Robert Hiromoto

Pseudo-random trees in Monte Carlo

We present the concept of a pseudo-random tree, and generalize the Lehmer pseudo-random number generator as an efficient implementation of the concept. Pseudo-random trees can be used to give reproducibility, as well as speed, in Monte Carlo computations on parallel computers with either the SIMD architecture of the current generation of supercomputer or the MIMD architecture characteristic of the next generation. Monte Carlo simulations based on pseudo-random trees are free of certain pitfalls, even for sequential computers, which can make them considerably more useful.

A collection of parallel linear equations routines for the Denelcor HEP

This paper describes the implementation and performance results for a few standard linear algebra routines on the Denelcor HEP computer. The algorithms used here are based on high-level modules that facilitate portability and perform efficiently in a wide range of environments. The modules are chosen to be of a large enough computational granularity so that reasonably optimum performance may be insured. The design of algorithms with such fundamental modules in mind will also facilitate their replacement by others more suited to gain the desired performance on a particular computer architecture.

A parallel Monte Carlo transport algorithm using a pseudo-random tree to guarantee reproducibility

Abstract We present a parallel Monte Carlo photon transport algorithm that insures the reproducibility of results. The important feature of this parallel implementation is the introduction of a pair of pseudo-random number generators. This pair of generators is structured in such a manner as to insure minimal correlation between the two sequences of pseudo-random numbers produced. We term this structure as a ‘pseudo-random tree’. Using this structure, we are able to reproduce results exactly in a asynchronous parallel processing environment. The algorithm tracks the history of photons as they interact with two carbon cylinders joined end to end. The algorithm was implemented on both a Denelcor HEP and a CRAY X-MP/48. We describe the algorithm and the pseudo-random tree structure and present speedup results of our implementation.

Mapping schemes of the particle-in-cell method implemented on the PAX computer

Abstract The particle-in-cell (PIC) model refers to the motion of many particles driven by a force that results in part from the field that they themselves generate. An example of the PIC model, an electrostatic electron plasma model, was processed by the parallel computer PAX. The potential field was solved by applying a Fast Fourier Transform to the Poisson equation. The workload in particle pushing was allocated by the Eulerian method (or present-address method) and the Lagrangian method (or birthplace method). Two schemes for the space mapping—direct and modular mappings—were also tested. It was demonstrated that modular mapping can overcome the efficiency degradation, which was observed in the direct mapping of the nonuniform particle distribution. The performance scaling law, a general expression for the execution time, and efficiency are given. Based on the scaling law, the performance is extended to a larger machine.

Experiences with the Denelcor HEP

Three FORTRAN codes, each typical of a class of simulation problems at Los Alamos National Laboratory, have been converted to execute on the Denelcor HEP. The codes are (i) PIC, a particle-in-cell code; (ii) SIMPLE, a two-dimensional Lagrangian hydrodynamics program, and (iii) TRAC, a nuclear reactor simulation. The programming paradigm that was used and the algorithmic nature of the concurrency are discussed. Speedups as a function of number of processes are given.

Some issues in parallel processing as encountered on the Denelcor HEP

Abstract We present a collection of differing parallel implementation of a single, computationally intensive algorithm that models the collisionless, electrostatic interaction between two relatively moving plasma beams. This numerical simulation uses a method, important in many scientific applications known as the Particle-in-Cell (PIC) method. Our aim in this study is to determine the advantages and disadvantages associated with those various parallel implementations. Our experiments with parallelizing this particular numerical simulation, referred to throughout this paper as the PIC code, were performed on a single Denelcor HEP Process Execution Module (PEM). A complete set of parallel processing speedups and execution times as a function of number of processes is presented.

The performance of asynchronous iteration schemes applied to the linearized Boltzmann transport equation

Abstract We present a summary of numerical experiments that explore the effects of asynchronous (chaotic) iteration schemes for solutions of the Boltzmann transport equation. Our experiments are performed on both common and distributed memory parallel processing systems. Two chaotic and one deterministic schemes are developed directly from a computational algorithm known as discrete ordinates that uses iterative techniques in solving the linearized Boltzmann particle transport equation. From an analysis based on the performance of these schemes on various parallel architectures, a third chaotic scheme is developed that executes faster in either parallel or sequential modes. The behavior of these methods, both deterministic and chaotic, will be examined for the Denelcor HEP, the Encore Multimax, and the Intel iPSC hypercube.

Developing a parallel Monte Carlo transport algorithm using large-grain data flow

Abstract We describe use of large-grain data flow to formulate a parallel solution for a moderately complex Monte Carlo particle transport problem. The large-grain data flow computation model combines the parallelism of traditional data flow and subroutine-like sequential programming. This paper summarizes our experience in implementing the solution and gives speedup results on the Denelcor HEP parallel processor.

Parallel-processing a large scientific problem

We discuss a parallel-processing experiment that uses a particle-in-cell (PIC) code to study the feasibility of doing large-scale scientific calculations on multiple-processor architectures. A multithread version of this Los Alamos PIC code was successfully implemented and timed on a UNIVAC System 1100/80 computer. Use of a single copy of the instruction stream, and common memory to hold data, eliminated data transmission between processors. The multiple-processing algorithm exploits the PIC codes high degree of large, independent tasks, as well as the configuration of the UNIVAC System 1100/80. Timing results for the multithread version of the PIC code using one, two, three, and four identical processors are given and are shown to have promising speedup times when compared to the overall run times measured for a single-thread version of the PIC code.