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

TL;DR

This paper introduces a parallel, dimension-independent node placement algorithm based on Poisson disc sampling, optimized for meshless PDE solvers, demonstrating high scalability and efficiency on complex 2D and 3D domains.

Contribution

It presents a novel parallel node positioning algorithm that is both efficient and adaptable to various domain shapes and densities, suitable for meshless numerical methods.

Findings

Achieves high speedups on multi-core processors.

Effectively handles complex non-rectangular domains.

Maintains quality of node distribution across different domain shapes.

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 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.