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We describe the use of supercomputers in general and the necessary considerations for their efficient use in ocean modelling. A brief history of supercomputer development is given, and the relative merits of the Cray X-MP and Cyber 205 (the two leading supercomputers at present) machines are compared. Automatic vectorization is described for both machines. Explicit vectorization via the Cyber 205 Fortran vector extensions is discussed.

The iterative methods for elliptic equations described in the preceding section have many attractive qualities. They require a minimal amount of computer storage, they almost always converge to the true solution to the partial differential equation and they are simple to implement in most situations. They have the disadvantage, however, that they can be very expensive, since they usually require a large number of iterations. There is another class of solvers, the direct methods, that treat the finite difference equations as a large linear system and employ some tools from linear algebra to operate on the matrix of the finite difference coefficients. These methods take advantage of the sparseness and regular structure of the coefficient matrices to minimize storage requirements and operation counts. Although they usually require more storage than the iterative methods, they require fewer operations. We describe four direct methods that can be generally divided into two categories. The first three methods seek to reduce the order of the system of equations by appropriate transformations, while the fourth method performs a lower-upper decomposition on the entire system of equations.

The increasing availability of supercomputers to the ocean modeling community in recent years is opening vast new possibilities for oceanographic research. Many research institutions in Europe and the United States now have access to supercomputers. This access not only changes the way one approaches a problem, but enables one to think of new problems that were previously intractable. Ocean modeling lends itself particularly well to supercomputing because of the structure of the partial differential equations involved and the numerical algorithms one must use to solve them. Ocean models usually “vectorize” very easily and require the storage of a large number of variables at a particular instant, enabling one to take full advantage of the capabilities of a supercompter.