Browsing by Author "Sun, Kai"

Now showing 1 - 3 of 3
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    Model order reduction and domain decomposition for large-scale dynamical systems
    (2008) Sun, Kai; Sorensen, Danny
    Domain decomposition and model order reduction are both very important techniques for scientific and engineering computing. Their goals are both trying to speed up computations, however by different approaches. Domain decomposition is based on the general concept of divide-and-conquer which partitions a large-scale problem into a sequence of smaller and easy-to-solve problems. Model order reduction tries to relieve the simulation loads of dynamical systems by reducing the size of the systems dramatically. In this thesis, I investigate some problems arising from these two areas and propose some potential applications of them. At first, I give a sensitivity analysis of Smith method via iterative solvers. Smith method is a very important for balance truncation model order reduction. Secondly, we introduce a new effective approach to compute the reduced order model based on balanced truncation for a class of descriptor systems. Computational results were presented which indicate this new approach is promising and very efficient computationally. Thirdly, by combining balanced truncation model order reduction and domain decomposition techniques together, the reduced order models for systems of discretized partial differential equations with a spatially localized nonlinearities is derived. Finally, I present fully parallel domain decomposition techniques for another kind of problems, fast simulations of large-scale linear circuits such as power grids.
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    Spatial domain decomposition and model reduction for parabolic optimal control problems
    (2006) Sun, Kai; Sorensen, Danny C.
    In this thesis, we propose a spatial domain decomposition method and model reduction techniques for the solution of linear-quadratic parabolic optimal control problems. Such problems arise directly from many applications such as the data assimilation, circuit design and oil reservoir modeling. The motivation for this work is threefold. First, we attempt to address the storage issue in numerically solving the parabolic optimal control problem. Secondly, spatial domain decomposition leads to parallelism. Therefore, data can be decomposed uniformly by assigning subdomains to each processor. Finally, for large-scale problems, the subproblems on the subdomains are still very large. Model reduction techniques applied to the subproblems are expected to dramatically reduce the size of the subproblems and save computational time.
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    The optimal use of management
    (Wiley, 2021) Sickles, Robin C.; Sun, Kai; Triebs, Thomas P.
    We analyze the management input from the perspective of shadow cost minimization. Using Bloom and Van Reenen's management measure, we estimate management's shadow price, dual Morishima elasticities of substitution, and relative price efficiencies. We find that the shadow price of management is about 1.3 million US dollars. Management is a weak dual complement for labor but a strong dual complement for capital. Increases in management reduce the relative income share of labor but not capital. Most firms use too little management, but relative use of management improves over time, with the combination of ownership and control, and competition.