  Efficient topology optimization based on the adaptive auxiliary reduced model
reanalysis (AARMR) is proposed to improve computational efficiency and scale.
In this method, a projection auxiliary reduced model (PARM) is integrated into
the combined approximation reduced model (CARM) to reduce the dimension of the
model in different aspects. First, the CARM restricts the solution space to
avoid large matrix factorization. Second, the PARM is proposed to construct the
CARM dynamically to save computational cost. Furthermore, the multi-grid
conjugate gradient method is suggested to update PARM adaptively. Finally,
several classic numerical examples are tested to show that the proposed method
not only significantly improves computational efficiency, but also can solve
large-scale problems that are difficult to solve by direct solvers due to the
memory limitations.
