A BEM-based topology optimization for acoustic problems considering tangential derivative of sound pressure

This paper employs a new tangential derivative of boundary integral equation for the optimization problems in the acoustic field with a objective function involving tangential derivatives of the sound pressure on the boundary. The level set method is adopted to generate the topological structure by updating the level set function which defines the boundary of the material domain with its zero contour line. The hyper singular integral is directly derived and singular terms are canceled due to the form of the tangential derivative at the boundary. The topological derivative is derived through the adjoint variable method(AVM) and the most of the unknowns in the variation of objective function can be canceled by evaluating the adjoint field. However, one of the terms which includes the variation of the tangential derivative of the sound pressure is evaluated using integration by parts. The remaining part having unknown variation of sound pressure is neglected by extending the objective function defined boundary by one elements at its start and end points. Numerical implementations demonstrate the effectiveness and correctness of the proposed method for topology optimization problems with the objective function involving tangential derivative quantities.