27 citations · 42 across the 9 of their papers we have counts for
9 papers
Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches
A. J. Roberts, Thien Tran-Duc, J. E. Bunder +1
Modern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and a…
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…
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…