Three-dimensional numerical simulations of the czochralski bulk flow on a CRAY X-MP multiprocessor architecture

ABSTRACT

Today, numerical simulation is used more and more to get detailed information about crystal growth processes. In the Czochralski crystal growth from electrically conductive melts, the application of an external magnetic field has become a very useful technique for improving crystal quality. The integration of the magnetic field into the simulation program leads to a system of coupled partial differential equations, i.e. incompressible Navier-Stokes equations and convective heat equations in combination with an external magnetic field, which have to be solved. Because of the regular access to data this problem is suitable for vector computers. The CRAY X-MP provides vectorization and multiprocessing capabilities. With multitasking it is possible to run different parts of one program in parallel. Both multitasking concepts, macrotasking and microtasking, were examined to evaluate their potential to speed-up the Czochralski crystal growth simulation program implemented on a CRAY X-MP. We will give a survey of the application, and will describe the concepts of macrotasking and microtasking on the CRAY X-MP architecture as well as the integration of these concepts into the simulation program. Timing results provide information about the user benefit obtained by using these techniques.

REFERENCES

• 1: COS Performance Utilities Reference Manual, CRAY-Research Inc, SN-0146 (1987).
• 2: Multitasking User Guide, Revision D, CRAY-Research Inc, SN-0222 (1987).
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• 9: M. Mihelcic and K. Wingerath, Numerical Simulations at the Czochralski Bulk Flow in an Axial Magnetic Fietd: Effects on the Flow and Temperature Oscillations in the Melt, Journal of Crystal Growth 71 (1985) 163-168.
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Finite difference methods

Additional Classification:
  C. Computer Systems Organization
  C.1 PROCESSOR ARCHITECTURES
      C.1.2 Multiple Data Stream Architectures (Multiprocessors)
          Subjects: Array and vector processors
  C.5 COMPUTER SYSTEM IMPLEMENTATION
      C.5.1 Large and Medium ("Mainframe") Computers
          Subjects: Super (very large) computers
          Nouns: CRAY X-MP

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Algorithms, Design