An Adaptive Eigenfunction Basis Strategy to Reduce Design Dimension in Topology Optimization

The concept of adaptive eigenspace basis (AEB) has recently proved effective for solving medium imaging problems. In this article, we present an AEB strategy design parameterization in topology optimization (TO) We seek the density field as a linear combination eigenfunctions, computed elliptic operator defined over structural domain, and solve associated eigenfunction coefficients. Restriction to truncated drastically reduces dimension imposes implicit regularization upon solution, removing need auxiliary filtering operations design-variable bound constraints. furthermore develop adaptation scheme inherent AEB, which iteratively recomputes conform evolving field, enabling further reduction acceleration process. known aptitude adapted eigenfunctions approximate piecewise constant fields is especially useful TO relevant subspaces can be given low-dimensional representations. propose criteria selection demonstrate use function means length scale control. compare performance against conventional implementations problems static linear-elasticity, showing comparable solutions, computational cost benefits, consistent reduction.