def identity_test(n, shape, subd=I_curve):
'''Averaging over indep coords of f'''
true = df.Expression('x[2]*x[2]', degree=2)
mesh = df.UnitCubeMesh(n, n, n)
V = df.FunctionSpace(mesh, 'CG', 2)
v = df.interpolate(true, V)
f = df.MeshFunction('size_t', mesh, 1, 0)
subd.mark(f, 1)
line_mesh = EmbeddedMesh(f, 1)
Q = average_space(V, line_mesh)
q = df.Function(Q)
Pi = avg_mat(V, Q, line_mesh, {'shape': shape})
Pi.mult(v.vector(), q.vector())
q0 = true
# Error
L = df.inner(q0 - q, q0 - q) * df.dx
e = q.vector().copy()
e.axpy(-1, df.interpolate(q0, Q).vector())
return df.sqrt(abs(df.assemble(L)))
def square_test(n, subd=I_curve):
'''Averaging over indep coords of f'''
size = 0.1
shape = Square(P=lambda x0: x0 - np.array(
[size + size * x0[2], size + size * x0[2], 0]),
degree=10)
foo = df.Expression('x[2]*((x[0]-0.5)*(x[0]-0.5) + (x[1]-0.5)*(x[1]-0.5))',
degree=3)
mesh = df.UnitCubeMesh(n, n, n)
V = df.FunctionSpace(mesh, 'CG', 3)
v = df.interpolate(foo, V)
f = df.MeshFunction('size_t', mesh, 1, 0)
subd.mark(f, 1)
true = df.Expression('x[2]*2./3*(size+size*x[2])*(size+size*x[2])',
degree=4,
size=size)
line_mesh = EmbeddedMesh(f, 1)
Q = average_space(V, line_mesh)
q = df.Function(Q)
Pi = avg_mat(V, Q, line_mesh, {'shape': shape})
Pi.mult(v.vector(), q.vector())
q0 = true
# Error
L = df.inner(q0 - q, q0 - q) * df.dx
e = q.vector().copy()
e.axpy(-1, df.interpolate(q0, Q).vector())
return df.sqrt(abs(df.assemble(L)))
def disk_test(n, subd=I_curve):
'''Averaging over indep coords of f'''
shape = Disk(radius=lambda x0: 0.1 + 0.0 * x0[2] / 2, degree=10)
foo = df.Expression('x[2]*((x[0]-0.5)*(x[0]-0.5) + (x[1]-0.5)*(x[1]-0.5))',
degree=3)
mesh = df.UnitCubeMesh(n, n, n)
V = df.FunctionSpace(mesh, 'CG', 3)
v = df.interpolate(foo, V)
f = df.MeshFunction('size_t', mesh, 1, 0)
subd.mark(f, 1)
true = df.Expression('x[2]*(0.1+0.0*x[2]/2)*(0.1+0.0*x[2]/2)/2', degree=4)
line_mesh = EmbeddedMesh(f, 1)
Q = average_space(V, line_mesh)
q = df.Function(Q)
Pi = avg_mat(V, Q, line_mesh, {'shape': shape})
Pi.mult(v.vector(), q.vector())
q0 = true
# Error
L = df.inner(q0 - q, q0 - q) * df.dx
e = q.vector().copy()
e.axpy(-1, df.interpolate(q0, Q).vector())
return df.sqrt(abs(df.assemble(L)))
def sanity_test(n, subd, shape):
'''Constant is preserved'''
mesh = df.UnitCubeMesh(n, n, n)
V = df.FunctionSpace(mesh, 'CG', 2)
v = df.interpolate(df.Constant(1), V)
f = df.MeshFunction('size_t', mesh, 1, 0)
subd.mark(f, 1)
line_mesh = EmbeddedMesh(f, 1)
Q = average_space(V, line_mesh)
q = df.Function(Q)
Pi = avg_mat(V, Q, line_mesh, {'shape': shape})
Pi.mult(v.vector(), q.vector())
q0 = df.Constant(1)
# Error
L = df.inner(q0 - q, q0 - q) * df.dx
e = q.vector().copy()
e.axpy(-1, df.interpolate(q0, Q).vector())
return df.sqrt(abs(df.assemble(L)))
def reduction_matrix(self, V, TV, reduced_mesh, data):
'''Algebraic representation of the reduction'''
return avg_mat(V, TV, reduced_mesh, data)
def reduction_matrix(self, V, TV, reduced_mesh, data):
'''Algebraic representation of the reduction'''
return avg_mat(V, TV, reduced_mesh, data)