THE ENVIRONMENT DYNAMICS IDENTIFICATION BASED ON THE MODULAR COMPUTING COMPLEX

The research aims at covering the mathematical modeling issues of multidimensional applied problems of ecology based on the application of a modular computing complex. The problem of modeling air pollution processes is solved by mathematical models that adequately describe fundamental processes. That reveals issues such as a detailed analysis of the atmosphere of the city or industrial area, short-term forecast of air quality in the region, assessment of long term air purification programs, optimal emission management, transboundary transfer, etc. At the same time, the formulation and methods of solving problems of environmental dynamics identification are considered, which essence is to estimate the input parameters based on the factual information about the modeled system known from the experiment. In these studies, the multidimensional equation of harmful impurities transfer was reduced to a sequence of schemes involving unknown values in a single direction, alternately in the longitudinal, transverse and vertical.The implicit schemes lead to systems of algebraic linear equations with a three-diagonal structure. Thus, the methodological basis of the difference splitting schemes provides the economic and sustainable implementation of numerical models by the scalar runs method. That approach focuses on the fact that the greatest effect of a parallel processor is achieved when it is used to perform matrix computations of linear algebra.In order to analyze the feasibility of mathematical models, a package of applications was developed to compute the transfer of harmful impurities. A solution to several applied problems for the identification of the environmental dynamics is given.

Linnea

The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for matrix computations (e.g., Matlab, Eigen) internally use optimized kernels such as those provided by BLAS and LAPACK; however, their translation algorithms are often too simplistic and thus lead to a suboptimal use of said kernels, resulting in significant performance losses. To combine the productivity offered by high-level languages, and the performance of low-level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem; as output, it returns an efficient sequence of calls to high-performance kernels. Linnea uses a custom best-first search algorithm to find a first solution in less than a second, and increasingly better solutions when given more time. In 125 test problems, the code generated by Linnea almost always outperforms Matlab, Julia, Eigen, and Armadillo, with speedups up to and exceeding 10×.