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We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…

Computational Engineering, Finance, and Science · Computer Science 2018-09-25 Mickaël Abbas , Alexandre Ern , Nicolas Pignet

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…

Numerical Analysis · Mathematics 2025-07-09 Yulei Liao , Pingbing Ming

We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector,…

Numerical Analysis · Mathematics 2018-04-09 Axel Målqvist , Tony Stillfjord

Leveraging strong optoelectronic responses to external stimuli, such as temperature and electric fields, is central to the development of advanced photonic technologies, including adaptive photodetectors and reconfigurable photovoltaic…

Materials Science · Physics 2026-02-25 Pol Benítez , Cibrán López , Edgardo Saucedo , Claudio Cazorla

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…

Numerical Analysis · Mathematics 2023-08-14 Jiale Linghu , Hao Dong , Junzhi Cui , Yufeng Nie

In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…

Numerical Analysis · Mathematics 2023-09-26 Gouranga Mallik , Thirupathi Gudi

We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Such result is new even for linear problems. Here we construct…

Analysis of PDEs · Mathematics 2019-12-04 Sunghan Kim , Ki-Ahm Lee

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

Mathematical Physics · Physics 2009-11-07 Axel Pelster , Hagen Kleinert , Michael Schanz

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…

Pattern Formation and Solitons · Physics 2007-05-23 Winfried Lohmiller , Jean-Jacques E. Slotine

In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…

Numerical Analysis · Mathematics 2026-01-29 Alina Chertock , Qingcheng Fu , Alexander Kurganov , Lorenzo Micalizzi

The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides the promise of accuracy…

Materials Science · Physics 2024-04-05 Shaun R. Cooke , Chadwick W. Sinclair , Daan M. Maijer

Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we…

Fluid Dynamics · Physics 2022-11-10 Andrea Nóvoa , Luca Magri

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

Numerical Analysis · Mathematics 2021-09-22 Alessandra Vizzaccaro , Andrea Opreni , Loïc Salles , Attilio Frangi , Cyril Touzé

Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic…

Computational Engineering, Finance, and Science · Computer Science 2017-07-17 Charilaos Mylonas , Valentin Bemetz , Eleni Chatzi

In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…

Numerical Analysis · Mathematics 2026-05-12 Shan Zhang , Yajun Wang , Xiaofei Guan

We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…

Numerical Analysis · Mathematics 2015-05-01 Axel Målqvist , Anna Persson

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…

Numerical Analysis · Mathematics 2020-03-17 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

An extension of the multi-level hp Finite Cell Method is proposed for the simulation of thermoviscoplastic problems with temperature-dependent material behavior. The approach combines hierarchical adaptive refinement with a non-negative…

Numerical Analysis · Mathematics 2026-04-20 Jan Niklas Schmäke , Oliver Wege , Martin Ruess

The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…

Numerical Analysis · Mathematics 2024-08-23 Herbert Egger , Felix Engertsberger , Bogdan Radu

A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure…

Materials Science · Physics 2020-10-20 Nathan Perchikov , Jacob Aboudi