A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis

A novel meshfree method based on spatio-temporal homogenization functions for one-dimensional fourth-order fractional diffusion-wave equations

The enriched quadrilateral overlapping finite elements for time-harmonic acoustics

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. 

A novel semi-analytical meshless method for the thickness optimization of porous material distributed on sound barriers

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with the implicit direct time integration method for the transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, the RPIM is adopted for the discretization of the overall space domain, while the discretization of the time domain is completed by employing the efficient Bathe time stepping scheme. The dispersion analysis demonstrates that, in wave analysis, the amount of numerical dispersion error resulting from the discretization in the space domain can be suppressed at a very low level when the employed nodal support domain of the interpolation function is adequately large. Meanwhile, it is also mathematically shown that the amount of numerical error resulting from the time domain discretization is actually a monotonically decreasing function of the non-dimensional time domain discretization interval. Consequently, the present simulation approach is capable of effectively handling the transient analysis of wave propagation dynamics in non-homogeneous media, and the disparate waves with different speeds can be solved concurrently with very high computation accuracy. This numerical feature makes the present simulation approach more suitable for complicated wave analysis than the traditional finite element approach because the waves with disparate speeds always cannot be concurrently solved accurately. Several numerical tests are given to check the performance of the present simulation approach for the analysis of wave propagation dynamics in non-homogeneous media.

/pdf/the-meshfree-radial-point-interpolation-method-rpim-for-wave-jnscrf3p.pdf

The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media

This paper presents an overview of the singular boundary method (SBM) and its various engineering applications. The basic concepts of the singular boundary method are first introduced, such as the collocation scheme, fundamental solutions and origin intensity factors (OIFs). In the SBM implementation, the OIF-determination approaches are then classified into three categories, namely, the inverse interpolation technique (IIT), the subtracting and adding-back technique (SABT) and the integral mean value (IMV). Several additional schemes are introduced to resolve the non-uniqueness issue encountered in the SBM, and enable the application of the SBM to large-scale engineering and scientific computing, nonhomogeneous partial differential equations (PDEs), non-isotropic problems and initial-boundary value problems. Several selected numerical examples are presented and discussed to show the recent developments and applications of the SBM to the solution of some typical boundary value problems, such as anomalous heat conduction, high wavenumber acoustic wave propagation, water wave-structure interaction, elastic wave propagation and structural vibration induced underwater acoustic radiation in the shallow ocean environment and so on. Besides, some efficient techniques, such as moment condition and modified combined Helmholtz integral equation formulation (CHIEF), are introduced into the SBM to enhance its performance. Finally, the essential conclusions of the SBM are summarized and some future trends in this interesting research field are highlighted. 

Singular boundary method: A review and computer implementation aspects

This paper presents a precorrected-FFT (pFFT) accelerated singular boundary method (SBM) for acoustic radiation and scattering in the high-frequency regime. The SBM is a boundary-type collocation method, which is truly free of mesh and integration and easy to program. However, due to the expensive CPU time and memory requirement in solving a fully-populated interpolation matrix equation, this method is usually limited to low-frequency acoustic problems. A new pFFT scheme is introduced to overcome this drawback. Since the models with lots of collocation points can be calculated by the new pFFT accelerated SBM (pFFT-SBM), high-frequency acoustic problems can be simulated. The results of numerical examples show that the new pFFT-SBM possesses an obvious advantage for high-frequency acoustic problems.

/pdf/precorrected-fft-accelerated-singular-boundary-method-for-3iib713q.pdf

Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering

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.

/pdf/a-fast-singular-boundary-method-for-the-acoustic-design-3m5b3v81.pdf

A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures

In this study, the singular boundary method, which is a boundary collocation method, is first employed to calculate the band structures of in-plane waves in two-dimensional phononic crystals. When a unit cell of a phononic crystal is considered, the whole boundaries, including the continuity and periodic boundaries are discretized by the singular boundary method. Then, a linear eigenvalue equation is derived. For a given frequency, an eigenvalue that involves the Block wave can be calculated. Therefore, by sweeping the frequencies, the band structure can be obtained. The accuracy, efficiency and convergence of the proposed method are tested by several numerical examples, and the results demonstrate that the singular boundary method can provide stable and efficient results for band structure calculations of in-plane waves in two-dimensional phononic crystals. 

Singular boundary method for band structure calculations of in-plane waves in 2D phononic crystals

A fast approach evaluating origin intensity factors on Neumann boundary in the singular boundary method

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