An organization of the extrapolation method for vector processing

Abstract

Evaluation of an integrand function in the process of numerical quadrature is known to be the major factor in the time to carry out the computation. This effect can grow dramatically with the dimension of the integral. The purpose of this research work is to investigate the possible reduction in time for the computation of a multidimensional integral with the use of the extrapolation technique by reducing the time required to evaluate the integrand function through vector processing. The basics of the extrapolation technique of numerical quadrature are given. A conventional implementation of the extrapolation algorithm over a triangular region is studied and the problems associated with its use on vector processos are discussed. An alternative, buffered, algorithm, which is shown to be suitable for both vector and parallel processing is introduced. A possible implementation of the new algorithm on the CDC STAR-100 is discussed. The effect of varying the buffer length on the performance of the vectorized and unvectorized parts of the algorithm is analysed. A method of determining a reasonable buffer size from essentially machine constants of a particular vector processor is represented. A slight variation of the same algorithm is efficiently implemented for domains triangulated into multiple triangles and it is shown that the algorithm may run at essentially vector instruction speeds in this case.