Hierarchization for the Sparse Grid Combination Technique

TL;DR

This paper introduces an optimized hierarchization algorithm that significantly enhances the efficiency of the sparse grid combination technique for high-dimensional numerical problems, achieving substantial speedups and stable performance.

Contribution

The paper presents a novel hierarchization algorithm that outperforms existing methods by up to 30 times and maintains stable, high-performance levels for large data sets.

Findings

Up to 30x speedup over baseline

Achieves close to 5% of peak performance

Stable performance for data sets up to 1 GB

Abstract

The sparse grid combination technique provides a framework to solve high dimensional numerical problems with standard solvers. Hierarchization is preprocessing step facilitating the communication needed for the combination technique. The derived hierarchization algorithm outperforms the baseline by up to 30x and achieves close to 5% of peak performance. It also shows stable performance for the tested data sets of up to 1 GB.