A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation

Maclean, John; Bunder, J. E.; Roberts, Anthony John

doi:10.1007/s11075-020-01027-z

Cited by 15 publications

(15 citation statements)

References 43 publications

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“…The qualitative properties of the patch simulation are like those of Figure 1 albeit here starting from a noisy initial condition. Such simulations as these are readily performed using our Matlab/Octave Toolbox (Maclean, Bunder, and Roberts 2020).…”

Section: Self-adjoint Coupling For 2dmentioning

confidence: 99%

“…Figure 16 plots a simulation of the ensemble-mean ū(x I i , y J j , t) := 1 p p−1 =0 u I,J i,j, (t) of the patch-ensemble scheme (23) for diffusivities (21)-the 2D heterogeneous diffusion (1) on patches of the twenty member ensemble of all phase-shifts of the diffusivities. It used spectral coupling via the Matlab/Octave Toolbox (Maclean, Bunder, and Roberts 2020). For better visualisation we use only 5 × 5 patches, with other parameters the same as Figure 14; that is, n x = 5 , n y = 4 and r x = 0.5 , r y = 0.4 .…”

Section: Verify Accuracy In An Examplementioning

confidence: 99%

“…The code developed herein now forms part of a flexible Matlab/Octave Toolbox (Maclean, Bunder, and Roberts 2020) for equation-free computations that any researcher can download and use for a variety of problems (Roberts, Maclean, and Bunder 2020). This Toolbox provides equation-free code suitable for many systems, such as diffusion and wave dynamics, and grants the user full flexibility in selecting one of the supplied projective integration and/or patch coupling schemes or importing user-written code.…”

mentioning

confidence: 99%

“…For simplicity, we introduce our approach for systems defined on a microscale spatial lattice, such as a spatial discretisations of pdes on the microscale length d. This section introduces how to construct patches for a 1D system so that a computational simulation on these patches efficiently and accurately predicts the macroscale of interest without needing to derive a macroscale closure. In this patch construction we focus on the specific example of 1D heterogeneous diffusion on a microscale lattice, but the new patch scheme is similar for a wide range of 1D systems, including nonlinear systems (e.g., via the toolbox by Maclean, Bunder, and Roberts 2020).…”

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confidence: 99%

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Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Bunder¹,

Kevrekidis²,

Roberts³

2020

Preprint

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Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in small patches spread across the space-time domain, with patch coupling conditions bridging the unsimulated space. For accurate simulations, care must be taken in designing the patch coupling conditions. Here we construct novel coupling conditions which preserve translational invariance, rotational invariance, and self-adjoint symmetry, thus guaranteeing that conservation laws associated with these symmetries are preserved in the macroscale simulation. Spectral and algebraic analyses of the proposed scheme in both one and two dimensions reveal mechanisms for further improving the accuracy of the simulations. Consistency of the patch scheme's

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Section: Self-adjoint Coupling For 2dmentioning

confidence: 99%

Section: Verify Accuracy In An Examplementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Bunder¹,

Kevrekidis²,

Roberts³

2020

Preprint

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“…The Equation-Free methodology has remarkably efficient scaling for multiscale systems in multiple spatial dimensions. The computational speedup for a multiscale system in n-D space, with scale separation parameter ε, is O ε −n as discussed for efficient algorithms implementing Equation-Free algorithms in 2D and 3D space (Roberts et al 2014, Maclean et al 2020, and including 2D wave systems (Bunder et al 2021b, §2.2.2).…”

Section: Introductionmentioning

confidence: 99%

Adaptively detect and accurately resolve macro-scale shocks in an efficient Equation-Free multiscale simulation

Maclean¹,

Bunder²,

Kevrekidis³

et al. 2021

Preprint

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The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction-the patch dynamics scheme. A recent novel patch scheme empowered the Equation-Free approach to simulate systems containing shocks on the macro-scale. However, the scheme did not predict the formation of shocks accurately, and it could not simulate moving shocks. This article resolves both issues, as a first step in one spatial dimension, by embedding the Equation-Free, shock-resolving patch scheme within a classic framework for adaptive moving meshes. Our canonical micro-scale problems exhibit heterogeneous nonlinear advection and heterogeneous diffusion. We demonstrate many remarkable benefits from the moving patch scheme, including efficient and accurate macro-scale prediction despite the unknown macro-scale closure. Equation-free methods are here extended to simulate moving, forming and merging shocks without a priori knowledge of the existence or closure of the shocks. Whereas adaptive moving mesh equations are typically stiff, typically requiring small time-steps on the macro-scale, the moving

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Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

2021

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A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation

Cited by 15 publications

References 43 publications

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Adaptively detect and accurately resolve macro-scale shocks in an efficient Equation-Free multiscale simulation

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

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