# Define the OpenMDAO problem and model
prob = om.Problem()
num_dof_density = pde_problem.inputs_dict['density'][
'function'].function_space().dim()
comp = om.IndepVarComp()
comp.add_output(
'density_unfiltered',
shape=num_dof_density,
val=np.ones(num_dof_density),
# val=np.random.random(num_dof_density) * 0.86,
)
prob.model.add_subsystem('indep_var_comp', comp, promotes=['*'])
comp = GeneralFilterComp(density_function_space=density_function_space)
prob.model.add_subsystem('general_filter_comp', comp, promotes=['*'])
group = AtomicsGroup(pde_problem=pde_problem)
prob.model.add_subsystem('atomics_group', group, promotes=['*'])
prob.model.add_design_var('density_unfiltered', upper=1, lower=5e-3)
prob.model.add_objective('compliance')
prob.model.add_constraint('avg_density', upper=0.50)
prob.driver = driver = om.pyOptSparseDriver()
driver.options['optimizer'] = 'SNOPT'
driver.opt_settings['Verify level'] = 0
driver.opt_settings['Major iterations limit'] = 100000
driver.opt_settings['Minor iterations limit'] = 100000