A BOUNDARY ELEMENT FORMULATION FOR ACOUSTIC SHAPE SENSITIVITY ANALYSIS

The Helmholtz integral equation forms a conventional basis for acoustic boundary element analysis (BEA). Implicit differentiation of the discretized Helmholtz integral equation is shown to yield an effective approach for the computation of rates of change (sensitivities) of acoustic response quantities with respect to changes in the shape of an acoustic model. A theoretical formulation is presented that allows for the reuse of the factorization of the overall BEA system left-hand side matrix formed in a previous analysis, thus obviating the need to factor perturbed matrices in the sensitivity analysis process. The singularity strengths of the new kernel functions utilized to compute sensitivities of matrix coefficients required by this approach are shown to be the same as those present in ordinary BEA. An indirect approach for the computation of the diagonal contributions to sensitivity matrices associated with these new kernels is also discussed. The sensitivity analysis formulation includes surface pressures and normal gradients (velocities), surface tangential pressure gradients, and pressure and pressure gradients at arbitrary domain sample points. It is concluded that the overall efficiency of implementations of these formulations is significant. Numerical results for a series of example problems are presented to quantify the accuracy and efficiency of this approach.