Singular boundary method for acoustic eigenanalysis

Abstract

a b s t r a c tThis paper applies the singular boundary method (SBM) to two-(2D) and threedimensional (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.

Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources

“…the problem of selecting auxiliary boundaries), an RMFS is proposed. Based on the idea of SBM [12] and SRMM [13], the proposed method also places the auxiliary boundaries on the real physical boundaries. 2) the fundamental solution has singularity when the field point coincides with the source point.…”

“…Some improved methods place the collocation points on the real physical boundaries, after further treatment of the singularities of the fundamental solution. This idea has been used to solve many engineering problems, such as the SBM for solving acoustic eigenvalue problems [12], the SRMM for Laplace problems [13] etc. In addition, when applying MFS to solve the waveguide eigenvalue problem, like MoM, it also encounters spurious frequencies or eigenvalues.…”

“…When the collocation point r m approaches the boundary, substituting Equations (11) and (12) into Equation (10), discretising Equation (10) and using the SAB technique, we obtain:…”

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

“…The developed meshless approaches can be classified into collocation-based and Galerkin-based methods. Compared with the latter, the meshless collocation methods have the advantages of no numerical quadrature and mesh generation, and some of these are the localized method of fundamental solutions (LMFS) [20][21][22], the generalized finite difference method (GFDM) [23][24][25][26][27][28][29][30][31][32][33], the localized Chebyshev collocation method [34], the singular boundary method (SBM) [35][36][37][38][39][40][41][42][43], and the localized knot method (LKM) [44].…”

Recent Advances in Localized Collocation Solvers Based on Semi-Analytical Basis Functions

“…To solve the above problems, global semi-analytical meshless collocation solvers are successively proposed, such as the method of fundamental solutions (MFS) [1], radial Trefftz collocation method (RTCM) [2], collocation Trefftz method (CTM) [3], singular boundary method (SBM) [4], and so on. In general, the above-mentioned semi-analytical meshless collocation solvers belong to the family of boundary meshless methods, which avoid the mesh generation.…”