THE STRUCTURE OF CUBATURE FORMULAS MODELLING FOR THE EFFICIENT FPGA IMPLEMENTATION
Keywords:
Cubature formula, theory of space granulation, space granules, high-performance computing, configurable computer, FPGAAbstract
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.
