Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport
نویسندگان
چکیده
In this paper we describe a fast algorithm for generating periodic RVEs of polycrystalline materials. particular, use the damped Newton method from semi-discrete optimal transport theory to generate 3D Laguerre tessellations (or power diagrams) with cells given volumes. Complex, polydisperse up 100,000 grains prescribed volumes can be created in few minutes on standard laptop. The relies Hessian objective function, which derive by extending recent results setting.
منابع مشابه
Inverting Laguerre Tessellations
A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tess...
متن کاملNumerical micromechanical modelling of brittle polycrystalline materials
A generally applicable framework for generating a nite element mesh that is based on the actual micro-structure of a material is developed. The procedure is applied to a microscopic image of a ceramic material. Special attention is paid to the modelling of the interfaces between adjoining grains. Plane strain and plane stress nite element calculations are performed. The observed e ective consta...
متن کاملA Newton algorithm for semi-discrete optimal transport
Many problems in geometric optics or convex geometry can be recast as optimal transport problems and a popular way to solve these problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We introduce a damped Newton’s algorithm for this type of problems, which is experimentally efficient, and we establish its ...
متن کاملOptimal expansions of discrete-time Volterra models using Laguerre functions
This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite dimensional representation. Fu and Dumont [14] indirectly approached this problem in the context of linea...
متن کاملRegularized Discrete Optimal Transport
This article introduces a generalization of discrete Optimal Transport that includes a regularity penalty and a relaxation of the bijectivity constraint. The corresponding transport plan is solved by minimizing an energy which is a convexification of an integer optimization problem. We propose to use a proximal splitting scheme to perform the minimization on large scale imaging problems. For un...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mechanics Research Communications
سال: 2023
ISSN: ['0093-6413', '1873-3972']
DOI: https://doi.org/10.1016/j.mechrescom.2022.104023