Vectorization of Computer Programs with Applications to Computational Fluid Dynamics

1. Introduction: Supercomputers in Computational Fluid Dynamics.- 2. Computer Architectures.- 2.1 The Basic Computer Systems.- 2.2. The CRAY-1 Series.- 2.3. The CDC CYBER 205.- 3. Vectorization of FORTRAN Programs.- 3.1 Implementation of Serial Programs on Vector Computers.- 3.2 Vectorization on the CRAY-1.- 3.3 Vectorization on the CDC CYBER 205.- 4. Vectorization of a Sample Program on Different Vector and Parallel Computers.- 4.1 Vectorization on the CRAY-1.- 4.2 Vectorization on the CDC CYBER 205.- 4.3 Vectorization on HITACHI's S9 with IAP.- 4.4 Vectorization on the ICL DAP.- 4.5 Parallelization on DENELCOR's HEP.- 5. Restructuring of Basic Linear Algebra Algorithms.- 5.1 Basic Vector Operations.- 5.2 Matrix Multiplication for Banded Matrices.- 5.3 Gaussian Elimination for the Solution of Algebraic Systems with Full Matrices.- 5.4 Linear and Nonlinear Recurrences.- 6. Iterative Methods for a Model Problem.- 6.1 Jacobi Type Methods.- 6.2 Gauss-Seidel Type Methods.- 6.3 Group Iterative Methods.- 7. Vectorization of Simple Numerical Algorithms.- 7.1 Polynomial Evaluation.- 7.2 The Power Method for the Computation of the Largest Eigenvalue of a Matrix.- 7.3 Cyclic Reduction.- 7.4 Systems of Nonlinear Equations.- 7.5 Runge-Kutta Time-Stepping Methods for Systems of Ordinary Differential Equations.- 7.6 An Explicit Superstep Method for the Solution of Parabolic Differential Equations.- 7.7 Finite Difference Smoothing.- 8. References to Chapters 1 to 7.- 8.1 Vector and Parallel Algorithms.- 8.2 Further Applications.- 9. Vectorization of Algorithms in Computational Fluid Dynamics on the CRAY-1 Vector Computer.- 9.1 MacCormack's Methods and Vectorization.- 9.2 Vectorization of the Implicit Beam and Warming Scheme.- 9.3 Vectorization of an Implicit Finite DifferenceMethod for the Solution of the Laminar Boundary-Layer Equations.- 9.4 Vectorization of the Galerkin-Method R. Kessler.- 9.5 Vectorization of the Direct Monte-Carlo Simulation.