Design and implementation of self-adaptable parallel algorithms for scientific computing on highly heterogeneous HPC platforms

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 inaccurate 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.