Related papers: Solution of generalized magnetothermoelastic probl…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
We present a thermodynamically consistent theoretical framework for lyotropic liquid crystals (LCs) based on the GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) formalism. This formalism ensures…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
In this work, we theoretically demonstrate that a strong enhancement of the Magnetocaloric Effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters…
A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a…
We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall…
The current-induced magnetisation dynamics in a ferromagnet at elevated temperatures can be described by the Landau--Lifshitz--Bloch (LLB) equation with spin-torque terms. In this paper, we focus on the regime above the Curie temperature.…
This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank--Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in $d$-dimensional space, $d=2,3$. We split the…
First we present the general equation form of a thermal explosion in a vessel with boundary values, later use central difference method and Newton iteration method to solve the relevant partial differential equations in one-dimensional and…
We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step…
In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Multilayer diffusion problems have found significant important that they arise in many medical, environmental and industrial applications of heat and mass transfer. In this article, we study the solvability of one-dimensional nonhomogeneous…