3,490 research outputs found

    Cross-Points in Domain Decomposition Methods with a Finite Element Discretization

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    Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to be able to converge to the underlying mono-domain solution. Well known such non-overlapping methods are the Dirichlet-Neumann method, the FETI and Neumann-Neumann methods, and optimized Schwarz methods. For all these methods, cross-points in the domain decomposition configuration where more than two subdomains meet do not pose any problem at the continuous level, but care must be taken when the methods are discretized. We show in this paper two possible approaches for the consistent discretization of Neumann conditions at cross-points in a Finite Element setting

    Hybrid organizations as a strategy for supporting new product development

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    Alliances between large, well-established corporations and highly creative small companies or consultancies can be an effective method for promoting innovation

    Designing Scalable Business Models

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    Digital business models are often designed for rapid growth, and some relatively young companies have indeed achieved global scale. However despite the visibility and importance of this phenomenon, analysis of scale and scalability remains underdeveloped in management literature. When it is addressed, analysis of this phenomenon is often over-influenced by arguments about economies of scale in production and distribution. To redress this omission, this paper draws on economic, organization and technology management literature to provide a detailed examination of the sources of scaling in digital businesses. We propose three mechanisms by which digital business models attempt to gain scale: engaging both non- paying users and paying customers; organizing customer engagement to allow self- customization; and orchestrating networked value chains, such as platforms or multi-sided business models. Scaling conditions are discussed, and propositions developed and illustrated with examples of big data entrepreneurial firms

    A new Algorithm Based on Factorization for Heterogeneous Domain Decomposition

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    Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection reaction diffusion type a heterogeneous domain decomposition algorithm which allows us to recover a solution that is very close to the solution of the fully viscous problem, but solves only an inviscid problem in parts of the domain. Our new algorithm is based on the factorization of the underlying differential operator, and we therefore call it factorization algorithm. We give a detailed error analysis, and show that we can obtain approximations in the viscous region which are much closer to the viscous solution in the entire domain of simulation than approximations obtained by other heterogeneous domain decomposition algorithms from the literature.Comment: 23 page

    Optimized Schwarz Methods for Maxwell equations

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    Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for which overlap is essential for convergence. Over the last decade, optimized Schwarz methods have been developed for elliptic partial differential equations. These methods use more effective transmission conditions between subdomains, and are also convergent without overlap for elliptic problems. We show here why the classical Schwarz method applied to the hyperbolic problem converges without overlap for Maxwell's equations. The reason is that the method is equivalent to a simple optimized Schwarz method for an equivalent elliptic problem. Using this link, we show how to develop more efficient Schwarz methods than the classical ones for the Maxwell's equations. We illustrate our findings with numerical results
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