Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.Comment: 24 pages, Elsevier Journal of Computational and Applied Mathematics, Dec 201

Division of Labour and Social Coordination Modes : A simple simulation model

This paper presents a preliminary investigation of the relationship between the process of functional division of labour and the modes in which activities and plans are coordinated. We consider a very simple production process: a given heap of bank-notes has to be counted by a group of accountants. Because of limited individual capabilities and/or the possibilities of mistakes and external disturbances, the task has to be divided among several accountants and a hierarchical coordination problem arises. We can imagine several different ways of socially implementing coordination of devided tasks. 1) a central planner can compute the optimal architecture of the system; 2) a central planner can promote quantity adjustments by moving accountants from hierarchical levels where there exist idle resources to levels where resources are insufficient; 3) quasi-market mechanisms can use quantity or price signals for promoting decentralized adjustments. By means of a simple simulation model, based on Genetic Algorithms and Classifiers Systems, we can study the dynamic efficiency properties of each coordination mode and in particular their capability, speed and cost of adaptation to changing environmental situations (i.e. variations of the size of the task and/or variations of agents' capabilities). Such interesting issues as returns to scale, specialization and workers exploitation can be easily studied in the same model

Global supply chains of high value low volume products

Imperial Users onl

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System