Paper

Robust topological construction of all-hexahedral boundary layer meshes
Reberol, Maxence; Verhetsel, Kilian; Henrotte, François; Bommes, David; Remacle, Jean-François
ACM Transactions on Mathematical Software, 2022

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Overview

This library contains the integer solver of the paper "Robust topological construction of all-hexahedral boundary layer meshes". Specifically, it solves the global integer problem (Eq. 3) with the Gecode library. The setup of the branch-and-bound search (including the conditions of Proposition 1) is implemented in src/solver.cpp. To call the integer solver from your code, call solveAllHexLayerTopology(...) which is declared in src/solver.h.

This code is distributed to supplement the manuscript. This is not a standalone meshing tool. Domain decomposition of the surface mesh and hexahedral mesh construction, which are necessary in practice, are not part of this repository.

The complete implementation (used to generate the results in the paper) is available in the official Gmsh repository. See the hexbl branch: https://gitlab.onelab.info/gmsh/gmsh/-/tree/hexbl

Compilation

This library depends on the Gecode library (https://www.gecode.org/, MIT license). CMake will look for a system-wide installation, which usually can be installed via the package manager of your distribution (or homebrew on MacOS).

On Linux / MacOS:

mkdir build 
cd build/ 
cmake ..
make 

Tests are implemented with Catch2 (https://github.com/catchorg/Catch2, BSL.1-0 License), whose single header is included in tests/.

Executables

Basic tests are available in tests/basic_tests.cpp and can be run with the executable basic_tests.

A list of disk triangulations (generated with plantri) is available in the file asset/disk_trgls_3.data.

Experimental proof of Proposition 2

The proof is implemented in tests/eproof.cpp and can be run with the executable experimental_proof.

If one uses large valence ranges, the executable may say that a disk triangulation boundary has not been found (e.g. n=[5,5,5,5,5]). This is because the disk triangulation is not in assert/disk_trgls.data, as the range is too large, and there would be too many disk triangulations (literally billions, trillions).