- 192 - TRENDS IN SUPERCOMPUTERS AND COMPUTATIONAL PHYSICS T. Bloch Centre de Calcul Vectoriel pour la Recherche, Ecole Polytechnique, Palaiseau 1. Introduction Investigation and evaluation of complex non-linear systems is frequently only possible using numerical modelling. This - almost experimental - computational science is increasing in scope and importance every day thanks to the combination of improved computational methods and the continuous development of faster and faster "supercomputers". Application fields which were pioneered in the 1950's and the 1960's have today entered the production stage; e.g. structural safety calculations, global circulation models for meteorological forecasting, aerodynamics' design, oil reservoir simulation. Use of supercomputers and numerical modelling permit considerable global economies in agriculture and transport due to improved weather forecasting and, in engineering applications, shorter development cycles, lower design costs and lighter end designs are achieved. Today, scientists using numerical models explore the basic mechanisms of semi• conductors, apply global circulation models to climatic and océanographie problems, probe into the behaviour of galaxies and try to verify basic theories of matter, such as Quantum Chromo Dynamics by simulating the constitution of elementary particles. Chemists, crystallographers and molecular dynamics researchers develop models for chemical reactions, formation of crystals and try to deduce the chemical properties of molecules as a function of the shapes of their states. Chaotic systems are studied extensively in turbulence (combustion included) and the design of the next generation of controlled fusion devices relies heavily on computational physics. Thus, many complex systems which cannot be studied analytically with present methods and which are not open to experimentation, are studied on supercomputers improving our basic scientific understanding. As a result the scientific and economic importance of supercomputers and the advanced use of them is now clearly perceived by all major industrial countries. More than 100 CRAY and Cyber 205 computers are installed world-wide with Europe accounting for about one third and Japan about 10%. Although Japan thus seems to lag slightly behind on supercomputer applications, the trend is to catch up very rapidly now that both Hitachi and Fujitsu have proven machines available (S-810 and VP-200) and NEC is bringing out the SX-2 by the middle of 1985. In the United States there are more supercomputer installations than anywhere else, but it has now been generally accepted - thanks for a large part to K. Wilson - that the access for the university research community has not been as good as in Europe where an appreciable proportion of supercomputers are installed in generally accessible regional or inter-university computer centres: one in Holland, two in the United Kingdom, one in France, one in Italy and four or five in Germany. A major effort is now under way in the United States to distribute the access to supercomputers much more - 193 - widely; this programme is handled through the National Science Foundation which, already in 1985, is funded to set up about three new supercomputer centres. 2. Examples taken from the early history of computational physics The starting point for using numerical methods in cases where analytical ones are no longer possible can perhaps be traced back to the work of W.F.Sheppard concerning the finite difference methods. This method was used by L.F. Richardson from 1910 to make a dam computation after which he went on to conceive the first global circulation model imagining 64,000 people in a huge amphitheatre, each advancing a time-step at a time based on the information from the neighbours under the baton of a conductor. R. Courant, R. Friedrichs and H. Lewy (1928) brought the theoretical foundation that partial differential equations are indeed approximated by the discretized equations under certain stability criteria. Around 1950, John von Neumann and a number of collaborators attacked new problems with the first digital computers (ENIAC in 1946, then MANIAC) and started to realize the programme of computational physics which he had published in 1946 together with H.H. Goldstine: develop stability criteria for time-step and grid size for finite difference methods to solve parabolic partial differential equations. make shock-wave calculations using smoothing techniques with boundary layers with at least the size of the grid. code the first barytropic (no temperature variation along isobars) general circula• tion model with a grid of 15 x 18 over the continental United States (with J.G. Charney, R. Fjörtoft and J. Smagorinski). make hydrodynamic instabilities and neutron cascade calculations with E. Fermi and S. Ulam in Los Alamos on MANIAC. On this occasion, S. Ulam discovered the Monte Carlo method. The discovery of solitons is a classic example of a new insight into physics found by computational physics: in about 1955, E. Fermi, J. Pasta and S. Ulam studied the motion of a chain on masses coupled by weakly non-linear springs. (They were trying to develop a theory explaining the finite thermal conductivity of solids.) Long wave• length disturbances of this system resulted, as expected, in a mix of shorter wave• length modes. However, after a finite time, the system was unexpectedly seen to revert to (almost) the initial state (without equi-partition of the energy). In the early 1960's, M. Kruskal and N. Zabusky found that the problem studied could be approximately reduced to the Korteweg-de Vries equation which is a well known hydrodynamics equation describing shallow water waves. Numerical studies of the solutions to this equation lead to the discovery that its complicated solutions could be classified as a set of pulse-like waves propagating at constant velocity with an unchanged shape, called solitons. A fertile period of analytic proofs of many new properties of a variety of non-linear partial differential equations used in physics then followed. - 194 - 3. Historical notes from the development of recent supercomputers Several definitions of supercomputers exist; from the fast(est) computer(s) of a given period to the only computers which, already on the day of their first delivery, are not fast enough. 3.1 The "pure FORTRAN" supercomputers up to 1969 From about 1956 to 1969, it was the reign of the FORTRAN-machine in the field of the fastest computers: UNIVAC, Ferranti, IBM and CDC installed computers such as the LARK, the 7090, the 6600, the STRETCH, the ATLAS, the 360-91 and the 7600. During this period the speed of computers increased by a factor of two every two or three years, without significantly affecting the price and without the user having to restructure his programs. (In practice, of course, reliability problems and the painful evolution of the first multiprogrammed, and later, time-sharing, operating systems left much to be desired in the service provided.) The first delivery of the CDC 7600 in 1969 marked the end of the reign of the FORTRAN machine in supercomputing; it was about 50 times faster than the IBM 7090, its senior by 10 years. Its basic circuits were about 10 times faster, and another factor of five has been achieved by internal improvements in architecture, allowing more things to go on in parallel both within the CPU itself, and also between the CPU and the stored information: multiple memory banks, instruction buffers and preloading of instructions, many more registers (programmable and otherwise) in the CPU, multiple and pipelined execution units (and the logic to keep track of what was going on where), etc... From 1969 on, two major factors became dominant in determining which super• computer could be developed: a) the basic technology no longer improved rapidly (the CRAY X-MP2, first delivered in 1983, is based on circuits only about three times faster than those of the CDC 7600) and the benefits even from these improvements became difficult to realise fully because the dominant factor in high-speed design has moved away from the switching speed of the active devices to the propaga• tion delays in the interconnecting conductors. b) higher speeds with the same technology can be obtained if one gives up the "simulation", vis-à-vis the user, of the basic "von Neumann" architecture of the CPU: fetch an instruction, decode it (being prepared for anything), fetch the operands (from anywhere), execute the operation, store the result anywhere and start all over again for the next instruction. The result is that new and faster "vector" computers are now available but the user must be soilici ted much more. He must collaborate in order to organize the execution of his program better, he must tell the computer clearly through the program how the access to operands is organized when there is regularity and he must avoid IFs where he can and try to organise the computation in long D0-loops. Ultimately, he must rethink the problem, the method and the coding to suit the internal organisation of the computer... The next step, already true for the CRAY X-MP and soon to be imposed by the CRAY-2, the ETA-10 and the Fujitsu VP-400 will be that the user must split his - 195 - problem into two, four or eight "pieces" which can execute concurrently on inde• pendent processors with a common main memory. The "Vector" supercomputers from 1974 to 1985 Two pioneering supercomputers with this new vector architecture were con• ceived from 1966 onwards and first delivered in 1973/1974, the CDC STAR-100 and the Texas Instruments ASC (Advanced Scientific Computer). They had rich instruc• tions sets including explicit vector instructions operating in a memory-to-memory fashion and multiple "pipelines" to execute them. However, they already clearly demonstrated the potential problems of these architectures: high peak vector speeds on long vectors contrasting only too sharply with the scalar speeds achieved.