Related papers: Parametrically Constrained Geometry Relaxations fo…
Structure optimization, which yields the relaxed structure (minimum-energy state), is essential for reliable materials property calculations, yet traditional ab initio approaches such as density-functional theory (DFT) are computationally…
We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
Digital stiffness programmability is fulfilled with a heterogeneous mechanical metamaterial. The prototype consists of an elastomer matrix containing tessellations of diamond shaped cavities selectively confined with semi-rigid plastic beam…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
To efficiently simulate very thin, inextensible materials like cloth or paper, it is tempting to replace force-based thin-plate dynamics with hard isometry constraints. Unfortunately, naive formulations of the constraints induce membrane…
Understanding the applicability and limitations of electronic-structure methods needs careful and efficient comparison with accurate reference data. Knowledge of the quality and errors of electronic-structure calculations is crucial to…
Metamaterial effective parameters may exhibit freedom from typical dispersion constraints. For instance, the emergence of a magnetic response in arrays of split-ring resonators for long wavelengths cannot be attained in a passive continuous…
Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…
This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…
The impressive capabilities of large foundation models come at a cost of substantial computing resources to serve them. Compressing these pre-trained models is of practical interest as it can democratize deploying them to the machine…
This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…