Efficient multi-partition topology optimization

In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees freedom such model can be partitioned in free and prescribed sets to define boundary conditions. A multi-partition problem involves multiple partitions same discretization, corresponding different loading scenarios. As result, solving problems factorization/preconditionings system matrix, requiring high computational effort. this paper, novel method proposed efficiently calculate responses accompanying design sensitivities using static condensation for use gradient-based optimization. main class that benefits from optimization small-displacement multi-input-multi-output compliant mechanisms. However, applicable any linear problem. We present its formulation an algorithmic complexity analysis estimate advantages both direct iterative solution methods solve equations, verified numerical experiments. It demonstrated substantial gains are achievable large-scale problems. This especially true with small set number fully describes performance structure large similarities between partitions. major contribution gain lack adjoint analyses required obtain measure.