36,549 research outputs found
Stencils and problem partitionings: Their influence on the performance of multiple processor systems
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
Parallel, iterative solution of sparse linear systems: Models and architectures
A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed
Verification of the proteus two-dimensional Navier-Stokes code for flat plate and pipe flows
The Proteus Navier-Stokes Code is evaluated for 2-D/axisymmetric, viscous, incompressible, internal, and external flows. The particular cases to be discussed are laminar and turbulent flows over a flat plate, laminar and turbulent developing pipe flows, and turbulent pipe flow with swirl. Results are compared with exact solutions, empirical correlations, and experimental data. A detailed description of the code set-up, including boundary conditions, initial conditions, grid size, and grid packing is given for each case
A model of asynchronous iterative algorithms for solving large, sparse, linear systems
Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension
Kinetics of the photosubstitution of cis-bis(benzonitrile)dichloroplatinum(II) in chloroform
Under 254 nm irradiation cis-[Pt(C6H5CN)2Cl2] is converted to H2PtCl6. Absorption of light by both the metal complex and the solvent contribute to the first step of this process, suggested to form HPt(C6H5CN) Cl3. A linear dependence of the reaction rate on light intensity appears to rule out chlorination by trichloromethyl radicals. However, at higher light intensities a higher order dependence on intensity develops, and under 313 nm irradiation is dominant, and a reaction between trichloromethyl radical and the excited state complex is proposed to account for this
Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
Integral functionals based on convex normal integrands are minimized subject
to finitely many moment constraints. The integrands are finite on the positive
and infinite on the negative numbers, strictly convex but not necessarily
differentiable. The minimization is viewed as a primal problem and studied
together with a dual one in the framework of convex duality. The effective
domain of the value function is described by a conic core, a modification of
the earlier concept of convex core. Minimizers and generalized minimizers are
explicitly constructed from solutions of modified dual problems, not assuming
the primal constraint qualification. A generalized Pythagorean identity is
presented using Bregman distance and a correction term for lack of essential
smoothness in integrands. Results are applied to minimization of Bregman
distances. Existence of a generalized dual solution is established whenever the
dual value is finite, assuming the dual constraint qualification. Examples of
`irregular' situations are included, pointing to the limitations of generality
of certain key results
[N]pT Monte Carlo Simulations of the Cluster-Crystal-Forming Penetrable Sphere Model
Certain models with purely repulsive pair interactions can form cluster
crystals with multiply-occupied lattice sites. Simulating these models'
equilibrium properties is, however, quite challenging. Here, we develop an
expanded isothermal-isobaric ensemble that surmounts this problem by
allowing both particle number and lattice spacing to fluctuate. We apply the
method with a Monte Carlo simulation scheme to solve the phase diagram of a
prototypical cluster-crystal former, the penetrable sphere model (PSM), and
compare the results with earlier theoretical predictions. At high temperatures
and densities, the equilibrium occupancy of
face-centered cubic (FCC) crystal increases linearly. At low temperatures,
although plateaus at integer values, the crystal
behavior changes continuously with density. The previously ambiguous crossover
around is resolved
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