DirectSolver

DirectSolver is a linear solver that assembles the system Jacobian and solves the linear system with LU factorization and back substitution. It can handle any system topology. Since it assembles a global Jacobian for all of its subsystems, any linear solver that is assigned in any of its subsystems does not participate in this calculation (though they may be used in other ways such as in subsystem Newton solves.)

Here we calculate the total derivatives of the Sellar system objective with respect to the design variable ‘z’.

SellarDerivatives class definition

class SellarDerivatives(om.Group):
    """
    Group containing the Sellar MDA. This version uses the disciplines with derivatives.
    """

    def setup(self):
        self.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2'])
        self.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2'])

        self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', obj=0.0,
                                                  x=0.0, z=np.array([0.0, 0.0]), y1=0.0, y2=0.0),
                           promotes=['obj', 'x', 'z', 'y1', 'y2'])

        self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1', con1=0.0, y1=0.0),
                           promotes=['con1', 'y1'])
        self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0', con2=0.0, y2=0.0),
                           promotes=['con2', 'y2'])

        self.set_input_defaults('x', 1.0)
        self.set_input_defaults('z', np.array([5.0, 2.0]))

import openmdao.api as om
from openmdao.test_suite.components.sellar_feature import SellarDerivatives

prob = om.Problem()
model = prob.model = SellarDerivatives()

model.nonlinear_solver=om.NonlinearBlockGS()
model.linear_solver = om.DirectSolver()

prob.setup()
prob.run_model()

wrt = ['z']
of = ['obj']

J = prob.compute_totals(of=of, wrt=wrt, return_format='flat_dict')
print(J['obj', 'z'][0][0])
print(J['obj', 'z'][0][1])

NL: NLBGS Converged in 8 iterations
9.610010556989952
1.7844853356313655

DirectSolver Options

Option	Default	Acceptable Values	Acceptable Types	Description
assemble_jac	True	[True, False]	['bool']	Activates use of assembled jacobian by this solver.
err_on_singular	True	[True, False]	['bool']	Raise an error if LU decomposition is singular.
iprint	1	N/A	['int']	whether to print output

DirectSolver Constructor

The call signature for the DirectSolver constructor is:

DirectSolver.__init__(**kwargs)

Initialize all attributes.