high performance computing on graphics processing units: hgpu.org

One of the key challenges in Computational Science is closing the gap between the available computer power and its effective utilization for the simulation of complex physical systems and engineering applications. In order to achieve this goal we must minimize the time-to-solution and the related energy requirements of simulations by developing scalable software and methods that achieve a prescribed accuracy with a minimum number of computational elements. These two objectives are in conflict as adaptive methods do not readily translate into scalable software with high computational efficiency. In this thesis we address both objectives by integrating the development of multiresolution discretization methods for non-linear partial differential equations and their implementation on multicore CPU and GPU architectures. These algorithms are in turn applied to the simulation of challenging fluid dynamics phenomena which are exemplary in their computational complexity for the broader field of Computational Science. What makes the simulation of fluid fows so challenging? Fluid flows evolve by the interaction of vortical structures with multiple spatial and temporal scales. The economy of accurately simulating vortex dynamics dictates multiresolution computational methods, since the small size of elements devoted to either the near-wall region of bluff body flows or around shocks is not necessary for tracking smoother vortical structures in the flow field. We develop grid- and particle-based methods to effectively resolve these flows that rely on wavelet-based multiresolution representations. The development of adaptive, multiresolution discretization methods entails complex data structures that do not readily render themselves to parallelization on multicore CPUs and GPUs. This thesis presents highly competitive techniques to effectively map wavelet-based multiresolution numerical methods onto multicore and heterogeneous multi-GPU/CPU systems. We develop scalable software and present simulations of bluff body and multiphase compressible flows at unprecedented resolution and minimum time-to-solution, enabling previously unattainable physical insight and fast engineering calculations.