Scalability Evaluation of Iterative Algorithms Used for Supercomputer Simulation of Physical processes

Abstract

The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on the BSF (Bulk Synchronous Farm) parallel computation model, which makes it possible to predict the upper scalability bound of an iterative algorithm in early phases of its design. The BSF model assumes the representation of the algorithm in the form of operations on lists using high-order functions. Two classes of representations are considered: BSF-M (Map BSF) and BSF-MR (Map-Reduce BSF). The proposed methodology is described by the example of the solution of the system of linear equations by the Jacobi method. For the Jacobi method, two iterative algorithms are constructed: Jacobi-M based on the BSF-M representation and Jacobi-MR based on the BSF-MR representation. Analytical estimations of the speedup, parallel efficiency and upper scalability bound are constructed for these algorithms using the BSF cost metrics on multiprocessor computing systems with distributed memory. An information about the implementation of these algorithms in C++ language using the BSF program skeleton and MPI parallel programming library are given. The results of large-scale computational experiments performed on a cluster computing system are demonstrated. Based on the experimental results, an analysis of the adequacy of estimations obtained analytically by using the cost metrics of the BSF model is made.

Scalable parallel algorithm for solving non-stationary systems of linear inequalities

“…This algorithm was presented as the ModAPL algorithm on lists using the higher-order functions M ap and Reduce. For the ModAPL algorithm, we obtained an estimation of the scalability bound of its parallel version using the cost metric of the BSF parallel computing model [18]. If a small part of the source data is dynamically changed during one iteration then the scalability bound is equal to O ( √ n), where n is the problem dimension.…”

“…To construct a parallel version of the algorithm ModAP, we use the BSF (Bulk Synchronous Farm) model of parallel computations [17]. In accordance to the technique proposed in [18], we represent the algorithm in the form of operations on lists using the higher-order functions M ap and Reduce defined in the Bird-Meertens formalism [19]. Let us define the list A = [(a 1 , b 1 ), .…”

“…To obtain an analytical estimation of the scalability of the parallel version of the ModAPL algorithm (Fig. 5) we use the cost metric of the BSF model [18]. It includes the following parameters: For the ModAPL algorithm we have…”

“…Using the scalability boundary equation from [18], and taking into account (18), we obtain from ( 26)-(30) the following estimation:…”

Scalable Method for Linear Optimization of Industrial Processes

“…We performed a parallel implementation of Algorithm 2 in C++ using the BSF skeleton [33] based on the MPI parallel programming library. The parallel implementation scheme is similar to the ones used in [34] and [31]. The source codes are freely available at https://github.com/leonid-sokolinsky/NSLP-Quest.…”