L23 - Computational Issues ? Computer technologies have been changing the environment of engineering design - enabling MDO ? Hardware: Advances in processor speed, memory and storage ? Software: Powerful disciplinary analysis and simulation programs (e.g. Nastran, Fluent …) ? This also creates new difficulties: Most activities involve stand-alone programs and many engineers spend 50-80% of their time organizing data and moving it back-and-forth between applications Data must be shared between disciplines more easily Computational requirements increase High Performance Computing ? MDO requires large computing power for realistic problems ? Computer power: clock speed, memory, # of processor ? IBM 3090 and CRAY-1/2 used to be workhorses, but now many engineering applications run on Windows/Linux PC’s ? Many applications have benchmarks, e.g. Matlab “bench” ? Various architectures are now in use for HPC: ? (a ) Single mainframe supercomputer with batch execution ? (b ) Parallel computing promising, but many obstacles ? (c ) Distributed PC workstations on common LAN ? Holy Grail: Teraflop performance (10 12 operation per sec) ? Tradeoff between model fidelity and computational cost Runtime Reduction Strategies ? Model Reduction ? Parallel Computation ? Exploiting Sparsity and Model Structure ? Going to compiled/lower level functions ? Using a more powerful processor MATLAB Benchmark Computer performance typically assessed via benchmarks Execution time Relative Speed ODE LU Sparse 3-D 2-D 0.38 0.22 0.33 0.82 1.16This computer 0.70 0.30 0.43 0.94 0.73DEC Alpha, 600 Pentium II, NT, 400 0.76 0.46 0.44 1.61 1.19 Pentium II, Linux, 400 0.65 0.42 0.52 1.72 1.19 SGI Octane, 195 1.10 0.43 0.60 1.63 1.19 Pentium II, Win98, 350 0.84 0.51 0.50 1.34 1.85 Sparc Ultra 2, 300 0.82 0.60 0.66 1.73 1.31 Pentium II Laptop, NT, 266 1.02 0.67 0.64 1.78 2.50 Pentium Pro, Linux, 200 1.21 0.83 1.05 2.45 1.57 HP 780, 180 1.69 0.46 1.13 2.83 2.24 IBM RS6000, 167 1.42 0.50 0.77 3.39 2.98 Sparc 10, Dual 160 2.12 1.07 1.29 4.50 3.08 SGI O2, 180 2.52 1.73 1.60 3.99 2.62 Sparc 2 (circa 1992) 10.00 10.00 10.00 10.00 10.00 0 1 2 3 4 5 6 7 8 9 1011 121314 1516 17 Type: >> bench at MATLAB command line Reference Stanford University Course “Parallel Methods in Numerical Analysis” http://www.stanford.edu/class/cs238/ Prof. Juan Alonso