Revision as of 03:10, 24 January 2011 (view source)← Older edit Latest revision as of 01:33, 6 January 2012 (view source) (Blanked the page) (18 intermediate revisions not shown) Line 1: Line 1: - As its name means, gradient-based methods need the gradient of objective functions to design variables. The evaluation of gradient can be achieved by [[finite difference method, linearized method or adjoint method]]. Both finite difference method and linearized method has a time-cost proportional to the number of design variables and not suitable for design optimization with a large number of design variables. Apart from that, finite difference method has a notorious disadvantage of subtraction cancellation and is not recommended for practical design application. - Suppose a cost function $J$ is defined as follows, - - $J=J(U(\alpha),\alpha)$ - - where $U$ and $\alpha$ are the flow variable vector and the design variable vector respectively. $U$ and $\alpha$ are implicitly related through the flow equation, which is represented by a residual function driven to zero. - - $R(U,(\alpha))=0$ - - Finite difference method: - - Linearized method: - - Adjoint method: