Download Scientific Computing on Supercomputers III by F. W. Wray (auth.), Jozef T. Devreese, Piet E. Van Camp PDF

By F. W. Wray (auth.), Jozef T. Devreese, Piet E. Van Camp (eds.)

The foreign Workshop on "The Use of Supercomputers in Theoretical technology" came about on January 24 and 25, 1991, on the collage of Antwerp (UIA), Antwerpen, Belgium. It used to be the 6th in a chain of workshops, the 1st of which came about in 1984. The primary objective of those workshops is to give the cutting-edge in clinical large-scale and excessive speed-computation. Computational technology has built right into a 3rd method both vital now as its theoretical and experimental partners. progressively educational researchers got entry to a number of supercomputers and hence computational technological know-how has turn into a tremendous software for his or her paintings. it's a excitement to thank the Belgian nationwide technology starting place (NFWO-FNRS) and the Ministry of medical Affairs for sponsoring the workshop. It used to be geared up either within the framework of the 3rd Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental application in info Technology". We additionally a great deal want to thank the collage of Antwerp (Universitaire Instelling Antwerpen -VIA) for monetary and fabric help. targeted thank you are as a result of Mrs. H. Evans for the typing and enhancing of the manuscripts and for the coaching of the writer and topic indexes. J.T. Devreese P.E. Van Camp college of Antwerp July 1991 v CONlENTS excessive Perfonnance Numerically extensive purposes on allotted reminiscence Parallel desktops .................... . F.W. Wray summary ......................................... .

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2. Muitigrid Solver In the multigrid method a coarser grid is constructed by considering 2 x 2 neighbouring cells of the fine grid as one new cell of the next coarser grid. Hence, the finest but one grid contains (Nx / 2) x (Ny / 2) cells, and so on. The optimal number of multigrid levels to be used depends very much on the problem. On a sequential computer, 1 multigrid levels can be used when both N x and Ny are a multiple of 21-1• On a parallel computer a problem arises when the number of cells per node in the x or y direction becomes odd after some coarsening steps.

Further, in an agglomeration phase the nodes that go idle send their information to another node and in a deagglomeration phase idle nodes await a message to become active. Because of the "perimeter effect" [5] the communication time becomes a larger fraction of the total execution time on the coarser grids, especially when the start-up time for communication is high. Note for example that for the test problem considered here the grids of levels 5 and 6 contain more boundary grid points than interior grid points.

7 23 We now transform the modified matrix using the mapping dermed above. 8. We now eliminate the non-zero sub-diagonal matrix in the fIrst column of the block matrix using the fIrst row, and so on until the block matrix becomes block upper triangular. We modify the right hand side as appropriate. The matrices remain simple as this elimination proceeds and as before their data need only move locally. 10 describe the form of the matrix as this elimination proceeds. We should note that if we had not made the minor restriction on pivoting an extra subdiagonal block matrix would have been introduced.

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