麻省理工学院：《Multidisciplinary System》Lecture23 computation

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

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 PCs 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( 1012 operation per sec Tradeoff between model fidelity and computational cost

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 (1012 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

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 This computer 0.380.220.330.821.16 DEC Alpha, 600 0.700.300430.940.73 Pentium INT. 400 0.760.460.441.611.19 Pentium l. Linux, '400 0.650.420.521.721.19 SGl Octane. 195 1.100.430.601.631.19 Pentium ll, Win98, 350 0.840.510.501.341.85 Sparc Ultra 2, 300 0.820.600.661.731.3 Pentium II Laptop, N, 266. 1.020.670.641.782.50 Pentium Pro, Linux, 2p0 1.210.831.052451.57 HP780.180 1.690.461.132.832.24 BMRS6000.167 1420.500.773.392.98 Sparc 10, Dual 160 2.121.071.294.503.08 sG|o2.180 2.521.731.603.992.62 Sparc 2(circa 1992) 10.0010.0010.0010.001000 01234567891011121314151617 Type: > bench at MATLAB command line

MATLAB Benchmark Computer performance typically assessed via benchmarks Execution time Relative Speed ODE LU Sparse 3-D 2-D This computer 0.38 0.22 0.33 0.82 1.16 DEC Alpha, 600 0.70 0.30 0.43 0.94 0.73 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 10111213141516 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

Reference Stanford University Course “Parallel Methods in Numerical Analysis” http://www.stanford.edu/class/cs238/ Prof. Juan Alonso