GPU Gems 2

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Part VI: Simulation and Numerical Algorithms

Part VI: Simulation and Numerical Algorithms

Real-world computational problems have a variety of needs. Some computations, such as everyday office tasks like word processing, are inherently sequential in nature; others, such as computer graphics, physics simulation, and image processing, exhibit a large amount of data parallelism. Most applications require a mix of sequential and data-parallel computation, and modern computer systems are evolving to support these needs. The wide availability and relatively low cost of GPUs make them uniquely suited to serving the data-parallel needs of modern computing. This part of the book focuses on several examples of data-parallel computations that perform well on GPUs.

Bioinformatics and computational biology and chemistry are fast-growing areas in scientific computing. Chapter 43, "GPU Computing for Protein Structure Prediction," by Paulius Micikevicius of Armstrong Atlantic State University, presents a GPU implementation of a simple but important problem in the study of protein structure. The algorithm is highly data-parallel and is based on the well-known Floyd-Warshall all-pairs shortest-paths algorithm.

Systems of linear equations are very common in many types of problems. Chapter 44, "A GPU Framework for Solving Systems of Linear Equations," by Jens Krüger and Rüdiger Westermann of Technische Universität München, shows how to efficiently represent a variety of matrix and vector types on the GPU. Their framework provides basic operations that can be used to build up more complicated linear system solvers. As an example, they use the framework to build a conjugate gradient solver used in the simulation of the 2D wave equation.

Another growing area in parallel computing is computational finance. Investment firms currently use large clusters of processors to crunch huge amounts of data for purposes such as pricing stock options and credit derivatives. In Chapter 45, "Options Pricing on the GPU," Craig Kolb and Matt Pharr of NVIDIA describe an efficient GPU implementation of two widely used algorithms for options pricing.

Sorting is a fundamental algorithm in computer science. GPU implementation of sorting is important because when using the GPU for other parts of a computational system, even in cases where the CPU outperforms GPU-based sorting, it is more efficient to keep the data on the GPU and avoid unnecessary transfers back and forth to the CPU. In Chapter 46, "Improved GPU Sorting," Peter Kipfer and Rüdiger Westermann of Technische Universität München improve on the current state of the art in GPU-based sorting, showing how to bring as many GPU resources to bear on the problem as possible. The result is a useful and essential component for many applications.

Simulating fluid flow is important in many industries, from automotive and aerospace engineering to medicine. GPU simulation of fluids has been a popular topic for the past couple of years, because physically based simulation is a naturally data-parallel problem that maps well to the GPU architecture. Chapter 47, "Flow Simulation with Complex Boundaries," by Wei Li of Siemens Corporate Research and Zhe Fan, Xiaoming Wei, and Arie Kaufman of Stony Brook University, describes fluid simulation on the GPU using the Lattice-Boltzman technique, which models the transfer of "packets" of fluid between cells in a lattice. They also describe a novel technique for simulating the flow around arbitrary dynamic obstacles.

Electronic imaging has revolutionized how physicians diagnose and treat patients. Medical image processing is a growing field that involves large amounts of parallel computation. An essential algorithmic tool used in medical imaging (and any other type of signal processing) is the Fast Fourier Transform (FFT). Chapter 48, "Medical Image Reconstruction with the FFT," by Thilaka Sumanaweera and Donald Liu of Siemens Medical Solutions USA, presents an efficient implementation of the FFT on the GPU, including a number of insightful optimizations. Sumanaweera and Liu also describe how the FFT is used to reconstruct MRI and ultrasonic images on the GPU.

This part of the book demonstrates that GPUs are a powerful computational platform for solving a variety of data-parallel problems. The chapters included here are just a sample: many other types of computation have been implemented on GPUs, and I expect to see a wider variety, with even better performance, in the future. To keep up to date with developments in this exciting field, visit

Mark Harris, NVIDIA Corporation


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Library of Congress Cataloging-in-Publication Data

GPU gems 2 : programming techniques for high-performance graphics and general-purpose
computation / edited by Matt Pharr ; Randima Fernando, series editor.
    p. cm.
  Includes bibliographical references and index.
  ISBN 0-321-33559-7 (hardcover : alk. paper)
  1. Computer graphics. 2. Real-time programming. I. Pharr, Matt. II. Fernando, Randima.

  T385.G688 2005

GeForce™ and NVIDIA Quadro® are trademarks or registered trademarks of NVIDIA Corporation.

Nalu, Timbury, and Clear Sailing images © 2004 NVIDIA Corporation.

mental images and mental ray are trademarks or registered trademarks of mental images, GmbH.

Copyright © 2005 by NVIDIA Corporation.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior consent of the publisher. Printed in the United States of America. Published simultaneously in Canada.

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       Upper Saddle River, NJ 07458

Text printed in the United States on recycled paper at Quebecor World Taunton in Taunton, Massachusetts.

Second printing, April 2005


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