Conservative interpolation between volume meshes by local Galerkin projection

Farrell, Patrick E.; Maddison, James R.

doi:10.1016/j.cma.2010.07.015

Cited by 286 publications

(192 citation statements)

References 29 publications

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“…by minimizing the L 2 norm of the interpolation error [20]. In a discrete form, equation (3.1) involves solving a linear system of equations containing a mass matrix based on the basis functions of the target mesh and a mixed mass matrix formed of the basis functions of the target and donor meshes.…”

Section: Spatial Projections Between Fluid Solid and Shell Meshesmentioning

confidence: 99%

“…This can be done using either an R-tree spatial indexing algorithm [18] or an advancing front algorithm [19]. For each element of the shell mesh, a so-called supermesh is formed from the set of all the intersections, following a local supermeshing method [20]. Importantly, the order of the basis functions on the supermesh is equal to the maximum of their orders on the fluid and shell meshes.…”

Section: Spatial Projections Between Fluid Solid and Shell Meshesmentioning

confidence: 99%

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An immersed-shell method for modelling fluid–structure interactions

Viré

Xiang

Pain

2015

Phil. Trans. R. Soc. A.

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The paper presents a novel method for numerically modelling fluid-structure interactions. The method consists of solving the fluid-dynamics equations on an extended domain, where the computational mesh covers both fluid and solid structures. The fluid and solid velocities are relaxed to one another through a penalty force. The latter acts on a thin shell surrounding the solid structures. Additionally, the shell is represented on the extended domain by a non-zero shell-concentration field, which is obtained by conservatively mapping the shell mesh onto the extended mesh. The paper outlines the theory underpinning this novel method, referred to as the immersed-shell approach. It also shows how the coupling between a fluid-and a structural-dynamics solver is achieved. At this stage, results are shown for cases of fundamental interest.

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Section: Spatial Projections Between Fluid Solid and Shell Meshesmentioning

confidence: 99%

Section: Spatial Projections Between Fluid Solid and Shell Meshesmentioning

confidence: 99%

An immersed-shell method for modelling fluid–structure interactions

Viré

Xiang

Pain

2015

Phil. Trans. R. Soc. A.

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“…As regards the differences and similarities between this work and [9]. In [9], they use local approach and an advancing front method for the intersection identification similar to the ones proposed in [6].…”

Section: Introductionmentioning

confidence: 99%

“…In [9], they use local approach and an advancing front method for the intersection identification similar to the ones proposed in [6]. The first difference lies in the computation and the meshing of the intersection between two elements.…”

Section: Introductionmentioning

confidence: 99%

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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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An efficient algorithm for mapping imaging data to 3D unstructured grids in computational biomechanics

Einstein

Kuprat

Jiao

et al. 2012

Numer Methods Biomed Eng

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SUMMARY Geometries for organ scale and multiscale simulations of organ function are now routinely derived from imaging data. However, medical images may also contain spatially heterogeneous information other than geometry that are relevant to such simulations either as initial conditions or in the form of model parameters. In this manuscript, we present an algorithm for the efficient and robust mapping of such data to imaging-based unstructured polyhedral grids in parallel. We then illustrate the application of our mapping algorithm to three different mapping problems: (i) the mapping of MRI diffusion tensor data to an unstructured ventricular grid; (ii) the mapping of serial cyrosection histology data to an unstructured mouse brain grid; and (iii) the mapping of computed tomography-derived volumetric strain data to an unstructured multiscale lung grid. Execution times and parallel performance are reported for each case.

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Conservative interpolation between volume meshes by local Galerkin projection

Cited by 286 publications

References 29 publications

An immersed-shell method for modelling fluid–structure interactions

An immersed-shell method for modelling fluid–structure interactions

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

An efficient algorithm for mapping imaging data to 3D unstructured grids in computational biomechanics

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