Intel Touchstone Delta System Research Articles

Environmental modeling on massively parallel computers

In a previous work we studied the concurrent implementation of a numerical model, CONDIFP, developed for the analysis of depth-averaged convection–diffusion problems. Initial experiments were conducted on the Intel Touchstone Delta System, using up to 512 processors and different problem sizes. As for other computation-intensive applications, the results demonstrated an asymptotic trend to unity efficiency when the computational load dominates the communication load. This paper relates some other numerical experiences, in both one and two space dimensions with various choices of initial and boundary conditions, carried out on the Intel Paragon XP/S Model L38 with the aim to illustrate the parallel solver versatility and reliability.

The Spectral Decomposition of Nonsymmetric Matrices on Distributed Memory Parallel Computers

The implementation and performance of a class of divide-and-conquer algorithms for computing the spectral decomposition of nonsymmetric matrices on distributed memory parallel computers are studied in this paper. After presenting a general framework, we focus on a spectral divide-and-conquer (SDC) algorithm with Newton iteration. Although the algorithm requires several times as many floating point operations as the best serial QR algorithm, it can be simply constructed from a small set of highly parallelizable matrix building blocks within Level 3 basic linear algebra subroutines (BLAS). Efficient implementations of these building blocks are available on a wide range of machines. In some ill-conditioned cases, the algorithm may lose numerical stability, but this can easily be detected and compensated for. The algorithm reached 31% efficiency with respect to the underlying PUMMA matrix multiplication and 82% efficiency with respect to the underlying ScaLAPACK matrix inversion on a 256 processor Intel Touchstone Delta system, and 41% efficiency with respect to the matrix multiplication in CMSSL on a 32 node Thinking Machines CM-5 with vector units. Our performance model predicts the performance reasonably accurately. To take advantage of the geometric nature of SDC algorithms, we have designed a graphical user interface to let the user choose the spectral decomposition according to specified regions in the complex plane.

Scalability and load balancing in adaptive algorithms for multidimensional integration

A parallel adaptive algorithm for the approximate computation of a multi-dimensional integral over an hyperrectangular region is described. This is a more general version of the well known algorithms presented in Genz (1987) and Lapegna and D'Alessio (1993) and it has been developed for an efficient implementation on a MIMD distributed memory multiprocessor. In order to achieve a good scalability, all global communications have been removed from the algorithm. The processor's network has been configured as a multidimensional periodical mesh, to distribute information about the integrand behavior fast enough in order to achieve a good load balancing. Test results on the Intel Touchstone Delta System are given.

A fast numerical method for mildly nonlinear parabolic initial boundary value problems II: The parallel implementation on the Intel Touchstone Delta system

This paper describes the parallel implementation of a fast method for solving mildly nonlinear parabolic initial boundary value problems on the Intel Touchstone Delta system. A theoretical time complexity analysis shows that the solver achieves a perfect speedup in the limit of large problem sizes. Experimental times confirm the analytical performance model.

NON-LINEAR STRUCTURAL RESPONSE USING ADAPTIVE DYNAMIC RELAXATION ON A MASSIVELY PARALLEL-PROCESSING SYSTEM

A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.

NON‐LINEAR STRUCTURAL RESPONSE USING ADAPTIVE DYNAMIC RELAXATION ON A MASSIVELY PARALLEL‐PROCESSING SYSTEM

A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for non-linear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly non-linear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly non-linear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the non-linear static response of two- and three-dimensional hyperelastic systems involving contact. Impressive relative speed-ups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.

Pipeline optimizations of the prime factor algorithm

AbstractThe prime factor algorithm (PFA) is an efficient discrete Fourier transform (DFT) computation algorithm used when the sequence length can be decomposed into mutually prime factors. Following our previous results on PFA decomposition carried out at Caltech on hypercube machines, we present in the paper a pipeline PFA implementation suitable for multiprocessor systems with distributed memory. This implementation achieves high values of efficiency and speed‐up when processing multiple sequences of data. The paper shows how an optimized structure can be obtained when the concurrency among computation and communications is exploited at each node of the pipe. Experimental results obtained on transputer‐based structures and on the Intel Touchstone Delta system are also reported.