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Abstract Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.
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Field-Aligned and Lattice-Guided Tetrahedral Meshing
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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- Award ID(s):
- 1657364
- PAR ID:
- 10097915
- Date Published:
- Journal Name:
- Computer graphics forum
- Volume:
- 37
- Issue:
- 5
- ISSN:
- 1467-8659
- Page Range / eLocation ID:
- 161 - 172
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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