160, in jit
header, source, dependencies = generate(jitable, name, signature, params["generator"])
File "/usr/lib/python2.7/dist-packages/ffc/jitcompiler.py", line 66, in jit_generate
prefix=module_name, parameters=parameters, jit=True)
File "/usr/lib/python2.7/dist-packages/ffc/compiler.py", line 141, in compile_form
prefix, parameters, jit)
File "/usr/lib/python2.7/dist-packages/ffc/compiler.py", line 183, in compile_ufl_objects
analysis = analyze_ufl_objects(ufl_objects, kind, parameters)
File "/usr/lib/python2.7/dist-packages/ffc/analysis.py", line 89, in analyze_ufl_objects
for form in forms)
File "/usr/lib/python2.7/dist-packages/ffc/analysis.py", line 89, in
for form in forms)
File "/usr/lib/python2.7/dist-packages/ffc/analysis.py", line 166, in _analyze_form
form_data = compute_form_data(form)
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/compute_form_data.py", line 309, in compute_form_data
form = apply_restrictions(form)
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/apply_restrictions.py", line 179, in apply_restrictions
only_integral_type=integral_types)
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/map_integrands.py", line 58, in map_integrand_dags
form, only_integral_type)
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/map_integrands.py", line 39, in map_integrands
for itg in form.integrals()]
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/map_integrands.py", line 46, in map_integrands
return itg.reconstruct(function(itg.integrand()))
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/map_integrands.py", line 57, in
return map_integrands(lambda expr: map_expr_dag(function, expr, compress),
File "/usr/lib/python2.7/dist-packages/ufl/corealg/map_dag.py", line 37, in map_expr_dag
result, = map_expr_dags(function, [expression], compress=compress)
File "/usr/lib/python2.7/dist-packages/ufl/corealg/map_dag.py", line 84, in map_expr_dags
r = handlersv._ufl_typecode_
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/apply_restrictions.py", line 166, in facet_normal
return self._opposite(o)
File "/usr/lib/python2.7/dist-packages/ufl/algorithms/apply_restrictions.py", line 71, in _opposite
error("Discontinuous type (null) must be restricted." 300._ufl_class_.name)
File "/usr/lib/python2.7/dist-packages/ufl/log.py", line 171, in error
raise self._exception_type(self._format_raw(*message))
UFLException: Discontinuous type FacetNormal must be restricted.
.
*** Where: This error was encountered inside jit.py.
*** Process: 0
*** DOLFIN version: 2016.2.0
*** Git changeset: unknown
*** -------------------------------------------------------------------------
