5 citations · 21 across the 14 of their papers we have counts for
14 papers
Efficient computational homogenisation of 2D beams of heterogeneous elasticity using the patch scheme
Thien Tran-Duc, J. E. Bunder, A. J. Roberts
Modern 'smart' materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science.…
Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves
J. Divahar, A. J. Roberts, Trent W. Mattner +2
Many multiscale wave systems exhibit macroscale emergent behaviour, for example, the fluid dynamics of floods and tsunamis. Resolving a large range of spatial scales typically requ…
Staggered grids for multidimensional multiscale modelling
J. Divahar, A. J. Roberts, Trent W. Mattner +2
Numerical schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence, numerical simulation…
Adaptively detect and accurately resolve macro-scale shocks in an efficient Equation-Free multiscale simulation
John Maclean, J. E. Bunder, I. G. Kevrekidis +1
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dyn…
Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling
J. E. Bunder, I. G. Kevrekidis, A. J. Roberts
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale sys…
Lyapunov exponents of the Kuramoto-Sivashinsky PDE
Russell A. Edson, J. E. Bunder, Trent W. Mattner +1
The Kuramoto-Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation pa…
Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains
A. J. Roberts, J. E. Bunder
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the…
Boundary conditions for macroscale waves in an elastic system with microscale heterogeneity
Chen Chen, A. J. Roberts, J. E. Bunder
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not syste…
Macroscale boundary conditions for a non-linear heat exchanger
Chen Chen, A. J. Roberts, J. E. Bunder
Multiscale modelling methodologies build macroscale models of materials with complicated fine microscale structure. We propose a methodology to derive boundary conditions for the m…
Accuracy of patch dynamics with mesoscale temporal coupling for efficient exascale simulation
J. E. Bunder, A. J. Roberts, I. G. Kevrekidis
Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor i…
Better buffers for patches in macroscale simulation of systems with microscale randomness
J. E. Bunder, A. J. Roberts, I. G. Kevrekidis
We consider one dimensional lattice diffusion model on a microscale grid with many discrete diffusivity values which repeat periodicially. Computer algebra explores how the dynamic…
Accurate macroscale modelling of spatial dynamics in multiple dimensions
A. J. Roberts, Tony MacKenzie, J. E. Bunder
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular…
Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions
Tony MacKenzie, A. J. Roberts
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. Here we explore the methodology applied to the gap-too…
Higher order accuracy in the gap-tooth scheme for large-scale solutions using microscopic simulators
A. J. Roberts, I. G. Kevrekidis
We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dyn…