Deterministic local sensitivity analysis of augmented systems - I: Theory

This work provides the theoretical foundation for the modular implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for large-scale simulation systems. The implementation of the ASAP commences with a selected code module and then proceeds by augmenting the size of the adjoint sensitivity system, module by module, until the entire system is completed. Notably, the adjoint sensitivity system for the augmented system can often be solved by using the same numerical methods used for solving the original, nonaugmented adjoint system, particularly when the matrix representation of the adjoint operator for the augmented system can be inverted by partitioning.