Abstract
differential equation with respect to the design variables. The accuracies of the convergence error and higher-order sensitivity estimation methods are verified using Laplace, Euler, and Navier–Stokes equations. The developed methods are used to improve the accuracy of the finite-difference sensitivity calculations in iteratively solved problems.Aboundonthenormvalueofthe finite-differencesensitivityerrorinthestatevariablesisminimizedwith respect to the finite-difference step size. The optimum finite-difference step size is formulated as a function of the norm values of both convergenceerror andhigher-order sensitivities. Thesensitivities calculated with the analytical and the finite-difference methods are compared. The performance of the proposed methods on the convergence of inverse design optimization is evaluated.
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