61 citations · 202 across the 47 of their papers we have counts for
48 papers
Embed to rigorously and accurately homogenise quasi-periodic multi-scale heterogeneous PDEs, with computer algebra
A. J. Roberts
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically…
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…
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Hassan Arbabi, Judith E. Bunder, Giovanni Samaey +2
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural…
A multiscale scheme accurately simulates macroscale shocks in an equation-free framework
John Maclean, J. E. Bunder, A. J. Roberts +1
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time o…
A toolbox of Equation-Free functions in Matlab\Octave for efficient system level simulation
John Maclean, J. E. Bunder, A. J. Roberts
The `equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform ma…
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…