Accuracy of Patch Dynamics with Mesoscale Temporal Coupling for Efficient Massively Parallel Simulations

Bunder, J. E.; Roberts, A. J.; Kevrekidis, Ioannis G.

doi:10.1137/15m1015005

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…Furthermore, the patch scheme does not necessarily need to communicate edge information in every microscale time step. Instead, in many scenarios and to a controllable accuracy, one may communicate macroscale edge information on mesoscale times 38 . However, whether such mesoscale communication is feasible for wave‐like systems remains an open question for research.…”

Section: Stagger Patches Of Staggered Microcode In 2d Spacementioning

confidence: 99%

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Bunder

Divahar

Kevrekidis

et al. 2020

Numerical Methods in Fluids

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A multiscale computational scheme is developed to use given small microscale simulations of complicated physical wave processes to empower macroscale system‐level predictions. By coupling small patches of simulations over unsimulated space, large savings in computational time are realizable. Here, we generalize the patch scheme to the case of wave systems on staggered grids in two‐dimensional (2D) space. Classic macroscale interpolation provides a generic coupling between patches that achieves consistency between the emergent macroscale simulation and the underlying microscale dynamics. Spectral analysis indicates that the resultant scheme empowers feasible computation of large macroscale simulations of wave systems even with complicated underlying physics. As an example of the scheme's application, we use it to simulate some simple scenarios of a given turbulent shallow water model.

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Section: Stagger Patches Of Staggered Microcode In 2d Spacementioning

confidence: 99%

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Bunder

Divahar

Kevrekidis

et al. 2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…However, Figure 17: Three patches are the shaded regions centred on macroscale lattice points X i−1 , X i and X i+1 . At times δt apart the coupling information from neighbouring patches is updated (Bunder et al 2016, Fig. 3).…”

Section: How Do Communication Delays Affect Such Simulations?mentioning

confidence: 99%

“…Alternatively, maybe we could communicate the inter-patch coupling less often? Bunder et al (2016) explored the effect on accuracy of communicating coupling on an intermediate time meso-scale-longer than micro-times, and shorter than macro-times. Figure 17 illustrates the idea.…”

Section: How Do Communication Delays Affect Such Simulations?mentioning

confidence: 99%

Multiscale modelling of microscale heterogeneous systems: analysis supports systematic and efficient macroscale modelling and simulation

Roberts

2019

Preprint

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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: Discuss a mix of new mathematical approaches for multiscale modelling, heterogeneous material in particular, along with corresponding novel computational techniques and issues. I include discussion of a developing toolbox that empowers you to implement effective multiscale 'equation-free' computation [https://github.com/uoa1184615/EquationFreeGit.git].Pre-requisites undergraduate ordinary and partial differential equations, state space, trajectories, stability, bifurcations, power series solutions, separation of variables, eigen-problems and Sturm-Liouville theory; basic numerical methods for time integration of ODEs and for spatial discretisation PDEs, some perturbation methodology.Pre-reading recommend the review article by Kevrekidis & Samaey (2009). Perhaps also get an idea of centre manifolds [https://en.wikipedia.org/wiki/Center_manifold].Activities sprinkled are some small activities for you.

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Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations

Arbabi

Bunder

Samaey

et al. 2020

JOM

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The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data. For learning coarse-scale PDEs from computational fine-scale simulation data, the training data collection process can be prohibitively expensive. We propose to transformatively facilitate this training data collection process by linking machine learning (here, neural networks) with modern multiscale scientific computation (here, equation-free numerics). These equation-free techniques operate over sparse collections of small, appropriately coupled, space-time subdomains ("patches"), parsimoniously producing the required macro-scale training data. Our illustrative example involves the discovery of effective homogenized equations in one and two dimensions, for problems with fine-scale material property variations. The approach holds promise towards making the discovery of accurate, macro-scale effective materials PDE models possible by efficiently summarizing the physics embodied in "the best" fine-scale simulation models available.

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Accuracy of Patch Dynamics with Mesoscale Temporal Coupling for Efficient Massively Parallel Simulations

Cited by 5 publications

References 26 publications

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Large‐scale simulation of shallow water waves via computation only on small staggered patches

Multiscale modelling of microscale heterogeneous systems: analysis supports systematic and efficient macroscale modelling and simulation

Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations

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