This paper presents a numerical analysis method of nonparametric boundary shape optimization problems with respect to boundary value problems of partial differential equations. The nonparametric boundary variation can be formulated by selecting a one parameter family of continuous one-to-one mappings from an original domain to variable domains. The shape gradient with respect to domain variation can be evaluated by the adjoint variable method. However, the direct application of the gradient method often results in oscillating shapes. It has been known that the oscillating phenomenon is caused by a lack of smoothness of the shape gradient. To make up the irregularity, a smoothing gradient method and its concrete numerical procedure called the traction method have been presented by the author and coworkers. However, in the previous papers, the numerical procedure of the traction method was not illustrated. This paper presents a generalized description of the traction method and gives a precise algorithm of the traction method.
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