Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs

Abstract

In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on Poisson disc sampling is parallelized for use on shared-memory computers, such as the modern workstations with multi-core processors. The parallel algorithm uses a global spatial indexing method with its data divided into two levels, which allows for an efficient multi-threaded implementation. The addition of bootstrapping enables the algorithm to use any number of parallel threads while remaining as general as its sequential variant. We demonstrate the algorithm performance on six complex 2- and 3-dimensional domains, which are either of non rectangular shape or have varying nodal spacing or both. We perform a run-time analysis of the algorithm, to demonstrate its ability to reach high speedups regardless of the domain and to show how well it scales on the experimental hardware with 16 processor cores. We also analyse the algorithm in terms of the effects of domain shape, quality of point placement, and various parallelization overheads.