OpenMDAO Solvers

Every OpenMDAO solver is either a linear solver, inheriting from the LinearSolver class, or a nonlinear solver, inheriting from the NonlinearSolver class. A solver can be either monolithic or recursive in behavior. Monolithic solvers treat the associated system as a single block. Recursive solvers, as the name suggests, recurse down through their system hierarchy asking each sub-system to operate on itself.

The following is a list of available OpenMDAO solvers separated by type:


  • Monolithic

    • DirectSolver

    • PETScKrylov

    • ScipyKrylov

    • LinearUserDefined

  • Recursive

    • LinearBlockGS

    • LinearBlockJac

    • LinearRunOnce


  • Monolithic

    • Newton (options[‘solve_subsystems’] = False)

    • Broyden (options[‘solve_subsystems’] = False)

    • BoundsEnforceLS (options[‘solve_subsystems’] = False)

    • ArmijoGoldsteinLS (options[‘solve_subsystems’] = False)

  • Recursive

    • NonlinearBlockGS

    • NonlinearBlockJac

    • NonlinearRunOnce

    • Newton (options[‘solve_subsystems’] = True)

    • BoundsEnforceLS (options[‘solve_subsystems’] = True)

    • ArmijoGoldsteinLS (options[‘solve_subsystems’] = True)

Below is a figure depicting how a model containing both recursive and monolithic solvers would function. The numbered circles represent the order of calls to subsystems in the model.

Solver execution example

Writing Custom Solvers

If your solver will be linear, you’ll need to inherit from LinearSolver, or perhaps from BlockLinearSolver. If your solver will be nonlinear, inherit from NonlinearSolver. If your solver will be monolithic, you’ll most likely override the entire solve function, and if your solver will be recursive, you may be able to get away with only overriding a couple of lower level functions like _iter_initialize and _single_iteration. The best thing to do is to start with the OpenMDAO solver that is most similar to what you want to do and go from there.

Some solvers, especially recursive ones, can have confusing calling structures, because it’s not always obvious which class is the owner of a given method. A command line tool, openmdao call_tree was developed to help clarify what the actual call structure is. So, for example, if we wanted to see the call structure of NonlinearBlockGS.solve, we could do the following:

openmdao call_tree openmdao.api.NonlinearBlockGS.solve

The output above shows that NonlinearBlockGS does not override the solve method, but instead overrides some lower level methods like _iter_initialize, _run_apply, and _single_iteration and relies on the Solver._solve method to provide the main skeleton for the entire solve including the iteration loop.