Numerical Computations with GPUs

1. Front Matter

   Pages i-x

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2. Linear Algebra

   1. Front Matter

      Pages 1-1

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   2. Accelerating Numerical Dense Linear Algebra Calculations with GPUs

      • Jack Dongarra, Mark Gates, Azzam Haidar, Jakub Kurzak, Piotr Luszczek, Stanimire Tomov et al.

      Pages 3-28

   3. A Guide for Implementing Tridiagonal Solvers on GPUs

      • Li-Wen Chang, Wen-mei W. Hwu

      Pages 29-44

   4. Batch Matrix Exponentiation

      • M. Graham Lopez, Mitchel D. Horton

      Pages 45-67

   5. Efficient Batch LU and QR Decomposition on GPU

      • William J. Brouwer, Pierre-Yves Taunay

      Pages 69-86

   6. A Flexible CUDA LU-Based Solver for Small, Batched Linear Systems

      • Antonino Tumeo, Nitin Gawande, Oreste Villa

      Pages 87-101

   7. Sparse Matrix-Vector Product

      • Zbigniew Koza, Maciej Matyka, Łukasz Mirosław, Jakub Poła

      Pages 103-121

3. Differential Equations

   1. Front Matter

      Pages 123-123

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   2. Solving Ordinary Differential Equations on GPUs

      • Karsten Ahnert, Denis Demidov, Mario Mulansky

      Pages 125-157

   3. GPU-Based Parallel Integration of Large Numbers of Independent ODE Systems

      • Kyle E. Niemeyer, Chih-Jen Sung

      Pages 159-182

   4. Finite and Spectral Element Methods on Unstructured Grids for Flow and Wave Propagation Problems

      • Dominik Göddeke, Dimitri Komatitsch, Matthias Möller

      Pages 183-206

   5. A GPU Implementation for Solving the Convection Diffusion Equation Using the Local Modified SOR Method

      • Yiannis Cotronis, Elias Konstantinidis, Nikolaos M. Missirlis

      Pages 207-221

   6. Finite-Difference in Time-Domain Scalable Implementations on CUDA and OpenCL

      • Lídia Kuan, Pedro Tomás, Leonel Sousa

      Pages 223-242

4. Random Numbers and Monte Carlo Methods

   1. Front Matter

      Pages 243-243

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   2. Pseudorandom Numbers Generation for Monte Carlo Simulations on GPUs: OpenCL Approach

      • Vadim Demchik

      Pages 245-271

   3. Monte Carlo Automatic Integration with Dynamic Parallelism in CUDA

      • Elise de Doncker, John Kapenga, Rida Assaf

      Pages 273-298

   4. GPU: Accelerated Computation Routines for Quantum Trajectories Method

      • Joanna Wiśniewska, Marek Sawerwain

      Pages 299-318

   5. Monte Carlo Simulation of Dynamic Systems on GPU’s

      • Jonathan Rogers

      Pages 319-336

5. Fast Fourier Transform and Localized n-Body Problems

   1. Front Matter

      Pages 337-337

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This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to reusable, adaptable and scalable code fragments. This book also serves as a GPU implementation manual for many numerical algorithms, sharing tips on GPUs that can increase application efficiency. The valuable insights into parallelization strategies for GPUs are supplemented by ready-to-use code fragments. Numerical Computations with GPUs targets professionals and researchers working in high performance computing and GPU programming. Advanced-level students focused on computer science and mathematics will also find this book useful as secondary text book or reference.

• Differential equations
• GPUs
• Iterative solvers
• Linear algebra
• Monte Carlo
• Numerical methods
• Parallel algorithms
• Random number generators

From the book reviews:

“This book attempts to provide some guidance for researchers who develop HPC codes and want to run them on GPU-based systems. … The intended readership consists of people who already have a certain amount of experience in working with GPUs … . For readers with such a background, it will prove to be useful reading.” (Kai Diethelm, Computing Reviews, November, 2014)

• National Center for Supercomputing Applications, University of Illinois, Urbana, USA

  Volodymyr Kindratenko

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