Field-Aligned and Lattice-Guided Tetrahedral Meshing

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John Wiley & Sons Ltd.

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Abstract

We present a particle-based approach to generate field-aligned tetrahedral meshes, guided by cubic lattices, including BCC and FCC lattices. Given a volumetric domain with an input frame field and a user-specified edge length for the cubic lattice, we optimize a set of particles to form the desired lattice pattern. A Gaussian Hole Kernel associated with each particle is constructed. Minimizing the sum of kernels of all particles encourages the particles to form a desired layout, e.g., field-aligned BCC and FCC. The resulting set of particles can be connected to yield a high quality field-aligned tetrahedral mesh. As demonstrated by experiments and comparisons, the field-aligned and lattice-guided approach can produce higher quality isotropic and anisotropic tetrahedral meshes than state-of-the-art meshing methods.

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Computer graphics, Lattice theory, Numerical grid generation (Numerical analysis)

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National Science Foundation (NSF) under Grant No. IIS‐1149737; NSF ACI‐1657364; NSFC (No. 61522209, 6121000).

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©2018 The Authors and The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.

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