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We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
The automatic shape control of deformable objects is a challenging (and currently hot) manipulation problem due to their high-dimensional geometric features and complex physical properties. In this study, a new methodology to manipulate…
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of…
Experimental analysis of the mechanics of a deformable object, and particularly its stability, requires repetitive testing and, depending on the complexity of the object's shape, a testing setup that can manipulate many degrees of freedom…
We investigate the optimal shapes of the hydrodynamic resistance of a rigid body set in motion in a Stokes flow. In this low Reynolds number regime, the hydrodynamic drag properties of an object are encoded in a finite number of parameters…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
This work deals with the problem of stabilizing a multi-agent rigid formation on a general class of planar curves. Namely, we seek to stabilize an equilateral polygonal formation on closed planar differentiable curves after a path sweep.…
Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…
In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…
In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring convexity constraints. The method utilizes bubble functions as…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In this first one we present the…
We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a channel, which motivated the imposition of a Poiseuille-like…