scholarly journals Analytical evaluation of the origin intensity factor of time-dependent diffusion fundamental solution for a matrix-free singular boundary method formulation

2017 ◽  
Vol 49 ◽  
pp. 647-662 ◽  
Author(s):  
Fajie Wang ◽  
Wen Chen ◽  
Chuanzeng Zhang ◽  
Ji Lin
Keyword(s):  
Intensity Factor ◽  
Fundamental Solution ◽  
Time Dependent ◽  
Singular Boundary ◽  
Analytical Evaluation ◽  
Boundary Method ◽  
Method Formulation ◽  
Matrix Free ◽  
Singular Boundary Method

An Improved Formulation of Singular Boundary Method

2012 ◽  
Vol 4 (5) ◽  
pp. 543-558 ◽  
Author(s):  
Wen Chen ◽  
Yan Gu
Keyword(s):  
Intensity Factor ◽  
Neumann Boundary ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Benchmark Problems ◽  
Singular Boundary ◽  
Boundary Method ◽  
New Formulation ◽  
Physical Boundary ◽  
Singular Boundary Method

AbstractThis study proposes a new formulation of singular boundary method (SBM) to solve the 2D potential problems, while retaining its original merits being free of integration and mesh, easy-to-program, accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary. This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques. And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition. Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method (BEM), MFS, regularized meshless method (RMM) and boundary distributed source (BDS) method.

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.

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