Numerical Computations with GPUs

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.

Table of Contents

Part I Linear Algebra
Chapter 1 Accelerating Numerical Dense Linear Algebra Calculations with GPUs
Chapter 2 A Guide for Implementing Tridiagonal Solvers on GPUs
Chapter 3 Batch Matrix Exponentiation
Chapter 4 Efficient Batch LU and QR Decomposition on GPU
Chapter 5 A Flexible CUDA LU-Based Solver for Small, Batched Linear Systems
Chapter 6 Sparse Matrix-Vector Product

Part II Differential Equations
Chapter 7 Solving Ordinary Differential Equations on GPUs
Chapter 8 GPU-Based Parallel Integration of Large Numbers of Independent ODE Systems
Chapter 9 Finite and Spectral Element Methods on Unstructured Grids for Flow and Wave Propagation Problems
Chapter 10 A GPU Implementation for Solving the Convection Diffusion Equation Using the Local Modified SOR Method
Chapter 11 Finite-Difference in Time-Domain Scalable Implementations on CUDA and OpenCL

Part III Random Numbers and Monte Carlo Methods
Chapter 12 Pseudorandom Numbers Generation for Monte Carlo Simulations on GPUs: OpenCL Approach
Chapter 13 Monte Carlo Automatic Integration with Dynamic Parallelism in CUDA
Chapter 14 GPU: Accelerated Computation Routines for Quantum Trajectories Method
Chapter 15 Monte Carlo Simulation of Dynamic Systems on GPU’s

Part IV Fast Fourier Transform and Localized n-Body Problems
Chapter 16 Fast Fourier Transform (FFT) on GPUs
Chapter 17 A Highly Efficient FFT Using Shared-Memory Multiplexing
Chapter 18 Increasing Parallelism and Reducing Thread Contentions in Mapping Localized N-Body Simulations to GPUs