Problem

Note

This section is under construction.

Problem

aim to solve one step of : min F s.t. C <= 0

proceedure sensitivity (both F and C)

Contains:
current design (design x)
Objective - (object) general
    - determine objective function value (function) F
    - Compute dFdx

instantiated from objective:
        easy_one - (derived from objective)
            - determine objective function value (function) F
            - Compute dFdx (from design variable)
            eg, volume constraints

        fluid/adjoint - (derived from objective)
        contains:
        fluid
            - init: compute objective
        adjoint
            - init: adjoint forcing

        proceedures
            - determine objective function value (function) F
            - Compute dFdx
                * determine adjoint forcing (source term)
                * compute sensitivity (proceedure) 

We also need something similar for constraints

objective F
constraints C[:]


Should be able to:
compute F
compute C

compute dF/dx
compute dC[i]/dx


"find min F s.t. ..."





type(case_t) :: C
type(adjoint_obj) :: adj

!
call init_problem(P)
!
            call user_setup(C%usr)
            call neko_init(C)


            call init_problem_from_json(P)
                ! init design
                ! init F
                        call adj%init(C)
                ! init C
                ! loop all constraints
                    know C[i]

! compute F and dF/Dx 
! compute C[i] and dC[i]/dx
!------------------------
call solve()
            "steady"
            call neko_solve(C)
            call solve_adjoint(adj)
            call sensitivity
            or 
            something else....
!----------------------

call neko_finalize(C)

call mma(P)