Many important algorithms in fields such as image processing or physical simulation necessitate solving systems of partial differential equations. Multigrid methods belong to the fastest and most versatile numerical schemes available for this purpose. With the advent of programmable graphics processing units (GPUs) there have been numerous efforts to use their capabilities - massively parallel floating point computation and high memory bandwidth - in high performance computing. In this work, multigrid methods are evaluated for their suitability towards a GPU implementation. After some introductory material on general purpose GPU programming and a short mathematical overview, a multigrid solver for the 2D Poisson equation built on C++, OpenGL and GLSL is presented in detail. The performance of various implementation techniques is benchmarked and interpreted, a number of optimization strategies are tested and the final results are compared across different hardware platforms and to a traditional CPU-based implementation. This book is aimed at scientists and programmers interested in using the potential of GPUs to speed up their multigrid-based numerical solvers. Skryť popis