13 problems

In topology optimization, each discrete element is assigned a material-presence decision, so the latent representation may be modeled using either a Bernoulli distribution, taking…

Let a topology optimization problem have a specified baseline method, and let neural topology optimization reparameterize the problem using a neural architecture. Neural architectu…

An optimized acoustic low-pass filter design has a topology formed by structures clustered inside the design domain, with performance measured by how well its transmission $S(f)$ f…

Let $L_c$ be the macroscale characteristic length and let $alpha_\text{max}$ denote the maximum Brinkman penalization value. The numerical study considers their relation through a…

The Brinkman penalization term is studied through the maximum velocity in solid regions and state-variable errors in fluid regions, with $alpha_\text{max}$ denoting the maximum pen…

Constituent-dependence conjecture. The main reason behind the issue is that the forces experienced by the structure are not only related to $Re$ but rather to its constituents, nam…

Efficiency-difference conjecture. The difference is due to the design domain being more compact rather than elongated, the low Reynolds number, and the dependence on the initial de…

The mesh deformation models use layered selective stiffening: consecutive layers of elements adjacent to the fluid-structure interface are stiffened by multiplying the elastic modu…

Let a density filter be represented by an affine mapping with weighting function $w_e(\mathbf{x}_i)$, and let a design point specify the element design variables. Filtering-induced…

Consider the interpolation used in the three-dimensional compliance topology-optimization problem, and suppose that it has nonzero derivative values at the void value $\nu=0$. RAMP…

In the three-dimensional compliance problem, let $D\theta$ denote the derivative used by the $\mathbb{R}^n$ algorithm and let $\nabla\theta=\mathbf{M}^{-1}D\theta$ denote the gradi…

A three-dimensional photonic crystal is a periodic structure whose electromagnetic spectrum may contain an omnidirectional band gap, meaning a frequency interval with no propagatin…

In topology optimization, let the design found using an adaptively refined mesh be compared with the solution obtained on a uniform fine mesh, and let compliance measure the object…