Johnson, Olin G., IBM Scientific Center
In this paper, we describe an array or vector processor that, with only one basic arithmetic operation, can be used in parallel with a central processor for numerical reservoir simulation. In doing so, we demonstrate a partitioning of the problem to balance the partitioning of the problem to balance the computational load between the processors under the constraints imposed by the instruction sets and the relative speeds. We also discuss certain mathematical aspects of the partitioning and the iterative algorithms. Finally, we present results from numerical experiments using present results from numerical experiments using the IBM 2938 Array Processor with an IBM 360/85, 75, 65 or 44.
Index Terms for IBM Subject Index
Array Processing Mathematics Reservoir Modeling Numerical Analysis ADI Computer Applications SOR IBM 2938
Much has been written recently in the area of parallel computation. Some problems have been attacked by using several identical general purpose processing units sharing a common purpose processing units sharing a common memory bank. Other problems have motivated the design of some highly parallel, special purpose arithmetic units arranged in two-dimensional arrays, each with its own memory and each with the ability to communicate with some of its neighboring units.
In this paper, we consider a very elementary type of parallel computation that is a combination of these two types. The idea is to augment a general purpose computer with an auxiliary arithmetic unit of special type. The computational objective is to place a large part of the computational load arising out of problems such as numerical reservoir simulation in problems such as numerical reservoir simulation in the special unit. This objective dictates that the unit be floating point and operate at high speed on vectors and band matrices. The economic objectives are to create a system that is much less expensive than two general purpose central processing units and that is several times as fast as a stand-alone central processor. processor. In particular, we show that if the auxiliary arithmetic unit, which we will henceforth call the array processor, contains only one basic vector function, then we can construct a parallel algorithm for reservoir simulation. parallel algorithm for reservoir simulation. Further, we have implemented this algorithm on an IBM 360/44, 65, 75, 85 with an IBM 2938 array processor and we present numerical results from processor and we present numerical results from these programs. In Section 2, we give a functional description of the array processor. In Section 3, we identify the basic computation kernels in a standard reservoir model.