Related papers: Choose interelement coupling to preserve self-adjo…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to…
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
Accurately predicting friction in sliding interfaces that contain third body wear particles is critical for engineering applications such as sliding movement in pistons, bearings, or metal forming. We present a hierarchical multiscale…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…
A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…
In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…