16,928 research outputs found

    Domain decomposition algorithms and computation fluid dynamics

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    In the past several years, domain decomposition was a very popular topic, partly motivated by the potential of parallelization. While a large body of theory and algorithms were developed for model elliptic problems, they are only recently starting to be tested on realistic applications. The application of some of these methods to two model problems in computational fluid dynamics are investigated. Some examples are two dimensional convection-diffusion problems and the incompressible driven cavity flow problem. The construction and analysis of efficient preconditioners for the interface operator to be used in the iterative solution of the interface solution is described. For the convection-diffusion problems, the effect of the convection term and its discretization on the performance of some of the preconditioners is discussed. For the driven cavity problem, the effectiveness of a class of boundary probe preconditioners is discussed

    Domain-decomposed preconditionings for transport operators

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    The performance was tested of five different interface preconditionings for domain decomposed convection diffusion problems, including a novel one known as the spectral probe, while varying mesh parameters, Reynolds number, ratio of subdomain diffusion coefficients, and domain aspect ratio. The preconditioners are representative of the range of practically computable possibilities that have appeared in the domain decomposition literature for the treatment of nonoverlapping subdomains. It is shown that through a large number of numerical examples that no single preconditioner can be considered uniformly superior or uniformly inferior to the rest, but that knowledge of particulars, including the shape and strength of the convection, is important in selecting among them in a given problem

    Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

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    Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

    A unified multilevel framework of upscaling and domain decomposition

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    We consider multiscale preconditioners for a class of mass-conservative domain-decomposition (MCDD) methods. For the application of reservoir simulation, we need to solve large linear systems, arising from finite-volume discretisations of elliptic PDEs with highly variable coefficients. We introduce an algebraic framework, based on probing, for constructing mass-conservative operators on a multiple of coarse scales. These operators may further be applied as coarse spaces for additive Schwarz preconditioners. By applying different local approximations to the Schur complement system based on a careful choice of probing vectors, we show how the MCDD preconditioners can be both efficient preconditioners for iterative methods or accurate upscaling techniques for the heterogeneous elliptic problem. Our results show that the probing technique yield better approximation properties compared with the reduced boundary condition commonly applied with multiscale methods

    A multiblock grid generation technique applied to a jet engine configuration

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    Techniques are presented for quickly finding a multiblock grid for a 2D geometrically complex domain from geometrical boundary data. An automated technique for determining a block decomposition of the domain is explained. Techniques for representing this domain decomposition and transforming it are also presented. Further, a linear optimization method may be used to solve the equations which determine grid dimensions within the block decomposition. These algorithms automate many stages in the domain decomposition and grid formation process and limit the need for human intervention and inputs. They are demonstrated for the meridional or throughflow geometry of a bladed jet engine configuration

    A unified multilevel framework of upscaling and domain decomposition

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    Presented at CMWR 2010 - XVIII International Conference on Computational Methods in Water Resources, June 21-24, 2010, Barcelona, SpainWe consider multiscale preconditioners for a class of mass-conservative domain-decomposition (MCDD) methods. For the application of reservoir simulation, we need to solve large linear systems, arising from finite-volume discretisations of elliptic PDEs with highly variable coefficients. We introduce an algebraic framework, based on probing, for constructing mass-conservative operators on a multiple of coarse scales. These operators may further be applied as coarse spaces for additive Schwarz preconditioners. By applying different local approximations to the Schur complement system based on a careful choice of probing vectors, we show how the MCDD preconditioners can be both efficient preconditioners for iterative methods or accurate upscaling techniques for the heterogeneous elliptic problem. Our results show that the probing technique yield better approximation properties compared with the reduced boundary condition commonly applied with multiscale methods.publishedVersio

    Compressed absorbing boundary conditions via matrix probing

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    Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer-stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose to bypass the elimination procedure, and directly fit the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter.Comment: 29 pages with 25 figure

    Cross-Layer Peer-to-Peer Track Identification and Optimization Based on Active Networking

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    P2P applications appear to emerge as ultimate killer applications due to their ability to construct highly dynamic overlay topologies with rapidly-varying and unpredictable traffic dynamics, which can constitute a serious challenge even for significantly over-provisioned IP networks. As a result, ISPs are facing new, severe network management problems that are not guaranteed to be addressed by statically deployed network engineering mechanisms. As a first step to a more complete solution to these problems, this paper proposes a P2P measurement, identification and optimisation architecture, designed to cope with the dynamicity and unpredictability of existing, well-known and future, unknown P2P systems. The purpose of this architecture is to provide to the ISPs an effective and scalable approach to control and optimise the traffic produced by P2P applications in their networks. This can be achieved through a combination of different application and network-level programmable techniques, leading to a crosslayer identification and optimisation process. These techniques can be applied using Active Networking platforms, which are able to quickly and easily deploy architectural components on demand. This flexibility of the optimisation architecture is essential to address the rapid development of new P2P protocols and the variation of known protocols
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