WIP: General unsteady adjoint weighted integration #3247
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… and its 1st level derived classes. 1) The new advance_postprocessing_timestep takes a vector of std::function as arguments and provides these functions with the right time integration quadrature. 2) advance_postprocessing_timestep manages the time incrementation, retrieval of solutions and meshes.
…for 1st order fixed timestep solvers.
…r adaptive time solver and subclasses.
…rder time solvers.
…tion to adjoints example 7.
1) Provide user access to the last used timestep. Overloaded, since adaptive time solver needs to ask core solver what deltat it used last.
…tep API for postprocessing calculations.
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This PR aims to condense and organize the different integrate_xyz_timestep methods currently present in TimeSolver. The scattered integrate_xyz_timestep implementations will be consolidated into a single advance_postprocessing_timestep method.
TS::integrate_qoi_timestep, integrate_adjoint_sensitivity and integrate_adjoint_refinement_error_estimate will be removed from the library and moved to user/example code. The lambda's to achieve their functionality will be added to relevant adjoint examples.
More details:
In general, to integrate a function f across a time interval [0, T], we have the quadrature:
int_{0}^{T} f(u,z) dt ~ (sum_{i=1}^{N_outer_timesteps} ( sum_{j=1}^{N_inner_steps} w_ij f(u^j,z^j) )