Computational physics on the CM2 supercomputer
Abstract
The Connection Machine Supercomputer system is described with emphasis on the solution to large scale physics problems. Numerous parallel algorithms as well as their implementation are given that demonstrate the use of the Connection Machine for physical simulations. Applications discussed include classical mechanics, quantum mechanics, electromagnetism, fluid flow, statistical physics and quantum field theories. The visualization of physical phenomena is also discussed and in the lectures video tapes demonstrating this capability are shown. Connection Machine performance and I/O characteristics are also described as well as the CM-2 software.
- The computational modelling of optoelectronic guided-wave devices in 3-dimensions is usually very demanding in terms of computer time because of the size of typical devices, which are generally much longer than a wavelength. In these circumstances, it is natural to turn to parallel processing implementations in order to achieve practical run times for realistic devices. Not all serial methods are readily adapted to the parallel environment, however, and care needs to be exercised in selecting the appropriate method for parallelisation. In general, for MIMD architectures one should seek to minimise the time spent in communicating between processors, and one is therefore led to prefer methods which can be localised onto separate processors. Finite-difference methods are intrinsically local in the configuration domain, and hence very suitable for parallel processing.
- In this work, we show the implementation of two explicit three-dimensional finite-difference beam propagation methods (BPM) on two different parallel computers, namely a transputer array and a Connection Machine (CM). To assess the performance of using parallel computers, serial computer codes of the two methods have ben implemented and a comparison between the speed of the serial and paralledl codes has been made. Large gains in the speed of the paralled FD-BPMs has been obtained compared to the serial implementations. In addition, a comparison between the performance of the transputer array and the CM in executing the two FD-BPMs has been discussed. Finally, to assess and compare the two methods, three different rib waveguides and three different directional couplers have been analysed and the results compared with published results.
- The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ‘‘phase-matching’’ criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ‘‘plateau’’ regime, the phases exhibit only weak dependence upon the intensity of the driving field. ©1996 The American Physical Society.
- Nonrelativistic quantum-mechanical scattering in two dimensions is studied numerically by integrating the time-dependent Schrödinger equation. A partial-wave analysis is used to discuss the numerical results. A potential barrier, a square well and a single slit are considered as the scattering potentials.
- This book contains the proceedings of the 1988 conference on Scientific Applications of the Connection Machine. Included are the following articles: A Connection Machine Implementation of Tracer Particle Flow Visualization, Dynamic Finite Element Simulations on the Connection Machine, 3 D Image Synthesis on the Connection Machine.
- We describe the details involved in presenting the time development of one-dimensional quantum-mechanical systems in the form of computer-generated motion pictures intended for pedagogic purposes. Concentrating on reflection-transmission phenomena, we formulate the problem in terms of a Gaussian wave packet impinging on a square well or barrier and being reflected and transmitted. The wave equation is solved numerically by methods discussed in detail and photographs of the wave packet vs position at a variety of times and for a range of projectile energies are given.
- Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
- We implement parallel algorithms for solving the time-dependent Schrödinger equation on the CM-2 supercomputer. These methods are unconditionally stable as well as unitary at each time step and have the advantage of being spatially local and explicit. We show how to visualize the dynamics of quantum scattering using techniques for visualizing complex wave functions. Several scattering problems are solved to demonstrate the use of these methods.
- This paper introduces a new family of explicit and unconditionally stable algorithms for solving linear parabolic difference equations. The mathematical foundation is presented and it is shown how the algorithms can be implemented on scalar and vector processors. The performance is evaluated and compared to standard methods. It is demonstrated that some of the proposed algorithms are orders of magnitude more efficient than conventional schemes. The most efficient algorithm is employed to solve Schrödinger equations for problems including, localization in an almost-periodic potential and two-dimensional Anderson localization. By combining product formula algorithms and the variational principle a method is devised to compute the low-lying states of a quantum system, capable of separating nearly-degenerate eigenstates. The usefulness of this method is illustrated by applying it to spin-boson system.
- The characteristics of the waves guided along a plane [I] P. S. Epstein, “On the possibility of electromagnetic surface waves, ” Proc. Nat’l dcad. Sciences, vol. 40, pp. 1158-1165, Deinterface which separates a semi-infinite region of free cember 1954. space from that of a magnetoionic medium are investi- [2] T. Tamir and A. A. Oliner, “The spectrum of electromagnetic waves guided by a plasma layer, ” Proc. IEEE, vol. 51, pp. 317gated for the case in which the static magnetic field is 332, February 1963. oriented perpendicular to the plane interface. It is [3] &I. A. Gintsburg, “Surface waves on the boundary of a plasma in a magnetic field, ” Rasprost. Radwvoln i Ionosf., Trudy found that surface waves exist only when w,<wp and NIZMIRAN L’SSR, no. 17(27), pp. 208-215, 1960. that also only for angular frequencies which lie bet\\-een [4] S. R. Seshadri and A. Hessel, “Radiation from a source near a plane interface between an isotropic and a gyrotropic dielectric,” we and 1/42 times the upper hybrid resonant frequency. Canad. J. Phys., vol. 42, pp. 2153-2172, November 1964. The surface waves propagate with a phase velocity [5] G. H. Owpang and S. R. Seshadri, “Guided waves propagating along the magnetostatic field at a plane boundary of a semiwhich is always less than the velocity of electromagnetic infinite magnetoionic medium, ” IEEE Trans. on Miomave waves in free space. The attenuation rates normal to the Tbory and Techniques, vol. MTT-14, pp. 136144, March 1966. [6] S. R. Seshadri and T. T. \Vu, “Radiation condition for a maginterface of the surface wave fields in both the media are netoionic medium. ” to be Dublished. examined. Kumerical results of the surface wave characteristics are given for one typical case.
- We have designed and built the Orrery, a special computer for high-speed high-precision orbital mechanics computations. On the problems the Orrery was designed to solve, it achieves approximately 10 Mflops in about 1 ft3of space while consuming 150 W of power. The specialized parallelarchitecture of the Orrery, which is well matched to orbital mechanics problems, is the key to obtaining such high performance. In this paper we discuss the design, construction, and programming of the Orrery. Copyright © 1985 by The Institute of Electrical and Electronics Engineers, Inc.
- Thinking Machines Corporation
- C User
C* User's Guide, Thinking Machines Corporation, Cambridge, MA 02142-1214. - Molecular dynamics on the Connection Machine, Thinking Machines tech, rep
- B Murray
- Pa Bash
- M Karplus
B. Murray, PA. Bash and M. Karplus, Molecular dynamics on the Connection Machine, Thinking Machines tech, rep. CB88-3. - Thinking Machines Corporation, Cambridge, MA 02142-1214 The Architecture of the CM-2 Data Processor, Thinking Machines tech, rep
- D B Douglas
- A Kahie
- Vasilevsky
CM-2 Technical Summary, Thinking Machines Corporation, Cambridge, MA 02142-1214. [31 D. Douglas. B. Kahie and A. Vasilevsky, The Architecture of the CM-2 Data Processor, Thinking Machines tech, rep. HA89-l (1988).
