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In this paper, we present a novel computational approach (named ACA-BM-SBM) for the calculation of 2D acoustic sensitivity by combining the Burton-Miller-type singular boundary method (BM-SBM) with the adaptive cross-approximation (ACA) algorithm. The BM-SBM circumvents the source singularities of the fundamental solutions by introducing the origin intensity factors, and it eliminates the fictitious frequency problem in external acoustic fields by introducing the Burton-Miller formula. As a semi-analysis meshless method, the BM-SBM can accurately solve the external acoustic problem governed by the Helmholtz equation. Nevertheless, the computational inefficiency introduced by the dense coefficient matrix renders this method suboptimal, particularly for large-scale simulations. As the number of nodes increases, the computation time and store memory increase dramatically. ACA is a purely algebraic method based on hierarchical matrices which can be used to partition the coefficient matrix step by step. By employing ACA, the BM-SBM can be effectively accelerated, and this results in less computation time, as well as fewer memory requirements. Numerical experiments, including Dirichlet and Neumann boundary conditions, illustrate that the proposed approach is an accurate, efficient and fast numerical method for acoustic sensitivity analysis.

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures. [ABSTRACT FROM AUTHOR]

In this paper, a novel Burton-Miller-type singular boundary method (BM-SBM) formulation is proposed for the acoustic design sensitivity analysis, with the help of the direct differentiation method. The Burton-Miller formulation is employed to overcome the fictitious frequency problem in the numerical solutions of exterior acoustic problems. The simple empirical formulas are used to estimate the origin intensity factors in the BM-SBM. Compared with the traditional methods, the present scheme is an accurate and semi-analytical approach with the merits of truly meshless, integration-free, mathematical simplicity, and easy-to-program. As a boundary-type method based on the fundamental solution, furthermore, the BM-SBM is straightforward for addressing the exterior Helmholtz problems encountered in the acoustic design sensitivity analysis. Numerical experiments, including 2D and 3D geometries with Neumann boundary conditions, indicate that the proposed methodology is an accurate, stable, and convergent numerical approach for the acoustic design sensitivity analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures.

This paper presents a novel semi-analytical meshless method to optimize the thickness of porous material distributed on sound barriers, by employing the Burton–Miller-type singular boundary method in conjunction with the method of moving asymptotes. Firstly, the Delany–Bazley–Miki model is utilized to characterize the acoustic property of sound barrier with a porous sound-absorbing material. Then, the sensitivity formula with respect to the thickness of the porous layer is derived based on the analytical computation and the adjoint variable formula, in which the design variable is a thickness parameter distributed between [0,1]. Finally, the optimal thickness distribution is achieved by solving the optimization model using the method of moving asymptotes. Compared to traditional algorithms, the proposed new method is simple, accurate, easy-to-program, and free of mesh and integration. Numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a novel semi-analytical method for the two- and three-dimensional acoustic design sensitivity analysis by combining the Burton–Miller-type singular boundary method (BM-SBM) and the adjoint variable method. The BM-SBM is an accurate, stable and boundary-type meshless approach, and can effectively avoid the fictitious frequency issue in the numerical solutions of exterior acoustic problems due to the introduction of the Burton–Miller formula. The origin intensity factors in the BM-SBM are evaluated by employing the empirical formulas and the subtraction and adding-back technique, which is straightforward, accurate and efficient. Unlike the direct differentiation method, the adjoint variable method can save computation time and computer resources since it avoids computing the gradients of state variables by introducing adjoint state space equations. Compared with the existing methods, the present scheme can be regarded as a competitive alternative of acoustic design sensitivity analysis, due to the aforementioned merits. Three numerical examples are provided to illustrate the effectiveness and accuracy of the developed method. [ABSTRACT FROM AUTHOR]