  Real-world structural optimisation problems involve multiple loading
conditions and design constraints, with responses typically depending on states
of discretised governing equations. Generally, one uses gradient-based nested
analysis and design approaches to solve these problems. Herein, solving both
physical and adjoint problems dominates the overall computational effort.
Although not commonly detected, real-world problems can contain linear
dependencies between encountered physical and adjoint loads. Manually keeping
track of such dependencies becomes tedious as design problems become
increasingly involved. To detect and exploit such dependencies, this work
proposes the use of a Linear Dependency Aware Solver (LDAS), which is able to
efficiently detect linear dependencies between all loads to avoid unnecessary
solves entirely and automatically. Illustrative examples are provided that
demonstrate the need and benefits of using an LDAS, including a run-time
experiment.
