12,240 research outputs found

    Stencils and problem partitionings: Their influence on the performance of multiple processor systems

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    Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems

    Smooth-Particle Phase Stability with density and density-gradient potentials

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    Stable fluid and solid particle phases are essential to the simulation of continuum fluids and solids using Smooth Particle Applied Mechanics. We show that density-dependent potentials, such as Phi=(1/2)Sum (rho-rho_0)^2, along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that a special stabilization potential, Phi=(1/2)Sum (delrho)^2, not only stabilizes crystalline solid phases (or meshes) but also provides a surface tension which is missing in the usual density-dependent-potential approach. We illustrate these ideas for two-dimensional square, triangular, and hexagonal lattices.Comment: 10 pages, 5 figure
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