Convert ARKode interfaces to conform to our callback policy.

[bangerth]

Like in #15178 and #15186. Implements the resolution in #15112, #15146.

I have not actually managed to write a test case where ARKode recovers after a recoverable error, but it correctly reports that it has received a recoverable error code. The new test checks this.

[drwells]

I'm getting caught up on the new convention for exceptions - I like it.

Things are failing to compile because of some ODE routines with attached linear solvers. Something like this compiles but doesn't handle the exception correctly:

    template <typename VectorType>
    int
    arkode_linsol_solve(SUNLinearSolver LS,
                        SUNMatrix /*ignored*/,
                        N_Vector x,
                        N_Vector b,
                        realtype tol)
    {
      auto content = access_content<VectorType>(LS);

      auto *src_b = unwrap_nvector_const<VectorType>(b);
      auto *dst_x = unwrap_nvector<VectorType>(x);

      SundialsOperator<VectorType> op(content->A_data,
                                      content->a_times_fn
#  if DEAL_II_SUNDIALS_VERSION_GTE(6, 0, 0)
                                      ,
                                      content->linsol_ctx
#  endif
      );

      SundialsPreconditioner<VectorType> preconditioner(
        content->P_data,
        content->preconditioner_solve,
#  if DEAL_II_SUNDIALS_VERSION_GTE(6, 0, 0)
        content->linsol_ctx,
#  endif
        tol);

      try
        {
          content->lsolve(op, preconditioner, *dst_x, *src_b, tol);
          return 0;
        }
      catch (RecoverableUserCallbackError &)
        {
          return SUNLS_PACKAGE_FAIL_REC;
        }
      catch (...)
        {
          return SUNLS_PACKAGE_FAIL_UNREC;
        }
    }

[bangerth]

I don't know how I missed that. I'll get to it on Monday (travel and family stuff before then).

[bangerth]

@drwells I got it done today after all.