2020 Volume 2020 Issue 1 Pages 20201002
This paper describes optimization algorithms as numerical methods to find the centroidal Voronoi tessellation (CVT). The CVT can expect to put particles at evenly spaced apart with capturing the curvature of the boundary and then generate an efficient initial particle distribution for the particle methods to analyze the fluid flow problems with slopes and curved walls. However, a problem to find CVT is classified as the NP-hard. Therefore, there is a great demand for an algorithm to solve the problem efficiently. This paper considers finding CVT as optimization problem about finding minimum energy and then applies optimizers in the field of machine learning such as the Momentum SGD and the Adam. Moreover, this paper discusses on hyperparameters of optimizers and performances of iteration counts to find CVT.
