Details of tetrahedral anisotropic mesh adaptation

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• 作者：Kristian Ejlebjerg Jensen ^{kristianejlebjerg+cpc@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Gerard Gorman ; ^{g.gorman@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Anisotropic ; Mesh ; Adaptation ; Refinement ; Swapping
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：201
• 期：Complete
• 页码：135-143
• 全文大小：1392 K

文摘

We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for-N$N$ loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.

Program summary

Program title: trullekrul v0.1.0

Catalogue identifier: AEZC_v1_0

Program summary URL:ac.uk/summaries/AEZC_v1_0.html">http://cpc.cs.qub.ac.uk/summaries/AEZC_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: New style BSD license

No. of lines in distributed program, including test data, etc.: 8395

No. of bytes in distributed program, including test data, etc.: 92021

Distribution format: tar.gz

Programming language: MATLAB/GNU Octave.

Computer: Single core desktops.

Operating system: Linux/Windows/Mac.

RAM: Variable, from megabytes to gigabytes

Classification: 4.2, 4.3, 4.12, 4.14.

Nature of problem: Adaptation of tetrahedral meshes to metric fields.

Solution method: Local operations, colouring and APL vectorised code.

Restrictions:   Region IDs/internal boundaries are not supported and 3D adaptation with 1M elements requires aca7b8332ff130d47e39eafbcc17abd"> memory.

Unusual features: Vectorised script implementation, signed distance functions, selection of refinement and coarsening techniques.

Running time: 2D problems solve in seconds, but 3D problems can take up to an hour without running out of memory.