Shape Design Sensitivity Analysis Using Boundary Integral Equation for Potential Problems

Abstract

A general method for shape design sensitivity analysis as applied to potential problems is developed with the standard direct boundary integral equation (BIE) formulation. The material derivative concept and adjoint variable method are employed to obtain an explicit expression for the variation of the performance functional in terms of the boundary shape variation. The adjoint problem defined in the present method takes a form of the indirect BIE. This adjoint problem can be solved using the same direct BIE of the original problem with a different set of boundary values, which brings about computational simplicity. The accuracy of the sensitivity formula is studied with a seepage problem. The detailed derivation of the formulas for general elliptic problems and a more elaborate numerical scheme will be described elsewhere.