D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution Algorithms for the Twodimensional Euler Equations on Unstructured Meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990. 12  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the test and set operation. Our scheduling scheme is distributed in nature and therefore is useful even for the cases in which the same communication pattern is used only a few times (or once) In contrast, some of the algorithms we have developed [12] may be more suitable for applications (e.g. [13]) in which the same schedule is used a large number of times so that the scheduling cost can be amortized. Our experimental results show that compared to naive algorithms, our algorithms can result in a significant reduction in the total amount of communication cost. The rest of this paper is ....

D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution Algorithms for the Twodimensional Euler Equations on Unstructured Meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990. 12

.... computational phase, which may be executed repeatedly without change [4] Examples of static single phase computations, which are iterative solvers using sparse matrix vector multiplications, can be found in [13] Examples of explicit unstructured mesh fluids calculations can be found in [14]. Figure 10 depicts a schematic outline of a kernel from a fluid dynamics simulation that represents a loop that sweeps over the edges of a mesh. The kernel is based on an algorithm that maps a computational domain with irregular polygons. The area and shape of the polygons are determined by ....

D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution algorithms for the twodimensional euler equations on unstructured meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....significant improvement over naive methods. Index Terms: Active Messages, communication latency, distributed scheduling, interrupt handler, node contention, personalized communication, unstructured communication. 1 Introduction Parallelization of many irregular and loosely synchronous problems [1, 3, 7, 9, 14, 16, 17] result in all to many personalized communication. An example of all to many personalized communication is given in Table 1. A 1 in the (i; j) entry represents the fact that processor P i needs to communicate to processor P j . Each message is of different size and each processor may send a ....

D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution algorithms for the twodimensional euler equations on unstructured meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....we accumulate to y. Note that the declarations in S1 and S3 in Figure 10 allow the compiler to determine that accumulations to y are local. 5.3. 2 The Fluxroe Kernel This kernel is taken from a program that computes convective fluxes using a method based on Roe s approximate Riemann solver [41] [42]; referred to as Fluxroe kernel in this paper. Fluxroe computes the flux across each edge of an unstructured mesh. Fluxroe accesses elements of array yold, carries out flux calculations and accumulates results to array y. As was the case in the sparse block matrix vector multiply kernel, four ....

D. L. Whitaker, D. C. Slack, and R. W. Walters, Solution algorithms for the two-dimensional Euler equations on unstructured meshes, in Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....phase computation consists of a single concurrent computational phase, which may be executed repeatedly without change. Examples of static single phase computations are iterative solvers using sparse matrix vector multiplications (e.g. 32] and explicit unstructured mesh fluids calculations (e.g. [42]) The key problem in efficiently executing these programs is partitioning the data and computation S1 do i=3D1,N S2 do j=3D1,M y(i) 3D y(i) a(i,j) x(col(i,j) end do end do Figure 1: Sparse Matrix Vector Multiply to minimize communication while balancing load. This partitioning then dictates ....

D. L. Whitaker, D. C. Slack, and R. W. Walters. Solution algorithms for the two-dimensional euler equations on unstructured meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....and load balancing [9, 13, 17] These packages derive the necessary communication information based on the nonlocal data required for performing the local computations. Consider the parallelization of single concurrent computational phase of an explicit unstructured mesh fluids calculation (e.g.[25]) This step is typically executed repeatedly without change in computational structure. The computational structure of the above code is given in Figure 1. Similar examples of such computations are iterative solvers using sparse matrix vector multiplications (e.g. 21] Further, a multiple phase ....

D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution algorithms for the twodimensional euler equations on unstructured meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....have been developed in [1, 16] Load balancing and reduction of communication are two important issues for achieving a good mapping. The directives of Fortran D [6] can be used to provide such a mapping for a large class of regular and synchronous problems. For some other classes of problems [3, 19, 20] that are irregular in nature, achieving a good mapping is considerably more difficult [7] Further, the nature of this irregularity may not be known at the time of compilation and can be ascertained only at runtime. The handling of irregular problems requires the use of runtime information to ....

D.L. Whitaker, D.C. Slack, and R.W. Walters. Solution Algorithms for the Twodimensional Euler Equations on Unstructured Meshes. In Proceedings AIAA 28th Aerospace Sciences Meeting, Reno, Nevada, January 1990.

....scheme in which f1Qg n is obtained through a sequence of iterates, f1Qg i which converge to f1Qg n . Note that several variations of classic relaxation procedures have been used in the past for solving the Euler equations on unstructured grids (see for example [21] 18] 1] and [22]) To clarify the scheme, A] n is first written as a linear combination of two matrices representing the diagonal and off diagonal terms [A] n = D] n [O] n (33) The simplest iterative scheme for obtaining a solution to the linear system of equations is a Jacobi type method in which ....

Whitaker, D. L., "Solution Algorithms for the Two-Dimensional Euler Equations on Unstructured Meshes," AIAA 90--0697, 1990.

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Whitaker, D. L.; Slack, David C.; and Walters, Robert W.: Solution Algorithms for the Two-Dimensional Euler Equations on Unstructured Meshes. AIAA-90-0697, Jan. 1990.

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