Source Intensity Factors Research Articles

Singular boundary method using time-dependent fundamental solution for scalar wave equations

This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.

Singular boundary method for acoustic eigenanalysis

This paper applies the singular boundary method (SBM) to two- (2D) and three-dimensional (3D) acoustics eigenproblems in simply- and multiply-connected domains. The SBM is a strong-form boundary discretization numerical method and is meshless, integration-free, and easy-to-implement. By introducing the concept of the source intensity factors, the singularity of fundamental solutions can be isolated to avoid the singular numerical integrals in the boundary element method (BEM). Similar to the BEM, the spurious eigenvalues may arise in the SBM computation. In order to extract out spurious eigenvalues from SBM results, the singular value decomposition updating techniques and the Burton–Miller method are implemented. Several 2D and 3D benchmark examples subjected to Dirichlet and Neumann boundaries are tested to examine the accuracy and stability of the present SBM strategy.

Numerical Investigation on Convergence Rate of Singular Boundary Method

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.

Singular Boundary Method for Various Exterior Wave Applications

This paper presents an improved singular boundary method (ISBM) to various exterior wave applications. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. In this study, we first derive the source intensity factors of the exterior Helmholtz equation by means of the source intensity factors of the exterior Laplace equation due to the same order of the singularities on their fundamental solutions. The source intensity factors of the exterior Laplace equation can be determined using the reference technique [Chen, W. and Gu, Y. [2011] "Recent advances on singular boundary method," Joint international workshop on Trefftz method VI and method of fundamental solution II, Taiwan]. Numerical illustrations demonstrate the efficiency and accuracy of the proposed scheme on four benchmark exterior wave examples.

Singular boundary method for water wave problems

This article presents the singular boundary method (SBM) for water wave-structure interaction analysis. The SBM is a novel recent boundary meshless collocation method, which uses the singular fundamental solutions of governing equation as basis function in the interpolation formulation and introduces the concept of source intensity factors to avoid the singularities of the fundamental solutions at origin. It is a strong-form meshless boundary collocation technique with the merits being easy-to-implement and integration-free. In this study, two types of water wave-structure interactions, water wave interaction of multiple-cylinder-array structure and semicircular harbor, are considered. Numerical results show the efficiency and accuracy of the present SBM scheme in comparison with the analytical solutions, the method of fundamental solutions and the null field boundary integral element method. Then the near trapped mode phenomenon of ten-cylinder structure and the focusing effect of the semicircular harbor are revisited by using the present SBM.

Burton–Miller-type singular boundary method for acoustic radiation and scattering

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller׳s formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton–Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.