Conservative interpolation between unstructured meshes via supermesh construction

Farrell, Patrick E.; Piggott, Matthew D.; Pain, Christopher C.; Gorman, Gerard J.; Wilson, C. R.

doi:10.1016/j.cma.2009.03.004

Cited by 152 publications

(138 citation statements)

References 36 publications

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“…-It is local and explicit, unlike optimization-based approaches (Jiao and Heath, 2004;Farrell et al, 2009) which may require an iterative solver to approximate the function on the target mesh. We do not seek a "best" approximation here but only suppose a quadrature scheme in order to test the conservation requirement.…”

Section: Introductionmentioning

confidence: 99%

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Conservative interpolation between general spherical meshes

Kritsikis

Aechtner²,

Meurdesoif

et al. 2017

Geosci. Model Dev.

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Abstract. An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitudelongitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a "supermesh", whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(N log N ) computational cost. The method presented is meant to be incorporated in pre-or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean.

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Section: Introductionmentioning

confidence: 99%

“…Our method relies on constructing a common refinement of the source and target meshes, called a supermesh in Farrell et al (2009). Assuming that the supermesh is known, formulae for second-order conservative interpolation are derived in Sect.…”

Section: Introductionmentioning

confidence: 99%

Conservative interpolation between general spherical meshes

Kritsikis

Aechtner²,

Meurdesoif

et al. 2017

Geosci. Model Dev.

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“…Between adapts, the solution field is interpolated using the simple linear interpolation implied by the underlying basis functions. For a discussion of more advanced interpolation options, see Farrell et al (2009).…”

Section: Examplesmentioning

confidence: 99%

Anisotropic mesh adaptivity for multi-scale ocean modelling

Piggott

Farrell²,

Wilson³

et al. 2009

Phil. Trans. R. Soc. A.

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Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimizationbased approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.

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“…A conservative interpolation based on a Galerkin projection has been proposed in [1,7,8]. The Galerkin projection requires the assembling and the resolution of a linear system.…”

Section: Introductionmentioning

confidence: 99%

“…To bound the projected quantities specific treatments have to be done [7]. A global supermesh construction is used in [7,8] but it limits considerably the efficiency of the method and the maximal size of the problem in 3D due to memory usage. A local approach has been proposed in [6] which improves the algorithm efficiency.…”

Section: Introductionmentioning

confidence: 99%

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

Alauzet

2016

Computer Methods in Applied Mechanics and Engineering

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This document presents an interpolation operator on unstructured tetrahedral meshes that satisfies the properties of mass conservation, P 1 -exactness (order 2) and maximum principle. Interpolation operators are important for many applications in scientific computing. For instance, in the context of anisotropic mesh adaptation for time-dependent problems, the interpolation stage becomes crucial as the error due to solution transfer accumulates throughout the simulation. This error can eventually spoil the overall solution accuracy. When dealing with conservation laws in CFD, solution accuracy requires enforcement of mass preservation throughout the computation, in particular in long time scale computations. In the proposed approach, the conservation property is achieved by local mesh intersection and quadrature formulae. Derivatives reconstruction is used to obtain a second order method. Algorithmically, our goal is to design a method which is robust and efficient. The robustness is mandatory to obtain a reliable method on real-life applications and to apply the operator to highly anisotropic meshes. The efficiency is achieved by designing a matrix-free operator which is highly parallel. A multi-thread parallelization is given in this work. Several numerical examples are presented to illustrate the efficiency of the proposed approach.Key-words: Solution interpolation, matrix-free conservative interpolation, parallel interpolation, unstructured mesh, mesh adaptation, conservation laws * INRIA, Équipe-projet Gamma3, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. email: frederic.alauzet@inria.fr A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes Résumé : Ce document présente un opérateur d'interpolation sur des maillages tétraé-driques non-structurés qui satisfait les propriétés de conservation de la masse, P 1 -exactitude (ordre 2) et principe du maximum.Mots-clés : Interpolation de solution, interpolation conservative sans matrice, interpolation parallèle, maillage non-structuré, adaptation de maillage, adaptation de maillage, loi de conservation A parallel matrix-free conservative solution interpolation on tetrahedral meshes 3

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Conservative interpolation between unstructured meshes via supermesh construction

Cited by 152 publications

References 36 publications

Conservative interpolation between general spherical meshes

Conservative interpolation between general spherical meshes

Anisotropic mesh adaptivity for multi-scale ocean modelling

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

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