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Konstantinos G. Kyprianidis Module Development 3.5.3 Benchmarks Despite the fact that the computational power of personal computers has been rising constantly over the past decades - as predicted by Moore’s Law [167] - the implementation of fast (and robust) numerical methods is of critical importance where radical design space exploration is concerned. The performance of the non-linear equation system solvers available in LISIS is presented in Table 3.5 and Table 3.6 in terms of number of functions evaluations required; the latter was chosen as a metric to make results hardware-independent (i.e. independent of computer specification), and also less dependent on the programming techniques, language, and compiler used. Convergence is assumed to have been achieved when the accuracy (tolerance) level set is reached for each (relativised) residual in the model. Various conclusions may be drawn, largely confirming expectations from the literature reviewed: • The use of quasi-Newton methods can significantly improve computational speed but the benefit is highly dependent on the number of independent variables that formulate the function used, and the accuracy required. Re- sults for the engine performance rubber deck (high accuracy option) in- dicate an up to a three-fold increase in function evaluations when quasi- Newton methods are not utilised. • Reuse of the inverted Jacobian, between different simulation points, can significantly improve computational speed but the benefit is highly depen- dent on the number of independent variables that formulate the function used and its nonlinearity, the differentiation method used, and the accuracy required. Results for the engine performance rubber deck (central differ- ences and low accuracy options) indicate an up to a twelve-fold increase in function evaluations when the inverted Jacobian is not used. • The computational penalty associated with using central differences is de- pendent on the number of independent variables that formulate the func- tion used and its nonlinearity. Reuse of the inverted Jacobian, between different simulation points, fully alleviates this penalty. 71PDF Image | Multi-disciplinary conceptual design of future jet engine systems
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