Semi-Implicit SDC Core (semi_implicit_sdc_core)

class pypint.solvers.cores.semi_implicit_sdc_core.SemiImplicitSdcCore

Bases: pypint.solvers.cores.sdc_solver_core.SdcSolverCore

Semi-Implicit SDC Core

run(state, **kwargs)

Semi-Implicit Euler step method.

\[\begin{split}u_{m+1}^{k+1} - \Delta_\tau F_I(t_{m+1}, u_{m+1}^{k+1}) = u_m^{k+1} &+ \Delta_\tau \left( F_I(t_{m+1}, u_{m+1}^k) - F_E(t_m, u_m^{k+1}) + F_E(t_m, u_m^k) \right) \\ &+ \Delta_t I_m^{m+1} \left( F(\vec{u}^k) \right)\end{split}\]

Notes

This step method requires the given problem to provide partial evaluation of the right-hand side.