Spectral Deferred Corrections

The Castro SDC solver couples the hydrodynamics tightly together, iteratively improving the convergence of the solution. This is the basis of the 4th order accurate Castro solver. The algorithm is described in [74].

Note

Here we are referring to the full SDC time integration scheme (castro.time_integration_method = 2), not the simplified-SDC solver.

The options that describe the quadrature and iterations are:

• castro.sdc_order : the desired spatial and temporal order. 2 and 4 are supported.

• castro.sdc_quadrature : the quadrature scheme used for the time-integration. This determines the number and location of the temporal nodes. Supported values are 0 for Gauss-Lobatto and 1 for Radau IIA.

• castro.sdc_extra : the number of extra iterations to take. By default the number of iterations used is equal to the value of sdc_order.

The options that affect the nonlinear solve are:

• sdc_solver : the method we use to do the nonlinear solution of the reaction system. Values are:

  • 1 : pure Newton iteration (we subdivide the time interval if needed to get the Newton method to converge).

  • 2 : use VODE to solve the nonlinear system by expressing it as an ODE system.

  • 3 : use VODE for the first iteration and then Newton for the subsequent iterations.

  The tolerances for both the Newton and VODE solver are controlled by the usual Microphysics parameters: integrator.rtol_spec, integrator.atol_spec, integrator.rtol_enuc, integrator.atol_enuc.

  In all cases, the type of Jacobian (analytic or numerical) is determined by integrator.jacobian.