English
Related papers

Related papers: Multiscale Finite Element Modeling of Nonlinear Ma…

200 papers

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…

Computational Physics · Physics 2021-04-07 Fanxiang Xu , Hadi Hajibeygi , Lambertus J. Sluys

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

Numerical Analysis · Mathematics 2025-12-16 Leonardo A. Poveda , Shubin Fu , Guanglian Li , Eric Chung

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

Numerical Analysis · Mathematics 2018-05-15 Lise-Marie Imbert-Gerard , Felipe Vico , Leslie Greengard , Miguel Ferrando

The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…

Numerical Analysis · Mathematics 2023-08-24 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

Numerical Analysis · Mathematics 2018-09-21 Nicola A. Nodargi

A macro-constitutive model for the deformation response of periodic rotating bistable auxetic surfaces is developed. Focus is placed on isotropic surfaces made of bistable hexagonal cells composed of six triangular units with two stable…

Applied Physics · Physics 2025-12-01 Emmanuel Sansusthy Tardio , Tian Chen , Theocharis Baxevanis

We prove the two-scale transformation method which allows rigorous homogenisation of problems defined on locally periodic domains by transformation on periodic domains. The idea to consider periodic substitute problems was originally…

Analysis of PDEs · Mathematics 2021-06-28 David Wiedemann

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating…

Superconductivity · Physics 2018-08-01 R. Prozorov , V. G. Kogan

We consider an advection-diffusion equation that is advection-dominated and posed on a perforated domain. On the boundary of the perforations, we set either homogeneous Dirichlet or homogeneous Neumann conditions. The purpose of this work…

Numerical Analysis · Mathematics 2017-10-26 Claude Le Bris , Frederic Legoll , Francois Madiot

The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to…

Materials Science · Physics 2024-08-12 Kamil Bieniek , Michał Majewski , Paweł Hołobut , Katarzyna Kowalczyk-Gajewska

In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…

Numerical Analysis · Mathematics 2017-07-27 Eric T. Chung , Yalchin Efendiev , Bangti Jin , Wing Tat Leung , Maria Vasilyeva

We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…

Numerical Analysis · Mathematics 2026-02-23 Tokuhiro Eto , Harald Garcke , Robert Nürnberg

This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…

Computational Engineering, Finance, and Science · Computer Science 2019-01-04 Annalisa Buffa , Jacopo Corno , Carlo de Falco , Sebastian Schöps , Rafael Vázquez

The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…

The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…

Numerical Analysis · Mathematics 2018-05-02 August Johansson , Mats G. Larson , Anders Logg

In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of…

Numerical Analysis · Mathematics 2019-08-09 Francesca Fantoni , Andrea Bacigalupo , Marco Paggi , Josè Reinoso

In this paper we study the homogenization of a linear elastodynamics system in an elastic body with soft inclusions, which is embedded in a highly oscillating magnetic field. We show two limit behaviors according to the magnetic field. On…

Analysis of PDEs · Mathematics 2019-10-04 Marc Briane , Juan Casado-Diaz

We develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. By upscaling the quasi-static Maxwell…

Analysis of PDEs · Mathematics 2020-12-02 Grigor Nika , Bogdan Vernescu

Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule…

Soft Condensed Matter · Physics 2014-10-22 Mihir R. Khadilkar , Fernando A. Escobedo

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

Numerical Analysis · Mathematics 2017-12-08 Brendan Keith , Socratis Petrides , Federico Fuentes , Leszek Demkowicz