A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method.

*(English)*Zbl 1282.74101Summary: We present a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

##### MSC:

74S10 | Finite volume methods applied to problems in solid mechanics |

74J25 | Inverse problems for waves in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

74P10 | Optimization of other properties in solid mechanics |

##### Keywords:

design sensitivity analysis; wideband FMBEM; Burton-Miller method; direct differentiation method
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\textit{L. Chen} et al., Comput. Mech. 52, No. 3, 631--648 (2013; Zbl 1282.74101)

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