Vector finite‐element analysis using IBM 3090–600e VF

Abstract

AbstractA finite‐element computer program consists of four basic modules, namely, computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses. Vector algorithms consisting of direct vector Fortran code and the Engineering and Scientific Subroutine Library (ESSL) routines are presented for these modules. Numerical investigations were conducted using the IBM 3090–600E VF computer.For element stiffness matrix calculation, using a vector length equal to the number of elements produced speed‐up in the range of 3·2 to 3·7 over the corresponding scalar code. The vectorized global element stiffness matrix assembly was accomplished with the help of an INDEX array and the ESSL routine DAXPYI that resulted in the speed‐up of 2·6 to 4·3. The ESSL routines DPBF and DPBS gave speed‐up of 7·7 to 53·6 over a scalar Gaussian solver. The scalar‐to‐vector speed‐up for the stress calculation ranges from 2·2 to 5·33. The speed‐up of the totally vectorized program over the scalar program is from 7·4 to 51·9.As would be expected, the equation solution takes up the most computational effort in a finite‐element analysis. For the models we analysed the equation solution consumed 93 per cent to almost 100 per cent of the total CPU time in the scalar computations. Vectorizing the equation solver only reduces the percentage of its share to the range of 63 per cent to 88 per cent. In a totally vectorized program, the share of the equation solver effort is 85 per cent to 97 per cent. For the models analysed, the additional speed‐up accomplished by vectorizing the whole program over the one with a vectorized equation solver only was from 10 per cent to 40 per cent.