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.

Many of today's complex scientific applications now require a vast amount of computational power. General purpose graphics processing units (GPGPUs) enable researchers in a variety of fields to benefit from the computational power of all the cores available inside graphics cards.Understand the Benefits of Using GPUs for Many Scientific Applications

More useful techniques, tips, and tricks for harnessing the power of the new generation of powerful GPUs.

Many of today’s complex scientific applications now require a vast amount of computational power. General purpose graphics processing units (GPGPUs) enable researchers in a variety of fields to benefit from the computational power of all the cores available inside graphics cards. Understand the Benefits of Using GPUs for Many Scientific Applications Designing Scientific Applications on GPUs shows you how to use GPUs for applications in diverse scientific fields, from physics and mathematics to computer science. The book explains the methods necessary for designing or porting your scientific application on GPUs. It will improve your knowledge about image processing, numerical applications, methodology to design efficient applications, optimization methods, and much more. Everything You Need to Design/Port Your Scientific Application on GPUs The first part of the book introduces the GPUs and Nvidia’s CUDA programming model, currently the most widespread environment for designing GPU applications. The second part focuses on significant image processing applications on GPUs. The third part presents general methodologies for software development on GPUs and the fourth part describes the use of GPUs for addressing several optimization problems. The fifth part covers many numerical applications, including obstacle problems, fluid simulation, and atomic physics models. The last part illustrates agent-based simulations, pseudorandom number generation, and the solution of large sparse linear systems for integer factorization. Some of the codes presented in the book are available online.

This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on High Performance Computing for Computational Science, VECPAR 2006, held in Rio de Janeiro, Brazil, in June 2006. The 44 revised full papers presented together with one invited paper and 12 revised workshop papers cover Grid computing, cluster computing, numerical methods, large-scale simulations in Physics, and computing in Biosciences.

An In-Depth, Practical Guide to GPGPU Programming Using Direct3D 11 GPGPU Programming for Games and Science demonstrates how to achieve the following requirements to tackle practical problems in computer science and software engineering: Robustness Accuracy Speed Quality source code that is easily maintained, reusable, and readable The book primarily addresses programming on a graphics processing unit (GPU) while covering some material also relevant to programming on a central processing unit (CPU). It discusses many concepts of general purpose GPU (GPGPU) programming and presents practical examples in game programming and scientific programming. The author first describes numerical issues that arise when computing with floating-point arithmetic, including making trade-offs among robustness, accuracy, and speed. He then shows how single instruction multiple data (SIMD) extensions work on CPUs since GPUs also use SIMD. The core of the book focuses on the GPU from the perspective of Direct3D 11 (D3D11) and the High Level Shading Language (HLSL). This chapter covers drawing 3D objects; vertex, geometry, pixel, and compute shaders; input and output resources for shaders; copying data between CPU and GPU; configuring two or more GPUs to act as one; and IEEE floating-point support on a GPU. The book goes on to explore practical matters of programming a GPU, including code sharing among applications and performing basic tasks on the GPU. Focusing on mathematics, it next discusses vector and matrix algebra, rotations and quaternions, and coordinate systems. The final chapter gives several sample GPGPU applications on relatively advanced topics. Web Resource Available on a supporting website, the author’s fully featured Geometric Tools Engine for computing and graphics saves you from having to write a large amount of infrastructure code necessary for even the simplest of applications involving shader programming. The engine provides robust and accurate source code with SIMD when appropriate and GPU versions of algorithms when possible.

The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11973, consists of 34 full and 18 short papers chosen among papers presented at special streams and sessions of the Conference. The papers in part I were organized following the topics of these special sessions: approximation: methods, algorithms, and applications; computational methods for data analysis; first order methods in optimization: theory and applications; high performance computing in modelling and simulation; numbers, algorithms, and applications; optimization and management of water supply.

Micromagnetics is a field of study considering the magnetization behavior in magnetic materials and devices accounting for a wide set of interactions and describing the magnetization phenomena from the atomistic scale to several hundreds of microns. Micromagnetic simulations are essential in understanding the behavior of many magnetic systems. Modeling complex structures can require a significant computational time and in some cases, the system complexity can make simulations prohibitively long or require a prohibitively large memory. In this thesis, we present a set of methods and their implementations that resulted in high-performance numerical micromagnetic tools for modeling highly complex magnetic materials and devices. The focus of the dissertation is on solving Landau-Lifshitz-Gilbert (LLG) equation efficiently, both with numerical methods and advanced hardware acceleration. To understand the numerical problem to be solved, the introduction Chapter 1 addresses the LLG equation and the governing interactions involved as well as numerical modeling basics on the Finite Difference Method (FDM) and the Finite Element Method (FEM). Chapter 1 also presents a versatile micromagnetic framework, referred to as FastMag, which implements some of these methods. Chapter 2 provides a detailed description of computing based on Graphics Processing Units (GPUs). The history of GPU programming model and the programming tips serve as the basis for understanding parallel computing on GPUs. It presents applications of GPUs on various platforms to demonstrate the current mainstream usage of GPUs and their promising future development direction. Chapter 2 also summarizes applications of GPUs in micromagnetics. Chapters 3 and 4 address two essential aspects of micromagnetic solvers: fast algorithms for computing the key interaction components and efficient time integration methods. Chapter 3 introduces a non-uniform Fourier transform (NUFFT) method, a scalar potential method, and sparse matrix-vector multiplication (SpMVM) algorithms implemented on GPUs to accelerate the magnetostatic and exchange interactions. Chapter 4 addresses basics of the time integration methods used in FastMag as well as a preconditioner to further accelerate the time integration process. Chapter 5 presents a numerical model for the current state-of-art magnetic recording system using advanced algorithms and GPU implementations described in Chapters 2-4.

This book presents a collection of state of the art research on GPU Computing and Application. The major part of this book is selected from the work presented at the 2013 Symposium on GPU Computing and Applications held in Nanyang Technological University, Singapore (Oct 9, 2013). Three major domains of GPU application are covered in the book including (1) Engineering design and simulation; (2) Biomedical Sciences; and (3) Interactive & Digital Media. The book also addresses the fundamental issues in GPU computing with a focus on big data processing. Researchers and developers in GPU Computing and Applications will benefit from this book. Training professionals and educators can also benefit from this book to learn the possible application of GPU technology in various areas.

High-performance system architectures are increasingly exploiting heterogeneity. The HipHaC workshop aims at combining new aspects of parallel, heterogeneous, and reconfigurable microprocessor technologies with concepts of high-performance computing and, particularly, numerical solution methods. Compute- and memory-intensive applications can only benefit from the fullhardware potential if all features on all levels are taken into account in a holistic approach.