Improved semi-analytic sensitivity analysis combined with a higher order approximation scheme in the framework of adjoint variable method

In the design sensitivity analysis, the adjoint variable method has been widely used for the sensitivity calculation. The adjoint variable method can reduce computation time and save computer resources because it can provide the sensitivity values only at the positions in which designers are willing to obtain. However, exact analytical differentiation with respect to the design variables is commonly employed in adjoint variable method. Although the exact derivative assures the accurate sensitivity, it is cumbersome to take differentiation in an exact manner for every given type of finite element. Therefore, in the present study, a new improved semi-analytic design sensitivity method is proposed in the framework of adjoint variable method. Recently, a numerical inaccuracy trouble in the traditional semi-analytic method has been settled by the rigid body mode separation technique and high order approximation scheme. Combining the adjoint variable method with improved semi-analytic design sensitivity scheme, the design sensitivity value can be calculated accurately and efficiently. Through numerical examples, the efficiency and accuracy of the proposed semi-analytic sensitivity scheme in the adjoint variable method are demonstrated.