scholarly journals FAST SINGULAR BOUNDARY METHOD: MATHEMATICAL BACKGROUND AND APPLICATION IN WAVE PROPAGATION ANALYSIS

2019 ◽  
Author(s):  
ZHUO-JIA FU ◽  
JUN-PU LI ◽  
QIANG XI
Keyword(s):  
Wave Propagation ◽  
Singular Boundary ◽  
Mathematical Background ◽  
Boundary Method ◽  
Propagation Analysis ◽  
Singular Boundary Method

Semi-Analytical Boundary Collocation Technique for Wave Propagation Applications

2015 ◽  
Author(s):  
Zhuo-Jia Fu
Keyword(s):  
Wave Propagation ◽  
Wave Structure ◽  
Fundamental Solutions ◽  
Singular Boundary ◽  
Sh Wave ◽  
Propagation Analysis ◽  
Collocation Technique ◽  
Singular Boundary Method ◽  
Wave Structure Interaction

This study presents on a recent semi-analytical boundary collocation technique, the singular boundary method (SBM), for exterior wave propagation analysis. The SBM is mathematically simple, easy-to-program, meshless and applies the concept of source intensity factors to eliminating the singularity of the fundamental solutions and avoiding singular numerical integrals in the boundary element method. The Burton and Miller’s method is introduced to the present SBM to enhance the quality of the solution, particularly in the vicinity of irregular frequencies. Then the present SBM is applied to water wave-structure interaction with four-cylinder structure and SH wave scattering in 2D hill.

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.

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