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A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek

We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…

Dynamical Systems · Mathematics 2023-07-21 Thomas Thurnher , George Haller , Shobhit Jain

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…

Numerical Analysis · Computer Science 2017-06-06 T. P. Fries

Forced response curves (FRCs) of nonlinear systems can exhibit complex behaviors, including hardening/softening behavior and bifurcations. Although topology optimization holds great potential for tuning these nonlinear dynamic responses,…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Hongming Liang , Matteo Pozzi , Jacopo Marconi , Shobhit Jain , Mingwu Li

In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy…

Machine Learning · Computer Science 2024-02-28 Bilal Mufti , Christian Perron , Dimitri N. Mavris

This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we…

Numerical Analysis · Mathematics 2024-07-02 Jesus-Pablo Toledo-Zucco , Denis Matignon , Charles Poussot-Vassal , Yann Le Gorrec

The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…

Numerical Analysis · Mathematics 2026-03-19 André de Figueiredo Stabile , Aurélien Grolet , Alessandra Vizzaccaro , Cyril Touzé

We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…

Dynamical Systems · Mathematics 2023-02-07 Dan Wilson , Kai Sun

The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

Numerical Analysis · Mathematics 2024-12-03 Ivan Zanardi , Alejandro N. Diaz , Seung Whan Chung , Marco Panesi , Youngsoo Choi

This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…

Numerical Analysis · Mathematics 2021-10-01 Marzieh Alireza Mirhoseini , Matthew J. Zahr

Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite…

Soft Condensed Matter · Physics 2021-07-01 Dong Yan , Arefeh Abbasi , Pedro M. Reis

Model order reduction encompasses mathematical techniques aimed at reducing the complexity of mathematical models in simulations while retaining the essential characteristics and behaviors of the original model. This is particularly useful…

Quantum Physics · Physics 2026-04-21 Wentao Fan , Hakan E. Türeci

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

Astrophysics · Physics 2009-10-30 David L. Meier

This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…

Numerical Analysis · Mathematics 2026-05-13 Ziqin Zhou

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…

Numerical Analysis · Mathematics 2021-06-07 Kevin Tolle , Nicole Marheineke

Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of high-dimensional, parametric systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs…

Machine Learning · Computer Science 2026-03-17 Nicolò Botteghi , Silke Glas , Christoph Brune

Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…

Dynamical Systems · Mathematics 2025-07-09 Peter Benner , Yevgeniya Filanova , Igor Pontes Duff , Jens Saak

Given a semi-Riemannian manifold $(M,\langle \cdot,\cdot\rangle_g),$ we use the transnormal functions defined on $M$ to reduce fully nonlinear first order PDEs of the form \[ F(x,u,\langle \nabla_g u, \nabla_g u \rangle_g) = 0,\qquad…

Analysis of PDEs · Mathematics 2024-07-03 Juan Carlos Fernández , Eddaly Guerra-Velasco , Oscar Palmas , Boris A. Percino-Figueroa

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations,…

Optimization and Control · Mathematics 2015-12-09 Lorenzo Fagiano , Rudolf Gati

This paper presents a parametric Model Order Reduction (MOR) method for weakly coupled thermo-mechanical Finite Element (FE) models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal…

Numerical Analysis · Mathematics 2020-09-30 Pablo Hernández-Becerro , Daniel Spescha , Konrad Wegener