def A(self):
u = firedrake.TrialFunction(self.target.function_space())
v = firedrake.TestFunction(self.target.function_space())
a = firedrake.inner(u, v)*firedrake.dx
if self.use_slate_for_inverse:
a = firedrake.Tensor(a).inv
A = firedrake.assemble(a, bcs=self.bcs,
form_compiler_parameters=self.form_compiler_parameters)
return A
def V_approx_inv_mass(self, V, DG):
"""
Approximate inverse mass. Computes (cellwise) (V, V)^{-1} (V, DG).
:arg V: a function space
:arg DG: the DG space
:returns: A PETSc Mat mapping from V -> DG.
"""
key = V.dim()
try:
return self._V_approx_inv_mass[key]
except KeyError:
a = firedrake.Tensor(firedrake.inner(firedrake.TestFunction(V),
firedrake.TrialFunction(V))*firedrake.dx)
b = firedrake.Tensor(firedrake.inner(firedrake.TestFunction(V),
firedrake.TrialFunction(DG))*firedrake.dx)
M = firedrake.assemble(a.inv * b)
M.force_evaluation()
return self._V_approx_inv_mass.setdefault(key, M.petscmat)
def DG_inv_mass(self, DG):
"""
Inverse DG mass matrix
:arg DG: the DG space
:returns: A PETSc Mat.
"""
key = DG.dim()
try:
return self._DG_inv_mass[key]
except KeyError:
M = firedrake.assemble(firedrake.Tensor(firedrake.inner(firedrake.TestFunction(DG),
firedrake.TrialFunction(DG))*firedrake.dx).inv)
M.force_evaluation()
return self._DG_inv_mass.setdefault(key, M.petscmat)
def DG_inv_mass(self, DG):
"""
Inverse DG mass matrix
:arg DG: the DG space
:returns: A PETSc Mat.
"""
cache = self.caches[DG.ufl_element()]
key = DG.dim()
try:
return cache._DG_inv_mass[key]
except KeyError:
M = firedrake.assemble(firedrake.Tensor(firedrake.inner(firedrake.TrialFunction(DG),
firedrake.TestFunction(DG))*firedrake.dx).inv)
return cache._DG_inv_mass.setdefault(key, M.petscmat)
if it % freq_res == 0 or t == sim_time:
if verbose:
contours = fd.tripcolor(c0)
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.colorbar(contours)
plt.show()
# Computed flux, scalar, and trace
c_h, q_h, lamb = w.split()
c_h.rename("c_h")
c_h.assign(c0)
q_h.rename("q_h")
# # scalar post-process
# ch_star, lamb_pp = ch_pp.split()
# ch_star.rename("ch_pp")
A = fd.Tensor(a_pp)
b = fd.Tensor(L_pp)
ch_star = fd.assemble((A.inv * b).blocks[0])
ch_star.rename("ch_star")
# print results
outfile.write(c_h, q_h, ch_star, time=t)
print('-- write results @ t= {}'.format(t))
print(f'DOF = {W.dim()}')
print(f'DOF = {W.sub(2).dim()}')
print('* normal termination.')
