61 citations · 202 across the 47 of their papers we have counts for
17 papers · 1 filter
Learning high-order spatial discretisations of PDEs with symmetry-preserving iterative algorithms
J. E. Bunder, A. J. Roberts
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 as…
Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion PDE
A. J. Roberts
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…
Multiscale modelling of microscale heterogeneous systems: analysis supports systematic and efficient macroscale modelling and simulation
A. J. Roberts
These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Dis…
Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems
J. E. Bunder, A. J. Roberts
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent struc…
Couple microscale periodic patches to simulate macroscale emergent dynamics
Hammad Alotaibi, Barry Cox, A. J. Roberts
This article proposes a new way to construct computationally efficient `wrappers' around fine scale, microscopic, detailed descriptions of dynamical systems, such as molecular dyna…
Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
J. E. Bunder, A. J. Roberts
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing…