Adaptive fast multipole methods on the GPU

TL;DR

This paper introduces a flexible and efficient GPU implementation of adaptive fast multipole methods in 2D, optimizing all algorithm steps and analyzing GPU architecture effects for high-performance computations.

Contribution

It presents a novel, highly general GPU-based implementation of adaptive fast multipole methods with an innovative asymmetric space discretization approach.

Findings

Efficient GPU implementation of all multipole algorithm steps.

Flexible adaptive space discretization enhances performance.

Timing experiments reveal architecture-specific optimization insights.

Abstract

We present a highly general implementation of fast multipole methods on graphics processing units (GPUs). Our two-dimensional double precision code features an asymmetric type of adaptive space discretization leading to a particularly elegant and flexible implementation. All steps of the multipole algorithm are efficiently performed on the GPU, including the initial phase which assembles the topological information of the input data. Through careful timing experiments we investigate the effects of the various peculiarities of the GPU architecture.