Directional integration on unstructured meshes via supermesh construction

Maddison, James R.; Farrell, Patrick E.

doi:10.1016/j.jcp.2012.02.009

Cited by 7 publications

(3 citation statements)

References 29 publications

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“…It works because most dual basis functionals involve either evaluating a point on the cell K, doing some integration over that cell, or evaluating a derivative component on it. So long as this can be done with sufficient accuracy in the finite element space we are interpolating from, we can perform our interpolation and get results which have properties which we expect the new space to give us, such as having particular values at particular points (for more see Maddison and Farrell (2012)).…”

Section: Point Evaluation As An Interpolation Operatormentioning

confidence: 99%

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Point Data Assimilation in Firedrake and Icepack

Nixon-Hill

Shapero

Cotter

et al. 2023

Preprint

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<div> <div>We present methods and tools which significantly improve the ability to estimate quantities and fields which are difficult to directly measure at large scales, such as the fluidity of ice, using point data sources from remote sensing. Our tools work with both sparse and dense point data with estimated quantities and fields becoming more accurate as the number of measurements are increased. These are often used as input variables to mathematical models that are used to make predictions so improving their accuracy is of vital importance.</div> <div>&#160;</div> <div>The tool we introduce, Firedrake, generates highly optimised code for solving PDEs via the finite element method. It is easy to use, can be integrated with other python libraries, and is scalable for use on high performance computers. As proof, we highlight Icepack, a Python library for solving the equations of motion of glacier flow, which is written using Firedrake. Firedrake has an interface to the dolfin-adjoint/pyadjoint tool which allows these data assimilation problems to be solved with just a few lines of code by automatically generating the adjoint system of PDEs.</div> <div>&#160;</div> <div>By carefully considering the nature of finite element method solutions, we show, using Firedrake and Icepack, how the choice of misfit functional (i.e. objective function) significantly impacts our inferred fields. This required the development of new infrastructure not previously available in these automated code generation tools.</div> </div>

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Section: Point Evaluation As An Interpolation Operatormentioning

confidence: 99%

“…Prior work on supermeshing(Maddison and Farrell, 2012;Farrell et al, 2009) provides a mathematical framework.…”

mentioning

confidence: 99%

Point Data Assimilation in Firedrake and Icepack

Nixon-Hill

Shapero

Cotter

et al. 2023

Preprint

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“…figure 1. Applications of supermeshes arise in adaptive remeshing, diagnostic computation, multimesh discretisations, cut finite element methods, and multilevel Monte Carlo, among others [1,3,4,7,11,14,15]. Several efficient algorithms for supermesh construction have been published (cf.…”

Section: Introductionmentioning

confidence: 99%

Complexity bounds on supermesh construction for quasi-uniform meshes

Croci

Farrell

2020

Journal of Computational Physics

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Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh n. Given any two quasi-uniform meshes of n A and n B cells respectively, we show under standard assumptions that n is proportional to n A +n B . This result substantially improves on the best currently available upper bound on n and is fundamental for the analysis of algorithms that use supermeshes.

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Coupled simulation of fluid flow and propellant burning surface regression in a solid rocket motor

Liu

et al. 2014

Computers & Fluids

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Directional integration on unstructured meshes via supermesh construction

Cited by 7 publications

References 29 publications

Point Data Assimilation in Firedrake and Icepack

Point Data Assimilation in Firedrake and Icepack

Complexity bounds on supermesh construction for quasi-uniform meshes

Coupled simulation of fluid flow and propellant burning surface regression in a solid rocket motor

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