High Performance Computing (HPC) aims at providing reasonably fast computing solutions to both scientific and real life technical problems. Many efforts have indeed been made on the way to powerful supercomputers, both generic and customized configurations. However, whatever their current and future breathtaking capabilities, supercomputers work by brute force and deterministic steps, while human mind works by few strokes of brilliance. Thus, in order to take a significant advantage of hardware advances, we need powerful methods to solve problems together with highly skillful programming efforts and relevant frameworks. The advent of multicore architectures is noteworthy in the HPC history, because it has brought the underlying concept of multiprocessing into common consideration and has changed the landscape of standard computing. At a larger scale, there is a keen desire to build or host frontline supercomputers. The yearly Top500 ranking nicely illustrates and orchestrates this supercomputers saga. For many years, computers have been falling in price while gaining processing power often strengthened by specialized accelerator units. We clearly see that what commonly springs up in mind when it comes to HPC is computer capability. However, this availability of increasingly fast computers has changed the rule of scientific discovery and has motivated the consideration of challenging applications. Thus, we are routinely at the door of large-scale problems, and most of time, the speed of calculation by itself is no longer sufficient. Indeed, the real concern of HPC users is the time-to-output. Thus, we need to study each important aspect in the critical path between inputs and outputs, and keep striving to reach the expected level of performance. This is the main concern of the viewpoints and the achievements reported in this book. The document is organized into five chapters articulated around our main contributions. The first chapter depicts the landscape of supercomputers, comments the need for tremendous processing speed, and analyze the main trends in supercomputing. The second chapter deals with solving large-scale combinatorial problems through a mixture of continuous and discrete optimization methods, we describe the main generic approaches and present an important framework on which we have been working so far. The third chapter is devoted to the topic accelerated computing, we discuss the motivations and the issues, and we describe three case studies from our contributions. In chapter four, we address the topic of energy minimization in a formal way and present our method based on a mathematical programming approach. Chapter five debates on hybrid supercomputing, we discuss technical issues with hierarchical shared memories and illustrate hybrid coding through a large-scale linear algebra implementation on a supercomputer.

Topographic depressions are naturally occurring low land areas surrounded by areas of high elevations, also known as “pits” or “sinks”, on terrain surfaces. Traditional watershed modeling often neglects the potential effects of depressions by implementing removal (mostly filling) procedures on the digital elevation model (DEM) prior to the simulation of physical processes. The assumption is that all the depressions are either spurious in the DEM or of negligible importance for modeling results. However, studies suggested that naturally occurring depressions can change runoff response and connectivity in a watershed based on storage conditions and their spatial arrangement, e.g., shift active contributing areas and soil moisture distributions, and timing and magnitude of flow discharge at the watershed outlet. In addition, recent advances in remote sensing techniques, such as LiDAR, allow us to examine this modeling assumption because naturally occurring depressions can be represented using high-resolution DEM. This dissertation provides insights on the effects of depressions on overland flow processes at multiple spatial scales, from internal depression areas to the watershed scale, based on hydrologic connectivity metrics. Connectivity describes flow pathway connectedness and is assessed using geostatistical measures of heterogeneity in overland flow patterns, i.e., connectivity function and integral connectivity scale lengths. A new algorithm is introduced here to upscale connectivity metrics to large gridded patterns (i.e., with > 1,000,000 cells) using GPU-accelerated computing. This new algorithm is sensitive to changes of connectivity directions and magnitudes in spatial patterns and is robust for large DEM grids with depressions. Implementation of the connectivity metrics to overland flow patterns generated from original and depression filled DEMs for a study watershed indicates that depressions typically decrease overland flow connectivity. A series of macro connectivity stages based on spatial distances are identified, which represent changes in the interaction mechanisms between overland flow and depressions, i.e., the relative dominance of fill and spill, and the relative speed of fill and formation of connected pathways. In addition, to study the role of spatial resolutions on such interaction mechanisms at watershed scale, two revised functional connectivity metrics are also introduced, based on depressions that are hydraulically connected to the watershed outlet and runoff response to rainfall. These two functional connectivity metrics are sensitive to connectivity changes in overland flow patterns because of depression removal (filling) for DEMs at different grid resolutions. Results show that these two metrics indicate the spatial and statistical characteristics of depressions and their implications on overland flow connectivity, and may also relate to storage and infiltration conditions. In addition, grid resolutions have a more significant impact on overland flow connectivity than depression removal (filling).