A novel three-dimensional mesh deformation method based on sphere relaxation

Zhou, Xuan; Li, Shuixiang

doi:10.1016/j.jcp.2015.05.046

Cited by 12 publications

(8 citation statements)

References 26 publications

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“…If the mesh deformation task is required to be performed once, physical analogy based techniques might be considered as an option. For these reasons, the recent trend in handling the mesh deformation problem has been focusing more on using interpolation based techniques [59][60][61].…”

Section: Discussionmentioning

confidence: 99%

Mesh Deformation Approaches – A Survey

Mm¹,

Rp²

2016

J Phys Math

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This survey reviews the recent development of mesh deformation methods. During the past two decades a vast number of researches have been concerned with developing an efficient and robust mesh deformation technique. This has been achieved either by proposing a novel approach, improving an existing one, or by combining two existing approaches together resulting in a new hybrid approach. It is important to keep track of the most up to date developments in the field of mesh deformation, in order to allow the researchers to adopt the most efficient and application compatible scheme as well as to propose new methods of improvements. In this survey the mesh deformation techniques have been classified into two main categories, 1) physical analogy based techniques and 2) interpolation based techniques. The most significant techniques under these two classes are reviewed and the aspects of strength and weaknesses are highlighted.

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Section: Discussionmentioning

confidence: 99%

Mesh Deformation Approaches – A Survey

Mm¹,

Rp²

2016

J Phys Math

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“…Allen [5] developed a fast algebraic interpolation strategy using inverse distance weighting, and particular attention was paid to the preservation of orthogonality. Similar inverse distance weighting methods were also presented in [35] and [36] and methods have also been presented using disk and then sphere relaxation methods [37,38]. 110 Recently there has been increased interest in radial basis function (RBF) interpolation for mesh deformation [6,1,2].…”

Section: Mesh Deformationmentioning

confidence: 93%

Efficient and exact mesh deformation using multiscale RBF interpolation

Kedward¹,

Allen

Rendall³

2017

Journal of Computational Physics

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Radial basis function (RBF) interpolation is popular for mesh deformation due to robustness and generality, but the cost scales with the number of surface points sourcing the deformation as O(N 3 s ). Hence, there have been numerous works investigating efficient methods using reduced datasets. However, although reduced-data methods are efficient, they require a secondary method to treat an error vector field to ensure surface points not included in the primary deformation are moved to the correct location, and the volume mesh moved accordingly.A new method is presented which captures global and local motions at multiple scales using all the surface points, and so no correction stage is required; all surface points are used and a single interpolation built, but the cost and conditioning issues associated with RBF methods are eliminated. Moreover, the sparsity introduced is exploited using a wall distance function, to further reduce the cost. The method is compared to an efficient greedy method, and it is shown mesh quality is always comparable with or better than with the greedy method, and cost is comparable or cheaper at all stages. Surface mesh preprocessing is the dominant cost for reduced-data methods and this cost is reduced significantly here: greedy methods select points to minimise interpolation error, requiring repeated system solution and cost O(N 4 red ) to select N red points; the multiscale method has no error, and the problem is transferred to a geometric search, with cost O(N s log(N s )), resulting in an eight orders of magnitude cost reduction for three-dimensional meshes. Furthermore, since the method is dependent on geometry, not deformation, it only needs to be applied once, prior to simulation, as the mesh deformation is decoupled from the point selection process.

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“…Similar inverse distance weighting methods are also presented in 33 and 34 and methods have also been presented using disk and then sphere relaxation methods. 35,36 Recently there has been increased interest in radial basis function (RBF) interpolation for mesh deformation 5, 1, 2 due to its generality, being able to operate on scattered data sets (requiring no connectivity) and having no limit on the dimensionality of the problem. Rendall and Allen used RBF interpolation in a unified approach to fluid-structure interaction, 1 wherein the universal characteristics of RBF interpolation as a mesh motion scheme were highlighted, and mesh quality is shown to be preserved well.…”

Section: Mesh Deformationmentioning

confidence: 99%

Efficient and Exact Mesh Deformation using Multi-Scale RBF Interpolation

Kedward

Allen

Rendall

2017

55th AIAA Aerospace Sciences Meeting

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Mesh deformation schemes are vital in many areas of numerical simulation, and radial basis function(RBF)-based interpolation schemes are popular due to their excellent quality preservation properties. However, the system solution cost scales with moving surface points as N 3 surf ace , and so there have been numerous works investigating efficient methods of reducing the data set. However, reduced data methods require the addition of a secondary 'correction vector field' to ensure surface points not included in the primary deformation are moved to the correct location, and the volume mesh moved accordingly. A new method is presented here, which captures global and local motions at multiple scales using all the surface points, and so there is no need for a correction stage. The multiscale formulation developed means that although all surface points are used and a single interpolation built, the cost and conditioning issues associated with RBF methods are eliminated while still retaining exact recovery of the surface. Moreover, the sparsity introduced can be exploited, using an existing wall distance function, to further reduce the cost. The method is compared with a conventional greedy method on two-and three-dimensional meshes with large deformations. It is shown that mesh quality is always comparable with or better than with the greedy method, and cost and complexity is also comparable or cheaper for all stages. The most expensive stage of reduced point methods is surface mesh preprocessing, and the cost is reduced significantly here; a three or four orders of magnitude reduction in cost is demonstrated compared to greedy-type methods.

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A novel three-dimensional mesh deformation method based on sphere relaxation

Cited by 12 publications

References 26 publications

Mesh Deformation Approaches – A Survey

Mesh Deformation Approaches – A Survey

Efficient and exact mesh deformation using multiscale RBF interpolation

Efficient and Exact Mesh Deformation using Multi-Scale RBF Interpolation

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