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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]

This article presents a fast direct solver based on surface integral equation (SIE) to solve electromagnetic (EM) scattering from homogeneous penetrable objects. The proposed method relies on a strong admissibility skeletonization factorization (SASF) algorithm and Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation. In the SASF scheme, only well-separated groups that satisfy the strong admissibility condition are considered to be compressed and thus relatively fewer skeleton basis functions are selected. It is an effective way to compress the matrix with small ranks. An independent compression technique is developed for dielectric problems involving electric and magnetic currents, in which skeleton basis functions representing electric and magnetic currents are obtained separately. Moreover, a novel strategy based on matrix normalization is proposed to treat the arising “fill-in” blocks when far-field interactions are compressed. Ultimately, the impedance matrix can be cast into products of a series of block unit triangular matrices and a block diagonal matrix. Several numerical results show that the proposed approach is effective and stable as well as provides an accurate solution for scattering problems of homogeneous penetrable objects. [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 study focuses on the efficient computational model for predicting the structural vibration induced underwater acoustic radiation in shallow marine environment. In the proposed model, the finite element method (FEM) is used to calculate the vibration response of the shell structures and the singular boundary method (SBM) with near-field and far-field Green's functions is used to simulate the underwater acoustic radiation excited by shell structural vibration in shallow water marine environment, namely, the hybrid FEM–SBM solver. For axisymmetric shell structures, the axisymmetric numerical formulation of the FEM–SBM solver is derived to save the computational cost. For general shell structures, the fast direct solver based on the recursive skeletonization factorization is introduced into the FEM–SBM solver to accelerate the computation of the underwater acoustic field. Numerical results demonstrate that the proposed FEM–SBM solver provides more efficient and reliable solutions in comparison with the coupled FEM/FEM solver (COMSOL software). The effect of the sound velocity profiles on the underwater acoustic radiation field in shallow water marine environment is numerically investigated. [ABSTRACT FROM AUTHOR]