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Related Experiment Video

Updated: Jun 12, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

GPU computing with Kaczmarz's and other iterative algorithms for linear systems.

Joseph M Elble¹, Nikolaos V Sahinidis, Panagiotis Vouzis

¹University of Illinois Urbana-Champaign, Department of Industrial and Enterprise Systems Engineering, Urbana, IL 61801.

Parallel Computing

|June 8, 2010

Summary

This summary is machine-generated.

Graphics processing units (GPUs) accelerate solving large linear systems from partial differential equations. GPU implementations of iterative methods, particularly the conjugate gradient normal residual (CGNR), outperform CPU and cluster-based approaches.

Related Experiment Videos

Last Updated: Jun 12, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

Numerical Analysis
High-Performance Computing
Computational Science

Background:

Large linear systems arise from discretizing partial differential equations (PDEs) in fields like fluid dynamics, heat transfer, and structural mechanics.
Solving these systems efficiently is crucial for advancing scientific simulations.
Iterative methods are commonly employed, but their performance can be limited by hardware.

Purpose of the Study:

To compare the performance of graphics processing unit (GPU) implementations against central processing unit (CPU) and parallel cluster implementations for solving large linear systems.
To evaluate several well-known iterative methods on dense and banded systems derived from convection-dominated PDEs.
To identify the most efficient algorithm and hardware combination for these specific computational challenges.

Main Methods:

Implementation of iterative solvers (Kaczmarz's, Cimmino's, component averaging, CGNR, SSOR-PCG, CARP-CG) on GPUs.
Comparison of GPU execution times with CPU and existing parallel implementations (Linux clusters, shared memory).
Testing on dense and general banded linear systems originating from convection-dominated PDEs.

Main Results:

GPU implementations consistently outperformed CPU implementations across all tested iterative methods.
The conjugate gradient normal residual (CGNR) method, when implemented on a GPU, demonstrated superior performance compared to other methods.
The GPU-based CGNR method even surpassed a cluster implementation of the conjugate-gradient-accelerated component-averaged row projections (CARP-CG) method.

Conclusions:

GPUs offer significant performance advantages for solving large linear systems derived from PDEs, especially for strongly convection-dominated problems.
The CGNR method, despite previous trends, is highly effective on GPUs for these types of systems.
This study highlights the potential of GPU computing to accelerate scientific simulations in various engineering and physics domains.