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We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…
Given a convex set $\Omega$ of $\mathbb{R}^n$, we consider the shape optimization problem of finding a convex subset $\omega\subset \Omega$, of a given measure, minimizing the $p$-distance functional $$\mathcal{J}_p(\omega) :=…
Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this…
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
Non-imaging optical lenses can shape the light intensity from incoherent sources to a desired target intensity profile, which is important for applications in lighting, solar light concentration, and optical beam shaping. Their surface…
In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…
Amorphous materials of homogeneous structures usually suffer from nonuniform deformation under shear, which can develop into shear localization and eventually destructive shear band. One approach to tackle this issue is to introduce an…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of…