Related papers: Parametric Topology Optimization with Multi-Resolu…
Black-box optimization is increasingly used in engineering design problems where simulation-based evaluations are costly and gradients are unavailable. In this context, the optimization community has largely analyzed algorithm performance…
We provide a compact 200 line MATLAB code demonstrating how topology optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as…
The authors have shown in previous contributions that reduced order modeling with optimal cubature applied to finite element square (FE2) techniques results in a reliable and affordable multiscale approach, the HPR-FE2 technique. Such…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be…
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…
General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…
Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…