Hi everyone
I'm working a spectral problem with the elasticity equations, with a DG method in a mixed formulation, where the stress tensor sigma is an unknown. My domain is the unit square. I need to impose a zero Dirichlet condition in the bottom of the square, and the normal component of sigma equal to zero on the other three sides of the square. My idea is to use the ideas in here.
The following parts of my code shows what i'm doing
degree =2
nn = 32
mesh = UnitSquareMesh(nn, nn)
bdr=MeshFunction("size_t",mesh,1)
bdr.set_all(0)
# ********* Boundary conditions ******* #
class botton(SubDomain):
def inside(self, x, on_boundary):
return near(x[1],0)
botton().mark(bdr, 30)
# discrete spaces for the DG method
V = TensorFunctionSpace(mesh, "DG", degree)
Q = FunctionSpace(mesh, "DG", degree-1)
W = MixedFunctionSpace([V, Q])
# defining the mixed boundary conditiosn on the square
class BoundarySource(Expression):
def __init__(self, mesh):
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 = 0.0
values[0] = g*n[0]
values[1] = g*n[1]
values[2] = g*n[0]
values[3] = g*n[1]
def value_shape(self):
return (2, 2)
G = BoundarySource(mesh)
# Define essential boundary
def boundary(x):
return x[0] < DOLFIN_EPS or x[1] > 1.0 - DOLFIN_EPS or x[0] > 1.0 - DOLFIN_EPS
bcsrest = DirichletBC(W.sub(0), G, boundary)
When i compile my code, my eigenvalues are complex and must be real. So, i think that i'm not impossign correctly the condition $\sigma\cdot n=0$. Any suggestion?
