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In particular, cosmology SAMR simulations are adaptive in that their computational load varies throughout the execution Ef ciently partitioning the cosmological workload and transferring excess workload from overloaded processors to underloaded processors during execution are critical techniques needed for the ef cient execution of distributed cosmology simulations The paper is focused on designing a load balancing scheme to improve the ef ciency of cosmology simulations in distributed computing environments The unique characteristics of cosmology simulations and the heterogeneous sharing features of distributed computing environments, however, pose several research challenges to dynamic load balancing of such simulations: r Unique Features of Cosmology SAMR Simulations: Several existing research on load balancing have been focused on graph-based partitioning [4, 9, 15, 19, 23, 33, 35, 36, 43, 46] With graph partitioning, the computational workload and the interprocessor communication are represented as a weighted graph of vertices and edges.

A nite difference approximation to / s can easily be described by a PETSc matrix, and once such a matrix object is initialized, it is straightforward to evaluate the curvilinear force density on the curvilinear mesh Note that since we express these nite difference operations as distributed matrix vector products, the application-speci c force evaluation routines that must be implemented by the programmer can be made essentially independent of the details of the parallel distribution of the curvilinear mesh In addition to evaluating the curvilinear elastic force density, which is a computation that involves only Lagrangian data, we must also be able to interpolate the velocity from the Cartesian grid to the curvilinear mesh and spread the force density from the curvilinear mesh to the Cartesian grid This is done by evaluating the discrete Lagrangian Eulerian interaction formulae, that is, equations (716 718) and (7.

The objective of graph partitioning is to nd a repartition of the graph so as to equalize the workload among processors and minimize the edge cut Cosmology SAMR applications have very different data structures from graphs used in graph-based partitioning schemes First, the basic building block used in cosmic modeling is grid, which is a self-contained object with dozens of variables that need to be calculated at runtime Besides, two other data structures are used to keep track of parent child and sibling relations among grids Second, both the computational workload per grid and the communication cost among grids are changing dynamically at runtime Hence, the complicated and dynamic data structures used in cosmology SAMR simulations cannot be transformed into a graph that is represented as a static set of vertices and edges.

24), on each level max grid patch Performing these operations within a particular patch requires not only data in the patch interior but also data values in a ghost cell region outside the patch boundary In particular, in the case of velocity interpolation, the Eulerian velocity u must be provided in a ghost cell region about each patch, whereas in the case of force spreading, the curvilinear force density F must be locally accessible both for the nodes that are located within the patch interior and also for those nodes that are embedded within the same ghost cell region To determine the size of this ghost cell region, suppose that force spreading is performed by the 4-point delta function, which has a support of four meshwidths in each coordinate direction If a curvilinear mesh node (q, r, s) is more than 1.

802.11 defines three types of network architecture: Independent basic service set (IBSS), basic service set (BSS) and extended service set (ESS). The wireless terminal in the 802.11 network is termed station .

In addition, cosmology SAMR applications have several unique adaptive characteristics, namely, high frequency of adaptations and different patterns of imbalances, that prevent the use of either scratch remap or diffusion-based repartitioning techniques [22]..

5 Cartesian meshwidths away from the interior of a particular Cartesian grid patch, the force associated with node (q, r, s) cannot be spread to any of the Cartesian grid cell centers in the interior of that patch Since the curvilinear mesh nodes are in motion, however, it is useful to keep track of the curvilinear mesh nodes in a somewhat larger ghost cell region Assuming that the nodes may move at most a single Cartesian meshwidth in any coordinate direction during a single timestep, it suf ces to provide curvilinear mesh data within a 25-cell ghost cell region, although in practice we round this number up to 3 Similarly, interpolating the Eulerian velocity u from the Cartesian grid to an arbitrary location in the interior of a grid patch requires that values of u be provided in a 2-cell-wide ghost cell region about that patch.

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