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The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show that it is possible to decouple the sparse matrix problem posed by KPM from main memory bandwidth both on CPU and GPU. To alleviate the effects of scattered data access we combine loosely coupled outer iterations with tightly coupled block sparse matrix multiple vector operations, which enables pure data streaming. All optimizations are guided by a performance analysis and modelling process that indicates how the computational bottlenecks change with each optimization step. Finally we use the optimized node-level KPM with a hybrid-parallel framework to perform large scale heterogeneous electronic structure calculations for novel topological materials on a petascale-class Cray XC30 system.

The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show that it is possible to decouple the sparse matrix problem posed by KPM from main memory bandwidth both on CPU and GPU. To alleviate the effects of scattered data access we combine loosely coupled outer iterations with tightly coupled block sparse matrix multiple vector operations, which enables pure data streaming. All optimizations are guided by a performance analysis and modelling process that indicates how the computational bottlenecks change with each optimization step. Finally we use the optimized node-level KPM with a hybrid-parallel framework to perform large scale heterogeneous electronic structure calculations for novel topological materials on a petascale-class Cray XC30 system.

This paper discusses some methodological considerations in the design of large scale systems engineering processes. We begin our effort by providing several definitions of system engineering. There are a number of impediments to the resolution of large scale issues in the public and private sectors and it is important that designers of appropriate and useful systems be aware of these. Following a discussion of these impediments, we present a structure describing the systems engineering process. This is used to motivate discussion of the functional considerations involved in a systemic process: systems science and operations research, systems methodology and design, and systems management. A brief discussion of methods for formulation, analysis an interpretation is followed by a discussion of systems management and the associated use of human judgement for the design of systemic processes. We believe the contingency task structure of systems management to be an especially useful guideline for the design of information systems for planning and decision support. We give a number of reasons supporting this belief and present a model for information aquisition and information evaluation based on our contingency task structure. A discussion of systems engineering in the political process and implications for professional practice is followed by delineation of the many potential benefits of the systems process. (Author)