Volume 8, Issue 5
Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1 -Conservative Interpolation

Adv. Appl. Math. Mech., 8 (2016), pp. 847-870.

Published online: 2018-05

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• Abstract

This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

• Keywords

Solution reconstruction, solution transfer, conservative interpolation, tetrahedral mesh, solution interpolation, mesh intersection.

41A05, 65D05

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@Article{AAMM-8-847, author = {Biao and Peng and and 19630 and and Biao Peng and Chunhua and Zhou and and 19631 and and Chunhua Zhou and Junqiang and Ai and and 19632 and and Junqiang Ai}, title = {Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1 -Conservative Interpolation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {847--870}, abstract = {

This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1087}, url = {http://global-sci.org/intro/article_detail/aamm/12120.html} }
TY - JOUR T1 - Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1 -Conservative Interpolation AU - Peng , Biao AU - Zhou , Chunhua AU - Ai , Junqiang JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 847 EP - 870 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1087 UR - https://global-sci.org/intro/article_detail/aamm/12120.html KW - Solution reconstruction, solution transfer, conservative interpolation, tetrahedral mesh, solution interpolation, mesh intersection. AB -

This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

Biao Peng, Chunhua Zhou & Junqiang Ai. (2020). Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1 -Conservative Interpolation. Advances in Applied Mathematics and Mechanics. 8 (5). 847-870. doi:10.4208/aamm.2015.m1087
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