Generation of high order geometry representations in Octree meshes

Harald G. Klimach, Jens Zudrop, Sabine P. Roller
2015 PeerJ Computer Science  
We propose a robust method to convert triangulated surface data into polynomial volume data. Such polynomial representations are required for high-order partial differential solvers, as low-order surface representations would diminish the accuracy of their solution. Our proposed method deploys a first order spatial bisection algorithm to find robustly an approximation of given geometries. The resulting voxelization is then used to generate Legendre polynomials of arbitrary degree. By embedding
more » ... gree. By embedding the locally defined polynomials in cubical elements of a coarser mesh, this method can reliably approximate even complex structures, like porous media. It thereby is possible to provide appropriate material definitions for high order discontinuous Galerkin schemes. We describe the method to construct the polynomial and how it fits into the overall mesh generation. Our discussion includes numerical properties of the method and we show some results from applying it to various geometries. We have implemented the described method in our mesh generatorSeeder, which is publically available under a permissive open-source license.
doi:10.7717/peerj-cs.35 fatcat:w3kicwwk7ngg7m7pvh5ugkpmna