Related papers: Reduced-order modeling for second-order computatio…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…
This paper introduces an efficient second-order method for solving the elastic net problem. Its key innovation is a computationally efficient technique for injecting curvature information in the optimization process which admits a strong…
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…
The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…
In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…
In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
Flexoelectricity shows promising applications for self-powered devices with its increased power density. This paper presents a second-order computational homogenization strategy for flexoelectric composite. The macro-micro scale transition,…
The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…