Fast harmonic tetrahedral mesh optimization

Abstract Mesh optimization is essential to enable sufficient element quality for numerical methods such as the finite method (FEM). Depending on required accuracy and geometric detail, a mesh with many elements necessary resolve small-scale details. Sequential of large meshes often imposes long run times. This especially an issue Delaunay-based methods. Recently, notion harmonic triangulations [1] was evaluated tetrahedral meshes, revealing significantly faster times than competing A crucial aspect efficiency high boundary treatment. We investigate directional derivatives treatment massively parallel GPUs optimization. Parallel flipping achieves compelling speedups by up $$318\times $$ 318× . accelerate $$119\times xmlns:mml="http://www.w3.org/1998/Math/MathML">119× preservation $$78\times xmlns:mml="http://www.w3.org/1998/Math/MathML">78× moving every vertex, while producing superior quality.