Heterogeneous multiscale method for high energy-density matter: Connecting kinetic theory and molecular dynamics

Shohet, Gil; Price, Jacob; Haack, J.; Marciante, Mathieu; Murillo, Michael S.

doi:10.1016/j.jcpx.2020.100070

Cited by 2 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Multiscale modelling aims to overcome this issue by efficiently approximating over the multiple scales to provide an accurate numerical model of the coherent dynamics of the system at the macroscale of interest. Numerous computational schemes have been developed for a wide variety of multiscale systems, from composite materials (Dutra et al 2020) to plasmas (Shohet et al 2020). However, many of these computational schemes are developed for specific systems and are not easily adaptable to other cases.…”

Section: Introductionmentioning

confidence: 99%

Learning high-order spatial discretisations of PDEs with symmetry-preserving iterative algorithms

Bunder¹,

Roberts²

2022

Preprint

View full text Add to dashboard Cite

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 without further tailored analysis are not suitable for systems with subgrid-scale heterogeneity or nonlinearities. We provide a new algebraic route to systematically approximate, in principle exactly, the macroscale closure of the spatially-discrete dynamics of a general class of heterogeneous non-autonomous reactionadvection-diffusion pdes. This holistic discretisation approach, developed through rigorous theory and verified with computer algebra, systematically constructs discrete macroscale models through physics informed by the pde out-of-equilibrium dynamics, thus relaxing many assumptions regarding the subgrid structure. The construction is analogous to recent gray-box machine learning techniques in that predictions are directed by iterative layers (as in neural networks), but informed by the subgrid physics (or 'data') as expressed in the pdes. A major development of the holistic methodology, presented herein, is novel inter-element coupling between subgrid fields which preserve self-adjointness of the pde after macroscale discretisation, thereby maintaining the spectral structure of the original system. This holistic methodology also encompasses homogenisation of microscale heterogeneous systems, as shown here with the canonical examples of heterogeneous 1D waves and diffusion.

show abstract

Section: Introductionmentioning

confidence: 99%