On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics

A modified Adjoint method is presented in which computation can be distributed to 2d+2 processors where d is the number of degrees of freedom of the multibody system and the Adjoint backward initial value problem (IVP) is replaced by a boundary value problem (BVP) which is solved through a backward multiple shooting algorithm. In the equivalent BVP formulation each time-step is solved in the backward direction but time-steps advance in the forward direction. As a result the memory load for storing generalized coordinates during integration of the DAE of motion is minimized. The specific objectives are (...) to develop a new method called the Piecewise Adjoint method that (1) requires the integration of a number of DAE that does not depend on the number of design parameters; (2) has a parallel computational structure; (3) progresses forward in time; and (4) minimizes the memory load required by the backward integration of the Adjoint DAE.