GENERALIZED ADJOINT FOR PHYSICAL PROCESSES WITH PARAMETERIZED DISCONTINUITIES - PART-V - COARSE-GRAIN ADJOINT AND PROBLEMS IN GRADIENT CHECK

When on/off switches are triggered at discrete time levels by a thresh old condition in a traditionally discretized model, the model solution is not continuously dependent on the initial state and this causes pr oblems in tangent linearization and adjoint computations. It is shown in this paper that the problems can be avoided by introducing coarse-g rain tangent linearization and adjoint without modifying the tradition al discretization, although the coarse-grain gradient check can be per formed only for finite perturbations.