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On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics
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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.
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