Fast high-dimensional node generation with variable density
For researchers needing point clouds with controlled separation-covering ratios in high-dimensional spaces, this provides a new generation method, but the contribution appears incremental as it combines existing techniques.
The paper presents an algorithm combining quasi-Monte Carlo methods and weighted Riesz energy minimization to generate discrete distributions with a prescribed nearest-neighbor distance function, producing node sets suitable for meshless solvers and interpolants. The method is demonstrated in three-dimensional atmospheric modeling applications.
We present an algorithm for producing discrete distributions with a prescribed nearest-neighbor distance function. Our approach is a combination of quasi-Monte Carlo (Q-MC) methods and weighted Riesz energy minimization: the initial distribution is a stratified Q-MC sequence with some modifications; a suitable energy functional on the configuration space is then minimized to ensure local regularity. The resulting node sets are good candidates for building meshless solvers and interpolants, as well as for other purposes where a point cloud with a controlled separation-covering ratio is required. Applications of a three-dimensional implementation of the algorithm, in particular to atmospheric modeling, are also given.