THE STRUCTURE OF CUBATURE FORMULAS MODELLING FOR THE EFFICIENT FPGA IMPLEMENTATION

Abstract

In the paper we present the new computing models for the common cubature formulas computing unit design and optimization. The basis of new modeling technique is related with the space granulation theory, developed in our recent papers. The Spatial Granulation Technique allows us to pass from computing in the metrical data points space to affine data space, contains the aggregated data units named as granules. The introduced data transformation based on the affineinvariant Cartesian granule model and on the optimal data points coarsening procedures. The useful properties of new data models allows to provide the very efficient multivariable data management procedures. The one of them is the multivariate cubature formulas calculation. The new theory provides the obvious matrix data processing models for the information graphs design andoptimization. We can perform the equivalent mappings for the complicated information graph models for the efficient structures matching. Optimized models of information graphs are used for the FPGA-based devices implementation. The main problem of FPGA design is the commutation structures complication for the large FPGA fields, obtained as the basic units for the reconfigurable cubature formulas computing units. In this work we use the high-level programming language COLAMO and assembler language Fire Constructor for the computing units implementation. As a result of new technique implementation we can provide the family of adequate and useful graphic representation for a multivariable cubature formulas over the matrix calculation. The provided models are suitable for the optimal design of configurable computing structures, universal and dedicated devices from the FPGA basis. For the device implementation the developed high-level software products are used. For the designed universal devices the testing procedures was performed and examined with the symbolic calculation software for the computing results evaluation.