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We previously introduced a preconditioner that has proven effective for h p -FEM discretizations of various challenging elliptic and hyperbolic problems. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precision, by Hierarchically-Semi-Separable matrices. The preconditioner is built as an approximate L D M t factorization through a divide-and-conquer approach. This implies an enhanced flexibility which allows to handle unstructured geometric meshes, anisotropies, and discontinuities. We build on our previous numerical experiments and develop a preconditioner-update strategy that allows us to handle matrix sequences arising from problems with slowly-varying coefficients. We investigate the performance of the preconditioner along with the update strategy in context of topology optimization of an acoustic cavity.

A new method for dose regularization in optimization-based proximity-effect-correction is proposed. In contrast to the commonly adopted approach of adding penalty terms to the objective function, a modified scheme is demonstrated where dose regularization is achieved via filtering and projection techniques. The resulting dose patterns are simple and two-toned, and can thus readily be applied in production. Furthermore, existing extensions developed in the context of topology optimization that build on top of the filtering framework, such as robust optimization and strict length scale control, can be adopted directly. The validity of the scheme is assessed in experiments, where the resolvable feature size of the considered 30 kV electron-beam lithography system is decreased from around 100 nm to a few tens of nm. A Python implementation of the scheme is made freely available.

This paper proposes a topology optimization based approach for designing meta materials exhibiting a desired negative refraction with high transmission at a given angle of incidence and frequency. The approach considers a finite slab of meta material consisting of axis-symmetric designable unit cells subjected to an exterior field. The unit cell is designed to achieve the desired properties based on tailoring the response of the meta material slab under the exterior field. The approach is directly applicable to physical problems modeled by the Helmholtz equation, such as acoustic, elastic and electromagnetic wave problems. Acoustic meta materials with unit cell size on the order of half the wave length are considered as examples. Optimized designs are presented and their performance under varying frequency and angle of incidence is investigated.