Yi Wu, Zhuojia Fu^*, Jian Min

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 377-393, 2023, DOI:10.32604/cmes.2022.023205

Abstract This paper proposes a modified formulation of the singular boundary method (SBM) by introducing the combined Helmholtz integral equation formulation (CHIEF) and the self-regularization technique to exterior acoustics. In the SBM, the concept of the origin intensity factor (OIF) is introduced to avoid the singularities of the fundamental solutions. The SBM belongs to the meshless boundary collocation methods. The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently. Consequently, by using the SBM coupled with the CHIEF scheme and the self-regularization technique, the accuracy of… More >

Yan Gu¹, Wen Chen^1,2, Xiao-Qiao He³

CMC-Computers, Materials & Continua, Vol.29, No.2, pp. 129-154, 2012, DOI:10.3970/cmc.2012.029.129

Abstract This paper applies an improved singular boundary method (SBM) in conjunction with domain decomposition technique to stress analysis of layered elastic materials. For problems under consideration, the interface continuity conditions are approximated in the same manner as the boundary conditions. The multi-layered coating system is decomposed into multiple subdomains in terms of each layer, in which the solution is approximated separately by the SBM representation. The singular boundary method is a recent meshless boundary collocation method, in which the origin intensity factor plays a key role for its accuracy and efficiency. This study also introduces new strong-form regularization formulas to… More >

W. Chen^1,2, C. J. Liu¹, Y. Gu^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 251-270, 2015, DOI:10.3970/cmes.2015.105.251

Abstract The singular boundary method (SBM) is a recently-developed meshless boundary collocation method. This method overcomes the well-known fictitious boundary issue associated with the method of fundamental solutions (MFS) while remaining the merits of the later of being truly meshless, integral-free, and easy-to-program. Similar to the MFS, this method, however, produces dense and unsymmetrical coefficient matrix, which although much smaller in size compared with domain discretization methods, requires O(N²) operations in the iterative solution of the resulting algebraic system of equations. To remedy this bottleneck problem for its application to large-scale problems, this paper makes the first attempt to develop a… More >

Zhuo-Jia Fu¹, Wen Chen^1,2, Jeng-Tzong Chen³, Wen-Zhen Qu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 417-443, 2014, DOI:10.3970/cmes.2014.099.417

Abstract This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy and stability of these three… More >

Wen Chen^1,2, Zhuojia Fu¹, Xing Wei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 65-86, 2009, DOI:10.3970/cmes.2009.054.065

Abstract This study investigates the singular boundary method (SBM), a novel boundary-type meshless method, in the numerical solution of potential problems. Our finding is that the SBM can not obtain the correct solution in some tested cases, in particular, in the cases whose solution includes a constant term. To remedy this drawback, this paper presents an improved SBM formulation which is a linear sum of the fundamental solution adding in a constant term. It is stressed that this SBM approximation with the additional constant term has to satisfy the so-called moment condition in order to guarantees the uniqueness of the solution.… More >

H. Htike^1,2, W. Chen^1,2,3, Y. Gu^1,2

CMC-Computers, Materials & Continua, Vol.24, No.1, pp. 1-14, 2011, DOI:10.3970/cmc.2011.024.001

Abstract In this paper, we investigate the application of the singular boundary method (SBM) to two-dimensional problems of steady-state heat conduction in isotropic bimaterials. A domain decomposition technique is employed where the bimaterial is decomposed into two subdomains, and in each subdomain, the solution is approximated separately by an SBM-type expansion. The proposed method is tested and compared on several benchmark test problems, and its relative merits over the other boundary discretization methods, such as the method of fundamental solution (MFS) and the boundary element method (BEM), are also discussed. More >