MasPar MP-1 Research Articles

Dynamic analysis of folded plate structures on a massively parallel computer

The spectral element method is a matrix method for the dynamic analysis of structures using Fourier transforms in time and space. It is particularly suited to solving wave propagation-type problems. We demonstrate how the method is implemented on a MasPar MP-1 computer with 16,384 processors. Coding is straightforward due to the inherent parallelism of the spectral method and the convenient parallel extensions of MP Fortran-90. Timing results are given for the MP-1 using from 512 to 16,384 processors, and several common workstations. We obtain near 100% efficiency on the MP-1, and speeds two to three orders of magnitude greater than the comparison platforms running the same, albeit sequential code.

A Parallel Implementation of a Hidden Markov Model with Duration Modeling for Speech Recognition

Hidden Markov models (HMMs) are currently the most successful paradigm for speech recognition. Although explicit duration continuous HMMs more accurately model speech than HMMs with implicit duration modeling, the cost of accurate duration modeling is often considered prohibitive. This paper describes a parallel implementation of an HMM with explicit duration modeling for spoken language recognition on the MasPar MP-1. The MP-1 is a fine-grained SIMD architecture with 16384 processing elements (PEs) arranged in a 128 × 128 mesh. By exploiting the massive parallelism of explicit duration HMMs, development and testing is practical even for large amounts of data. The result of this work is a parallel speech recognizer that can train a phone recognizer in real time. We present several extensions that include context dependent modeling, word recognition, and implicit duration HMMs.

Simulation of Compressible Flow on a Massively Parallel Architecture

This article describes the porting and optimization of an explicit, time‐dependent, computational fluid dynamics code on an 8,192‐node MasPar MP‐1. The MasPar is a very fine‐grained, single instruction, multiple data parallel computer. The code uses the flux‐corrected transport algorithm. We describe the techniques used to port and optimize the code, and the behavior of a test problem. The test problem used to benchmark the flux‐corrected transport code on the MasPar was a two‐dimensional exploding shock with periodic boundary conditions. We discuss the performance that our code achieved on the MasPar, and compare its performance on the MasPar with its performance on other architectures. The comparisons show that the performance of the code on the MasPar is slightly better than on a CRAY Y‐MP for a functionally equivalent, optimized two‐dimensional code.

Massively Parallel Molecular Dynamics and Simulations for Many-Body Potentials

AbstractWe discuss the implementation of classical molecular dynamics simulations on Single- Instruction Multiple-Data computers with two-dimensional mesh connectivity. Specific timing results are given for the MasPar MP-1, complemented by a general time complexity analysis. Our main interest is in simulations with a number of particles N that is comparable to the number of processors P. In particular, we discuss results for large Si-clusters with up to 2000 particles, using a Stillinger-Weber potential. Particular attention is paid to the problem of handling in an efficient way the calculation of the three-body potential and force.

Data-parallel lower-upper relaxation method for reacting flows

The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method of Yoon and Jameson is modified for use on massively parallel computers. The method has been implemented on the Thinking Machines CM-5 and the MasPar MP-1 and MP-2, where large percentages of the theoretical peak floating point performance are obtained. It is shown that the new data-parallel LU relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations. The convergence is also improved for five-species reacting air computations. The performance of the method on various partitions of the CM-5 and on the MasPar computers is discussed. The new method shows promise for the efficient simulation of very large perfect gas and reacting flows.

Quantum dynamics simulation of few body Coulomb systems

This paper describes a parallel algorithm for quantum dynamics simulations of three body Coulomb problems. The algorithm has been implemented on a SIMD (single instruction multiple data) computer (MasPar MP1). The algorithm employs the finite-difference and split operator (FD-SPO) method and variable time-step technique. A transformation of wavefunction to polar coordinates and a modified finite-difference method are introduced to reduce the number of the dimension and to handle singularities. The variable-time-step scheme improves the efficiency four times.

Load balancing for the parallel adaptive solution of partial differential equations

An adaptive technique for a partial differential system automatically adjusts a computational mesh or varies the order of a numerical procedure with a goal of obtaining a solution satisfying prescribed accuracy criteria in an optimal fashion. Processor load imbalances will, therefore, be introduced at adaptive enrichment steps during the course of a parallel computation. We develop and describe three procedures for retaining and restoring load balance that have low unit cost and are appropriate for use in an adaptive solution environment. Tiling balances load by using local optimality criteria within overlapping processor neighborhoods. Elemental data are migrated between processors within the same neighborhoods to restore balance. Tiling is restricted to uniform two-dimensional meshes and provides limited control of communications volume by priority-based element selection criteria. These shortcomings can potentially be overcome by creating a dynamic partition graph connecting processors and their neighboring regions. After coloring the edges of the graph, elemental data are iteratively transferred between processors by pairwise exchange to permit a more global migration. Octree decomposition of a spatial domain is a successful three-dimensional mesh generation strategy. The octree structure facilities a rapid load balancing procedure by performing tree traversals that (i) appraise subtree costs and (ii) partition spatial regions accordingly. Computational results are reported for two- and three-dimensional problems using nCUBE/2 hypercube, MasPar MP-2, and Thinking Machines CM-5 computers.

Parallel adaptive mesh refinement and redistribution on distributed memory computers

A procedure to support parallel refinement and redistribution of two-dimensional unstructured finite element meshes on distributed memory computers is presented. The procedure uses the mesh topological entity hierarchy as the underlying data structures to easily support the required adjacency information. Mesh refinement is done by employing links back to the geometric representation to place new nodes on the boundary of the domain directly on the curved geometry. The refined mesh is then redistributed by an iterative heuristic based on the Leiss-Reddy [1] load balancing criteria. A fast parallel tree edge-coloring algorithm is used to pair processors having adjacent partitions and forming a tree structure as a result of Leiss-Reddy load request criteria. Excess elements are iteratively migrated from heavily loaded to less loaded processors until load balancing is achieved. The system is implemented on a massively parallel MasPar MP-1 system with a SIMD style of computation and uses message passing primitives to migrate elements during the mesh redistribution phase. Performance results of the redistribution heuristics on various test meshes are given.

A massively parallel implementation of the spectral element method for impact problems in plate structures

The spectral element method is a frequency domain formulated matrix method for the dynamic analysis of structures. We show that an important attribute of the spectral formulation is its suitability for implementation on large multiprocessor computers. In this paper we summarize the development of the spectral element method for dynamic plate problems and outline the implementation of the algorithm on MasPar MP-1 and MP-2 computers with 16 384 processors each. The implementation exhibits near perfect scalability. A direct consequence of the ensuing high computational performance is the ability to solve inverse dynamic problems. Example solutions using experimentally measured acceleration response to find the impact site in plate structures are demonstrated.

An implementation of a tree code on a SIMD, parallel computer

We describe a fast tree algorithm for gravitational N-body simulation on SIMD parallel computers. The tree construction uses fast, parallel sorts. The sorted lists are recursively divided along their x, y and z coordinates. This data structure is a completely balanced tree (i.e., each particle is paired with exactly one other particle) and maintains good spatial locality. An implementation of this tree-building algorithm on a 16k processor Maspar MP-1 performs well and constitutes only a small fraction (approximately 15%) of the entire cycle of finding the accelerations. Each node in the tree is treated as a monopole. The tree search and the summation of accelerations also perform well. During the tree search, node data that is needed from another processor is simply fetched. Roughly 55% of the tree search time is spent in communications between processors. We apply the code to two problems of astrophysical interest. The first is a simulation of the close passage of two gravitationally, interacting, disk galaxies using 65,636 particles. We also simulate the formation of structure in an expanding, model universe using 1,048,576 particles. Our code attains speeds comparable to one head of a Cray Y-MP, so single instruction, multiple data (SIMD) type computers can be used for these simulations. The cost/performance ratio for SIMD machines like the Maspar MP-1 make them an extremely attractive alternative to either vector processors or large multiple instruction, multiple data (MIMD) type parallel computers. With further optimizations (e.g., more careful load balancing), speeds in excess of today's vector processing computers should be possible.

Massively parallel computer simulations of fullerenes and Si-clusters

A general overview of cluster and bulk molecular dynamics algorithms for parallel computers is given. Specific results are presented for the MasPar MP-1 (DECmpp 12000) series of computers, which possess a single-instruction multiple-data (SIMD) architecture with processors arranged in a two-dimensional mesh. Many-body potentials used were selected to describe CC- and Si-clusters and ground-states were determined through simulated annealing. The difficulty of attaining the absolute minimum in this way for larger clusters is discussed and some possible remedies are suggested.

Efficient massively parallel simulation of dynamic channel assignment schemes for wireless cellular communications

Fast, efficient parallel algorithms are presented for discrete event simulations of dynamic channel assignment schemes for wireless cellular communication networks. The driving events are called arrivals and departures, in continuous time, to cells geographically distributed across the service area. A dynamic channel assignment scheme decides which call arrivals to accept, and which channels to allocate to the accepted calls, attempting to minimize call blocking while ensuring co-channel interference is tolerably low. Specifically, the scheme ensures that the same channel is used concurrently at different cells only if the pairwise distances between those cells are sufficiently large. Much of the complexity of the system comes from ensuring this separation. The network is modeled as a system of interacting continuous time automata, each corresponding to a cell. To simulate the model, we use conservative methods; i.e., methods in which no errors occur in the course of the simulation and so no rollback or relaxation is needed. Implemented on a 16K processor MasPar MP-1, an elegant and simple technique provides speedups of about 15x over an optimized serial simulation running on a high speed workstation. A drawback of this technique, typical of conservative methods, is that processor utilization is rather low. To overcome this, we developed new methods that exploit slackness in event dependencies over short intervals of time, thereby raising the utilization to above 50% and the speedup over the optimized serial code to about 120x with respect to the workstation simulation.

Scalability of parallel algorithm-machine combinations

Scalability has become an important consideration in parallel algorithm and machine designs. The word scalable, or scalability, has been widely and often used in the parallel processing community. However, there is no adequate, commonly accepted definition of scalability available. Scalabilities of computer systems and programs are difficult to quantify, evaluate, and compare. In this paper, scalability is formally defined for algorithm-machine combinations. A practical method is proposed to provide a quantitative measurement of the scalability. The relation between the newly proposed scalability and other existing parallel performance metrics is studied. A harmony between speedup and scalability has been observed. Theoretical results show that a large class of algorithm-machine combinations is scalable and the scalability can be predicted through premeasured machine parameters. Two algorithms have been studied on an nCUBE 2 multicomputer and on a MasPar MP-1 computer. These case studies have shown how scalabilities can be measured, computed, and predicted. Performance instrumentation and visualization tools also have been used and developed to understand the scalability related behavior. >

Multiple Quadratic Forms: A Case Study in the Design of Data-Parallel Algorithms

Data-parallel implementations of the computationally intensive task of solving multiple quadratic forms (MQFs) have been examined. Coupled and uncoupled parallel methods are investigated, where coupling relates to the degree of interaction among the processors. Also, the impact of partitioning a large MQF problem into smaller non-interacting subtasks is studied. Trade-offs among the implementations for various data-size/machine-size ratios are categorized in terms of complex arithmetic operation counts, communication overhead, and memory storage requirements. Furthermore, the impact on performance of the mode of parallelism used is considered, specifically, SIMD versus MIMD versus SIMD/MIMD mixed-mode. From the complexity analyses, it is shown that none of the algorithms presented in this paper is best for all data-size/machine-size ratios. Thus, to achieve scalability (i.e., good performance as the number of processors available in a machine increases), instead of using a single algorithm, the approach discussed is to have a set of algorithms from which the most appropriate algorithm or combination of algorithms is selected based on the ratio calculated from the scaled machine size. The analytical results have been verified by experiments on the MasPar MP-1 (SIMD), nCUBE 2 (MIMD), and PASM (mixed-mode) prototype.

MESH ALGORITHMS FOR FINDING REPETITIONS AND PARTIAL SYMMETRIES IN ARRAYS

The two-dimensional mesh computer architecture has proven to be an appropriate means to apply parallel computation to problems in image processing. However, this is most often done using local-neighbourhood operations to accomplish image filtering and morphological transformations. The discovery of structures in an image such as repetitions and symmetries is another form of visual analysis, and yet relatively little has been done to apply mesh computers to this problem. In this paper, we apply the primitive operations of prefix scanning and sorting to efficiently implement a repetition finding algorithm for arrays. The computational complexity of the algorithm on a n×n mesh is O(n log k) where k is the width of the largest repeated block in the array. The algorithm was implemented on a MasPar MP-1 computer. We describe variations of the algorithm for solving several related problems including the detection of partial symmetries in an image and repetitions in images modulo pixel-value transformations.

Introducing parallel processing concepts using the MASPAR MP-1 computer

Introducing parallel processing concepts using the MASPAR MP-1 computer

A comparative study of the use of the data-parallel approach for compressible flow calculations

The results are presented of an investigation into the use of the data-parallel programming approach on four different massively-parallel computers: the MasPar MP-1 and MP-2 and the Thinking Machines CM-200 and CM-5. A code to calculate inviscid compressible flow, originally written in FORTRAN 77 for a traditional vector computer, has been re-written entirely in Fortran 90 to take advantage of the compilers available on the massively-parallel computers. It is shown that the discretization of the governing equations on a regular mesh is well adapted to data parallelism. For a typical test problem of supersonic flow through a ramped duct, computational speeds have been achieved using these massively-parallel computers that are superior to those obtained using a single processor of a Cray Y-MP. In addition, this study has enabled the question of code portability between the different computers to be assessed.

A comparative study of the use of the data-parallel approach for compressible flow calculations

The results are presented of an investigation into the use of the data-parallel programming approach on four different massively-parallel computers: the MasPar MP-1 and MP-2 and the Thinking Machines CM-200 and CM-5. A code to calculate inviscid compressible flow, originally written in FORTRAN 77 for a traditional vector computer, has been re-written entirely in Fortran 90 to take advantage of the compilers available on the massively-parallel computers. It is shown that the discretization of the governing equations on a regular mesh is well adapted to data parallelism. For a typical test problem of supersonic flow through a ramped duct, computational speeds have been achieved using these massively-parallel computers that are superior to those obtained using a single processor of a Cray Y-MP. In addition, this study has enabled the question of code portability between the different computers to be assessed.

Massively parallel calculations of the electronic structure of non-periodic micro-crystallites of transition metal oxides

We report massively parallel computations of the electronic density of states of a non-periodic micro-crystalline of rutile TiO 2 with a sample of 491 520 atoms. Mathematically, the problem is equivalent to solving an n× n eigenvalue problem, where n ∼ 2 500 000. We used MasPar MP-1 and MasPar MP-2 autonomous SIMD computers with up to 16 384 processing elements (PEs) with the entire computing time ∼ 1.5 h (on 4K MasPar MP-2). We used the equation of motion method and the non-trivial tight binding model in our calculations and conclude that these methods when implemented on the massively parallel SIMD computer architectures, are very well suited for studying the electronic structure of complex non-periodic systems with both point and extended defects.

Massively parallel algorithms for trace-driven cache simulations

Considers the use of massively parallel architectures to execute a trace-driven simulation of a single cache set. A method is presented for the least-recently-used (LRU) policy, which, regardless of the set size C, runs in time O(log N) using N processors on the EREW (exclusive read, exclusive write) parallel model. A simpler LRU simulation algorithm is given that runs in O(C log N) time using N/log N processors. We present timings of this algorithm's implementation on the MasPar MP-1, a machine with 16384 processors. A broad class of reference-based line replacement policies are considered, which includes LRU as well as the least-frequently-used (LFU) and random replacement policies. A simulation method is presented for any such policy that, on any trace of length N directed to a C line set, runs in O(C log N) time with high probability using N processors on the EREW model. The algorithms are simple, have very little space overhead, and are well suited for SIMD implementation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>