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It is worth noting that the expected values for each successive cut do not differ signi cantly. If expected value were the key issue, the second cut would provide all the precision needed and the rst cut would suf ce for many purposes. The difference in expected values between cuts is a function of the skew or asymmetry of the distribution, which is modest in this case. Extreme skew would make more intervals more desirable. It is worth noting that the variance (spread) increases as more detail is provided. This is a deliberate aspect of the process design, as noted earlier. It is also worth noting that the third cut provides all the precision needed for most purposes in terms of variance. Further, it is worth noting that any probability distribution shape can be captured to whatever level of precision is required by using more intervals: the simple scenario approach involves no restrictive assumptions at all and facilitates a trade-off between precision and effort that is clear and transparent. A range of well-known, alternative approaches to providing more detailed estimates are available, which may or may not help in a given situation. Some of these approaches are considered below.

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The consultant determined the approximate base load of the equipment in the proposed data center and suggested a raised floor design. The floor area was divided into functional areas such as NOC area, equipment staging area, network room, and data center area, which would have rack rows containing servers, storage, and other devices. Some floor area near the entrance was marked for large floor-standing servers and storage subsystems (which are not designed for racks). The consultant suggested a redundant three-phase UPS system and powerdistribution unit, backed by a diesel generator. The generator was located just outside the data center with exhausts facing away from the building. For redundancy, the data center had two power feeds from different grids. The HVAC unit was designed to be redundant. It had two units and subfloor air distribution systems. The return-air ducts were located in the ceiling

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timescale to only the time intervals that require it SAMR is based on block-structured re nements overlaid on a structured coarse grid, and provide an alternative to the general, unstructured AMR approach [5, 6] SAMR techniques have been widely used to solve complex systems of PDEs that exhibit localized features in varied domains, including computational uid dynamics, numerical relativity, combustion simulations, subsurface modeling, and oil reservoir simulation [1, 2, 7, 8] However, due to their dynamism and space time heterogeneity, scalable parallel implementation of SAMR applications remains a challenge This chapter presents the requirement analysis, design, and implementation of the GrACE (grid adaptive computational engine) framework and its associated runtime management strategies for SAMR applications GrACE provides easy-to-use application programming interfaces (API) and libraries for parallel programming, execution, visualization, and simulation.

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Furthermore, it offers a suite of extensible features and algorithms to support parallel and ef cient runtime management of large-scale SAMR applications in thousands of processors The development of GrACE follows a system engineering approach The term system engineering was carefully chosen to distinguish the development process we propose as appropriate for the development of high-performance computing software from the conventional software engineering development process High-performance systems are typically quite different from these information management systems They are often of only modest size by commercial standards but often have a high degree of internal complexity HPC applications are usually developed by small teams or even individuals There is no commodity implementation infrastructure to be used The execution environments are state-of-the-art, rapidly changing, frequently parallel computer system architectures The hardware execution environments are often novel architectures and for which there is little conventional wisdom concerning building programs that execute ef ciently.

These execution environments change much more rapidly than is the case for large commercially oriented systems The end-user requirements for HPC software systems typically evolve much more rapidly because they are used in research environments rather than in production environments There are often many variants of solution algorithms Time for endto-end execution (absolute performance) is usually the most critical property with adaptability to a multiplicity of applications and portability across the rapidly evolving platforms being other important issues Reuse of previously written code is also often desired The complexity of HPC systems primarily arises from the requirements of the applications for data management If HPC is to become an effective discipline, we must document good practice so that best practice can be identi ed This is particularly true for developers in infrastructure systems that are intended to be used by a broad community of users.

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