Load balancing is a widely accepted technique for performance optimization of scientific applications on parallel architectures. Indeed, balanced applications do not waste processor cycles on waiting at points of synchronization and data exchange, ma
ximizing this way the utilization of processors. In this paper, we challenge the universality of the load-balancing approach to optimization of the performance of parallel applications. First, we formulate conditions that should be satisfied by the performance profile of an application in order for the application to achieve its best performance via load balancing. Then we use a real-life scientific application, MPDATA, to demonstrate that its performance profile on a modern parallel architecture, Intel Xeon Phi, significantly deviates from these conditions. Based on this observation, we propose a method of performance optimization of scientific applications through load imbalancing. We also propose an algorithm that finds the optimal, possibly imbalanced, configuration of a data parallel application on a set of homogeneous processors. This algorithm uses functional performance models of the application to find the partitioning that minimizes its computation time but not necessarily balances the load of the processors. We show how to apply this algorithm to optimization of MPDATA on Intel Xeon Phi. Experimental results demonstrate that the performance of this carefully optimized load-balanced application can be further improved by 15% using the proposed load-imbalancing optimization.
Hardware-aware design and optimization is crucial in exploiting emerging architectures for PDE-based computational fluid dynamics applications. In this work, we study optimizations aimed at acceleration of OpenFOAM-based applications on emerging hybr
id heterogeneous platforms. OpenFOAM uses MPI to provide parallel multi-processor functionality, which scales well on homogeneous systems but does not fully utilize the potential per-node performance on hybrid heterogeneous platforms. In our study, we use two OpenFOAM applications, icoFoam and laplacianFoam, both based on Krylov iterative methods. We propose a number of optimizations of the dominant kernel of the Krylov solver, aimed at acceleration of the overall execution of the applications on modern GPU-accelerated heterogeneous platforms. Experimental results show that the proposed hybrid implementation significantly outperforms the state-of-the-art implementation.
Matrix multiplication is a very important computation kernel both in its own right as a building block of many scientific applications and as a popular representative for other scientific applications. Cannon algorithm which dates back to 1969 was th
e first efficient algorithm for parallel matrix multiplication providing theoretically optimal communication cost. However this algorithm requires a square number of processors. In the mid 1990s, the SUMMA algorithm was introduced. SUMMA overcomes the shortcomings of Cannon algorithm as it can be used on a non-square number of processors as well. Since then the number of processors in HPC platforms has increased by two orders of magnitude making the contribution of communication in the overall execution time more significant. Therefore, the state of the art parallel matrix multiplication algorithms should be revisited to reduce the communication cost further. This paper introduces a new parallel matrix multiplication algorithm, Hierarchical SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the communication cost of SUMMA by introducing a two-level virtual hierarchy into the two-dimensional arrangement of processors. Experiments on an IBM BlueGene-P demonstrate the reduction of communication cost up to 2.08 times on 2048 cores and up to 5.89 times on 16384 cores.
Traditional heterogeneous parallel algorithms, designed for heterogeneous clusters of workstations, are based on the assumption that the absolute speed of the processors does not depend on the size of the computational task. This assumption proved in
accurate for modern and perspective highly heterogeneous HPC platforms. New class of algorithms based on the functional performance model (FPM), representing the speed of the processor by a function of problem size, has been recently proposed. These algorithms cannot be however employed in self-adaptable applications because of very high cost of construction of the functional performance model. The paper presents a new class of parallel algorithms for highly heterogeneous HPC platforms. Like traditional FPM-based algorithms, these algorithms assume that the speed of the processors is characterized by speed functions rather than speed constants. Unlike the traditional algorithms, they do not assume the speed functions to be given. Instead, they estimate the speed functions of the processors for different problem sizes during their execution. These algorithms do not construct the full speed function for each processor but rather build and use their partial estimates sufficient for optimal distribution of computations with a given accuracy. The low execution cost of distribution of computations between heterogeneous processors in these algorithms make them suitable for employment in self-adaptable applications. Experiments with parallel matrix multiplication applications based on this approach are performed on local and global heterogeneous computational clusters. The results show that the execution time of optimal matrix distribution between processors is significantly less, by orders of magnitude, than the total execution time of the optimized application.
