Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg

Wallwork, Joseph G.; Barral, Nicolas; Knepley, Matthew G.

doi:10.48550/arxiv.2201.02806

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Support for mesh-to-mesh solution transfer by conservative interpolation is provided by libsupermesh (Farrell & Maddison, 2011). The Pyroteus goal-oriented mesh adaptation toolkit (Wallwork, 2022a) is used to handle the mesh adaptation fixed point iteration loop, including the solution of forward and adjoint problems across multiple meshes, with the mesh adaptation step itself done using Mmg (Dobrzynski & Frey, 2008;Wallwork, Knepley, et al, 2022).…”

Section: Appendix a Derivative Recoverymentioning

confidence: 99%

Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

Wallwork¹,

Angeloudis²,

Barral³

et al. 2022

Preprint

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Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation.Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements.Results: We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts moreenergy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs.Conclusion: The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using 10% as many degrees of freedom as a high resolution fixed mesh benchmark, they are shown to enable energy output differences smaller than 10%. Applied to a tidal array with aligned rows of turbines, the anisotropic adaptation scheme is shown to yield differences smaller than 1%.

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Section: Appendix a Derivative Recoverymentioning

confidence: 99%

Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

Wallwork¹,

Angeloudis²,

Barral³

et al. 2022

Preprint

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show abstract

“…Firedrake is a Python-based package, which automatically generates C code and uses PETSc [45,46] to provide its unstructured mesh concept and to solve the linear and nonlinear systems which underpin finite element problems. Metric-based mesh adaptation is achieved using Mmg [35], the coupling of which with PETSc's mesh representation was documented in [47].…”

Section: Appendix a Derivative Recoverymentioning

confidence: 99%

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Wallwork¹,

Lu²,

Zhang³

et al. 2022

Preprint

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Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-byelement construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-byelement approach implies reasonably low training costs.

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Tidal turbine array modelling using goal-oriented mesh adaptation

Wallwork,

Angeloudis,

Barral

et al. 2023

J. Ocean Eng. Mar. Energy

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To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation. The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements. We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts more energy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs. The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using only a tenth of the number of degrees of freedom as a high-resolution fixed mesh benchmark and lower overall runtime, they are shown to enable energy output differences smaller than 2% for a tidal array test case with aligned rows of turbines and less than 10% for a staggered array configuration.

show abstract

Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg

Cited by 3 publications

References 10 publications

Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Tidal turbine array modelling using goal-oriented mesh adaptation

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