ALBERT

Description: Considerations in the floating-point design of a supercomputer are discussed. Particular attention is given to word size, hardware support for extended precision, format, and accuracy characteristics. These issues are discussed from the perspective of the Numerical Aerodynamic Simulation Systems Division at NASA Ames. The features believed to be most important for a future supercomputer floating-point design include: (1) a 64-bit IEEE floating-point format with 11 exponent bits, 52 mantissa bits, and one sign bit and (2) hardware support for reasonably fast double-precision arithmetic.

Description: This paper briefly addresses the computational requirements for the analysis of complete configurations of aircraft and spacecraft currently under design to be used for advanced transportation in commercial applications as well as in space flight. The discussion clearly shows that massively parallel systems are the only alternative which is both cost effective and on the other hand can provide the necessary TeraFlops, needed to satisfy the narrow design margins of modern vehicles. It is assumed that the solution of the governing physical equations, i.e., the Navier-Stokes equations which may be complemented by chemistry and turbulence models, is done on multiblock grids. This technique is situated between the fully structured approach of classical boundary fitted grids and the fully unstructured tetrahedra grids. A fully structured grid best represents the flow physics, while the unstructured grid gives best geometrical flexibility. The multiblock grid employed is structured within a block, but completely unstructured on the block level. While a completely unstructured grid is not straightforward to parallelize, the above mentioned multiblock grid is inherently parallel, in particular for multiple instruction multiple datastream (MIMD) machines. In this paper guidelines are provided for setting up or modifying an existing sequential code so that a direct parallelization on a massively parallel system is possible. Results are presented for three parallel systems, namely the Intel hypercube, the Ncube hypercube, and the FPS 500 system. Some preliminary results for an 8K CM2 machine will also be mentioned. The code run is the two dimensional grid generation module of Grid, which is a general two dimensional and three dimensional grid generation code for complex geometries. A system of nonlinear Poisson equations is solved. This code is also a good testcase for complex fluid dynamics codes, since the same datastructures are used. All systems provided good speedups, but message passing MIMD systems seem to be best suited for large miltiblock applications.

Description: The present volume on parallel CFD discusses implementations on parallel machines, numerical algorithms for parallel CFD, and performance evaluation and computer science issues. Attention is given to a parallel algorithm for compressible flows through rotor-stator combinations, a massively parallel Euler solver for unstructured grids, a fast scheme to analyze 3D disk airflow on a parallel computer, and a block implicit multigrid solution of the Euler equations. Topics addressed include a 3D ADI algorithm on distributed memory multiprocessors, clustered element-by-element computations for fluid flow, hypercube FFT and the Fourier pseudospectral method, and an investigation of parallel iterative algorithms for CFD. Also discussed are fluid dynamics using interface methods on parallel processors, sorting for particle flow simulation on the connection machine, a large grain mapping method, and efforts toward a Teraflops capability for CFD.

Description: The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Description: In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

Description: The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

Description: We are surveying current projects in the area of parallel supercomputers. The machines considered here will become commercially available in the 1990 - 1992 time frame. All are suitable for exploring the critical issues in applying parallel processors to large scale scientific computations, in particular CFD calculations. This chapter presents an overview of the surveyed machines, and a detailed analysis of the various architectural and technology approaches taken. Particular emphasis is placed on the feasibility of a Teraflops capability following the paths proposed by various developers.

Description: Computational requirements of full scale computational fluid dynamics change as computation progresses on a parallel machine. The change in computational intensity causes workload imbalance of processors, which in turn requires a large amount of data movement at runtime. If parallel CFD is to be successful on a parallel or massively parallel machine, balancing of the runtime load is indispensable. Here a frame work is presented for dynamic load balancing for CFD applications, called Jove. One processor is designated as a decision maker Jove while others are assigned to computational fluid dynamics. Processors running CFD send flags to Jove in a predetermined number of iterations to initiate load balancing. Jove starts working on load balancing while other processors continue working with the current data and load distribution. Jove goes through several steps to decide if the new data should be taken, including preliminary evaluate, partition, processor reassignment, cost evaluation, and decision. Jove running on a single SP2 node has been completely implemented. Preliminary experimental results show that the Jove approach to dynamic load balancing can be effective for full scale grid partitioning on the target machine SP2.

Description: The Cray T3D is the first-phase system in Cray Research Inc.'s (CRI) three-phase massively parallel processing program. In this report we describe the architecture of the T3D, as well as the CRAFT (Cray Research Adaptive Fortran) programming model, and contrast it with PVM, which is also supported on the T3D We present some performance data based on the NAS Parallel Benchmarks to illustrate both architectural and software features of the T3D.

Description: In the last three years extensive performance data have been reported for parallel machines both based on the NAS Parallel Benchmarks, and on LINPACK. In this study we have used the reported benchmark results and performed a number of statistical experiments using factor, cluster, and regression analyses. In addition to the performance results of LINPACK and the eight NAS parallel benchmarks, we have also included peak performance of the machine, and the LINPACK n and n(sub 1/2) values. Some of the results and observations can be summarized as follows: 1) All benchmarks are strongly correlated with peak performance. 2) LINPACK and EP have each a unique signature. 3) The remaining NPB can grouped into three groups as follows: (CG and IS), (LU and SP), and (MG, FT, and BT). Hence three (or four with EP) benchmarks are sufficient to characterize the overall NPB performance. Our poster presentation will follow a standard poster format, and will present the data of our statistical analysis in detail.