Related papers: Multiscale Finite Element Modeling of Nonlinear Ma…
When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the…
Despite of the topical engineering need and all scientific investments, the mathematical formulation of modeling elastic deformations in magnetic systems is not yet fully established. Often, especially in electrical engineering…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
Composite materials consisting of coupled magnetic and ferroelectric layers hold the promise for new emergent properties such as controlling magnetism with electric fields. Obviously, the interfacial coupling mechanism plays a crucial role…
It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result…
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…
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…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
An effective model is identified for thin perfectly plastic plates whose microstructure consists of the periodic assembling of two elastoplastic phases, as the periodicity parameter converges to zero. Assuming that the thickness of the…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse…
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…
Multiperforated plates exhibit high gradients and a loss of regularity concentrated in a boundary layer for which a direct numerical simulation becomes very expensive. For elliptic equations the solution at some distance of the boundary is…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and…
The non-linear induction problem in ferromagnetic media is solved using the fixed-point iteration method, where the linearized problem at each iteration is treated by means of a modal approach. The proposed approach does not require meshing…
In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…