Download Applications of Supercomputers in Engineering II by J. B. Vos, C. M. Bergman (auth.), C. A. Brebbia, A. Peters, PDF

By J. B. Vos, C. M. Bergman (auth.), C. A. Brebbia, A. Peters, D. Howard (eds.)

This publication includes an edited model of the court cases of the second Interna­ tional convention on functions of Supercomputers in Engineering which came about on the Massachusetts Institute of know-how, Cambridge, united states in the course of August 1991. The convention used to be prepared by means of the Wessex Insti­ tute of know-how, Southampton, united kingdom with the help of the overseas Society for Boundary components. the 1st overseas convention on Ap­ plications of Supercomputers in Engineering held in Southampton, united kingdom in September 1989 used to be a really profitable assembly and the ensuing convention lawsuits are actually broadly disbursed through the international. The innovative points of the subsequent new release of desktops at the moment are absolutely acknowledged via many engineers and scientists. Vector and parallel desktops shape the root of the computing strength had to tackle the complicated prob­ lems with which engineers are confronted. the hot machines not just elevate the dimensions of the issues which might be solved, but additionally require a unique computational method of receive the best results.

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3(b), since we require the values of immediate neighbours in calculating the right hand side of equations (7) and (8). The problem is solved using a single Occam code which is loaded onto each processor. Each processor determines the position of its xnodes x ynodes submesh in the overall mesh from its coordinates (Xid, Yid) in the processor array, and sets up and initialises the problem accordingly. The decompositions in the r-direction are then started on the first processor in each row, sweeping forwards across both the submesh and the processor array, communicating the required last value of f on a processor, which becomes the first value of f on the adjacent processor, and similarly in the z-direction.

RI! = R~ . - 1. [( R: (R:)"i + ( R:ji - (R:t, '6-V'~C ",) ',) h A: 1- 1i,j A~ i-I,; A~ i,j A~ j,;-l 1 ' which is again a tridiagonal system in the form of equation(9). This time, however, the coefficients vary from iteration to iteration and the decompositions cannot therefore be done only once. Also, the order of solution of the rows (or columns) is important since it affects the rate of convergence of the method, and in this case we solve each row successively moving up the grid from the boundary (and across for columns).

The parallelized kernel is shown in figure 6. Two OCLs are included to indicate that there are no recurrencies. The compiler parallelizes automatically the outermost loop and realizes the necessary FORK/JOIN-mechanisms. OCL LOOP,NOPREC DO 30 IPROC=l,NPROC DO 20 ID=l,ND,NPROC . (index calculations) *YOCL LOOP,NOYREC DO 10 I=l,LD X(IP(I+IPO)+IXO,IPROC) & =X(IP(I+IPO)+IXO,IPROC) & +A(I+IAO)*B(IP(I+IPO)+IBO) 10 CONTINUE 20 30 . (index calculations) CONTINUE CONTINUE (process remaInIng diagonals if ND is not a multiple of NPROC) (sum up the solution arrays X ( .

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