Load Balanced Parallel Node Generation for Meshless Numerical Methods

TL;DR

This paper presents a parallel algorithm for node generation in meshless methods, improving efficiency and scalability by using coupled spatial indexing and work distribution hypertrees.

Contribution

It introduces a novel parallelization approach for Poisson disc sampling in meshless methods, reducing locking and collision handling overhead.

Findings

The algorithm effectively balances work units according to node density.

Performance comparisons show improved scalability over existing methods.

The approach can be adapted for distributed systems.

Abstract

Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical analysis is an n-dimensional Poisson disc sampling based method. It can handle complex geometries and supports variable node density, a crucial feature for adaptive analysis. We modify this method for parallel execution using coupled spatial indexing and work distribution hypertrees. The latter is prebuilt according to the node density function, ensuring that each leaf represents a balanced work unit. Threads advance separate fronts and claim work hypertree leaves as needed while avoiding leaves neighbouring those claimed by other threads. Node placement constraints and the partially prebuilt spatial hypertree are combined to eliminate the need to lock the tree while it is being modified. Thread collision handling is managed by the work hypertree at the leaf level, drastically reducing the number of required mutex acquisitions for point insertion collision checks. We explore the behaviour of the proposed algorithm and compare the performance with existing attempts at parallelisation and consider the requirements for adapting the developed algorithm to distributed systems.