Compact data structure and scalable algorithms for the sparse grid technique

Authors:
Alin Murarasu;Josef Weidendorfer;Gerrit Buse;Daniel Butnaru;Dirk Pflüger
Affiliations:
Technische Universität München, Garching, Germany;Technische Universität München, Garching, Germany;Technische Universität München, Garching, Germany;Technische Universität München, Garching, Germany;Technische Universität München, Garching, Germany
Venue:
Proceedings of the 16th ACM symposium on Principles and practice of parallel programming
Year:
2011

Citing 9
Cited 1

Multidimensional access methods

ACM Computing Surveys (CSUR)
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences

Computing
An Abstract Data Type for Parallel Simulations Based on Sparse Grids

EuroPVM '96 Proceedings of the Third European PVM Conference on Parallel Virtual Machine
Glift: Generic, efficient, random-access GPU data structures

ACM Transactions on Graphics (TOG)
Optimization principles and application performance evaluation of a multithreaded GPU using CUDA

Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
NVIDIA Tesla: A Unified Graphics and Computing Architecture

IEEE Micro
Benchmarking GPUs to tune dense linear algebra

Proceedings of the 2008 ACM/IEEE conference on Supercomputing
GPU based sparse grid technique for solving multidimensional options pricing PDEs

Proceedings of the 2nd Workshop on High Performance Computational Finance
Considering GPGPU for HPC centers: is it worth the effort?

Facing the multicore-challenge

Workload balancing on heterogeneous systems: a case study of sparse grid interpolation

Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing - Volume 2

Quantified Score

Hi-index	0.00

Visualization

Abstract

The sparse grid discretization technique enables a compressed representation of higher-dimensional functions. In its original form, it relies heavily on recursion and complex data structures, thus being far from well-suited for GPUs. In this paper, we describe optimizations that enable us to implement compression and decompression, the crucial sparse grid algorithms for our application, on Nvidia GPUs. The main idea consists of a bijective mapping between the set of points in a multi-dimensional sparse grid and a set of consecutive natural numbers. The resulting data structure consumes a minimum amount of memory. For a 10-dimensional sparse grid with approximately 127 million points, it consumes up to 30 times less memory than trees or hash tables which are typically used. Compared to a sequential CPU implementation, the speedups achieved on GPU are up to 17 for compression and up to 70 for decompression, respectively. We show that the optimizations are also applicable to multicore CPUs.