In this paper, we discuss a rather old and not well-exploited approach to ``Grand Challenge'' problems in computational sciences, namely to design and build the computer hardwares specialized and optimized for relatively narrow range of problems.
The primary reason why we discuss this approach is simply that our GRAPE project [8,6] to develop special-purpose computers for astrophysical N-body problems has been, at least in our opinion, highly successful, compared to the conventional approach to adopt the algorithms to available computer hardwares. Figure 1 shows the peak speed of our GRAPE systems and that of representative high-performance general-purpose computers. In year 1995, we completed GRAPE-4 with the peak speed of 1.08 Tflops. It was the fastest computer for scientific simulations at that time. In year 2001, we will complete the GRAPE-6 system, with the peak speed around 120 Tflops. The development costs, or the total budgets, of GRAPE-4 and GRAPE-6 are 2.5 and 4.5 million USD, respectively, which should be compared to around 100 million USD of latest ASCI machines (12 Tflops by the end of year 2000).
Figure 1: The evolution of GRAPE and general-purpose parallel computers. The peak speed is plotted against the year of delivery. Filled circles, open triangles and open squares denote GRAPEs, vector processors, and parallel processors, respectively.
Of course, the peak speed does not tell much, since the actual speed one can achieve is, by definition, lower than the peak speed. In addition, what ultimately matters is what kind of problems can actually be solved. Here, it would be sufficient to say that more than 100 copies of various versions of GRAPE hardwares have been manufactured and are now being used in more than 30 institutes worldwide to explore wide variety of problems in astrophysics.
In the rest of this paper, we first discuss the trends in the semiconductor technology and that of general-purpose computers in section 2. Our main point is that general-purpose computers now utilize only a small fraction of available number of transistors to do useful arithmetic operations. This ratio has been decreasing for the last 30 years, and will continue to do so for the foreseeable future. In section 3, we discuss the potential advantages and drawbacks of designing and developing special-purpose systems. The potential gain is very large, since, at least in some cases, we might be able to use a much larger fraction of available transistors to perform useful arithmetic operation. On the other hand, there are many practical difficulties which would offset the potential gain. In section 4, we discuss our GRAPE project as an example of, well, reasonably successful projects to develop special-purpose computers. In section 5, we speculate on the future of the large-scale scientific computing.