Explicit empirical formula evaluating original intensity factors of singular boundary method for potential and Helmholtz problems

2016 ◽  
Vol 73 ◽  
pp. 161-169 ◽  
Author(s):  
Junpu Li ◽  
Wen Chen ◽  
Zhuojia Fu ◽  
Linlin Sun
Keyword(s):  
Empirical Formula ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Boundary Method ◽  
Singular Boundary Method

scholarly journals Numerical Investigation on Convergence Rate of Singular Boundary Method

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Junpu Li ◽  
Wen Chen ◽  
Zhuojia Fu
Keyword(s):  
Short Communication ◽  
Convergence Rates ◽  
Fundamental Solutions ◽  
Benchmark Problems ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Collocation Points ◽  
Boundary Method ◽  
Collocation Scheme ◽  
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.

Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method

2015 ◽  
Vol 7 (1) ◽  
pp. 13-30 ◽  
Author(s):  
Wenzhen Qu ◽  
Wen Chen
Keyword(s):  
Fundamental Solution ◽  
Stokes Flow ◽  
Singular Boundary ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Flow Problems ◽  
Modified Method ◽  
Boundary Method ◽  
Singular Boundary Method

AbstractIn this paper, an improved singular boundary method (SBM), viewed as one kind of modified method of fundamental solution (MFS), is firstly applied for the numerical analysis of two-dimensional (2D) Stokes flow problems. The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives. The new contribution of this study is that the origin intensity factors for the velocity, traction and pressure are derived, and based on that, the SBM formulations for 2D Stokes flow problems are presented. Several examples are provided to verify the correctness and robustness of the presented method. The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.

Singular Boundary Method for Various Exterior Wave Applications

2015 ◽  
Vol 12 (02) ◽  
pp. 1550011 ◽  
Author(s):  
Zhuo-Jia Fu ◽  
Wen Chen ◽  
Ji Lin ◽  
Alexander H.-D. Cheng
Keyword(s):  
Fundamental Solution ◽  
Helmholtz Equation ◽  
Laplace Equation ◽  
International Workshop ◽  
Fundamental Solutions ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Trefftz Method ◽  
Boundary Method ◽  
Singular Boundary Method

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.

The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation

2021 ◽  
pp. 2150041
Author(s):  
Karel Kovářík ◽  
Juraj Mužík
Keyword(s):  
Diffusion Equation ◽  
Large Scale ◽  
Sparse Matrix ◽  
Singular Boundary ◽  
Tracer Transport ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Boundary Method ◽  
Local Variant ◽  
Singular Boundary Method

This work focuses on the derivation of the local variant of the singular boundary method (SBM) for solving the advection-diffusion equation of tracer transport. Localization is based on the combination of SBM and finite collocation. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows solving velocity vector variable tasks, which is a problem with global SBM. This paper compares the results on several examples for the steady and unsteady variant of the advection-diffusion equation and also examines the dependence of the accuracy of the solution on the density of the nodal grid and the size of the subdomain.

Sign in / Sign up

Export Citation Format

Share Document