We have recently designed a set of Fortran language extensions, called Opus, that allow for integrated support of task and data parallelism. The language introduces a new mechanism, shared data abstractions (SDAs) for...
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An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overheads, and is...
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An implicit, method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved ...
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This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integ...
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In this Brief Communication, we first note the strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation. We then applied the MHD phenomenologies of Krai...
In this Brief Communication, we first note the strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation. We then applied the MHD phenomenologies of Kraichnan [Phys. Fluids 8, 1385 (1965)] and Matthaeus and Zhou [Phys. Fluids B 1, 1929 (1989)] to rotating turbulence. We deduced a ''rule'' that relates spectral transfer time to the eddy turnover time and the time scale for decay of the triple correlations. Our hypothesis on the triple correlation decay rate leads to the spectral law, which varies between the ''-5/3'' (without rotation) and ''-2'' laws (with strong rotation). For intermediate rotation rates, the spectrum varies according to the value of a dimensionless parameter that measures the strength of the rotation wave number k(Omega)=Omega(3)/epsilon)(1/2) relative to the wave number k. The eddy viscosity is derived with an explicitly dependence on the rotation rate. (C) 1995 American institute of Physics.
Multigrid (MG) algorithms for large-scale eigenvalue problems (EP), obtained from discretizations of partial differential EP, have often been shown to be more efficient than single level eigenvalue algorithms. This pa...
Multigrid (MG) algorithms for large-scale eigenvalue problems (EP), obtained from discretizations of partial differential EP, have often been shown to be more efficient than single level eigenvalue algorithms. This paper describes a robust and efficient, adaptive MG eigenvalue algorithm. The robustness of the present approach is a result of a combination of MG techniques introduced here, i.e., the completion of clusters; the adaptive treatment of clusters; the simultaneous treatment of solutions in each cluster; the miltigrid projection (MGP) coupled with backrotations; and robustness tests. Due to the MGP, the algorithm achieves a better computational complexity and better convergence rates than previous MG eigenvalue algorithms that use only fine level projections. These techniques overcome major computational difficulties related to equal and closely clustered eigenvalues. Some of these difficulties were not treated in previous MG algorithms. Computational examples for the Schrödinger eigenvalue problem in two and three dimensions are demonstrated for cases of special computational difficulties, which are due to equal and closely clustered eigenvalues. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N, using a second order approximation. The total computational cost is equivalent to only a few Gause-Seidel relaxations per eigenvector.
Algorithms for nonlinear eigenvalue problems (EP’s) often require solving self-consistently a large number of EP’s. Convergence difficulties may occur if the solution is not sought in an appropriate region, if globa...
Algorithms for nonlinear eigenvalue problems (EP’s) often require solving self-consistently a large number of EP’s. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP’s obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP’s. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.
It is shown that Lam’s formulation of renormalization group theory [Phys. Fluids A 4, 1007 (1992)] is essentially the physical space version of the spectral classical closure theory [Leslie and Quarini, J. Fluid Mech...
It is shown that Lam’s formulation of renormalization group theory [Phys. Fluids A 4, 1007 (1992)] is essentially the physical space version of the spectral classical closure theory [Leslie and Quarini, J. Fluid Mech. 91, 65 (1979)].
Fully coupled numerical techniques are used to compute steady state solutions to a combusting, low Mach number compressible flow through a channel. The nonlinear governing equations are discretized on a staggered mesh...
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Parallel discrete event simulation offers the potential for significant speedup over sequential simulation. Unfortunately, high performance is often achieved only after rigorous fine tuning is used to obtain an effici...
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Parallel discrete event simulation offers the potential for significant speedup over sequential simulation. Unfortunately, high performance is often achieved only after rigorous fine tuning is used to obtain an efficient mapping of tasks to processors. In practice, good performance with minimal effort is often preferable to high performance with excessive effort. We discuss our research in adding automated load balancing to the SPEEDES simulation framework. Using simulation models of queuing networks and the National Airspace System, we demonstrate that using run time measurements, our automated load balancing scheme can achieve better performance than simple allocation methods that do not use run time measurements, particularly when large numbers of processors are used.
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