Evaluation of Singular Integrals in the Two-Dimensional Symmetric Galerkin Boundary Element Method

2009 ◽  
Author(s):  
W.F. Yuan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Two Dimensional ◽  
Galerkin Boundary Element Method ◽  
Element Method

A Symmetric Boundary Element Method/Finite Element Method Coupling Procedure for Two-Dimensional Elastodynamic Problems

2003 ◽  
Vol 70 (3) ◽  
pp. 451-454 ◽  
Author(s):  
G. Y. Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Memory Storage ◽  
Two Dimensional ◽  
Coupling Procedure ◽  
Double Space ◽  
Galerkin Boundary Element Method ◽  
Element Method

In this paper, a symmetric collocation boundary element method (SCBEM)/finite element method (FEM) coupling procedure is given and applied to a two-dimensional elastodynamic problem. The use of symmetry for the boundary element method not only saves memory storage but also enables the employment of efficient symmetric equation solvers. This is especially important for BEM/FEM coupling procedure. Compared with the symmetric Galerkin boundary element method (SGBEM) where double-space integration should be carried out, SCBEM is easier and faster.

A FORMULATION OF THE BOUNDARY ELEMENT METHOD FOR ACOUSTIC RADIATION AND SCATTERING FROM TWO-DIMENSIONAL STRUCTURES

2007 ◽  
Vol 15 (03) ◽  
pp. 333-352 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Ground Surface ◽  
Green Functions ◽  
Two Dimensional ◽  
Element Method

A code for the boundary element method (BEM) for two-dimensional acoustic radiation and scattering problems is developed. To overcome the singularity problem of the integral equations at characteristic frequencies, the Burton–Miller method is employed in the formulation. The integral equations are then discretized by using the two-nodal constant elements and a collocation procedure. The hyper and weakly singular integrals in each element containing the collocation points are computed analytically and numerically respectively (stark singularity does not appear). In outdoor acoustic, the ground surface can be seen occasionally as an infinite surface with a given constant impedance. In this case the ground surface can either be discretized by using finite and infinite boundary elements or simulated by using the Green functions for impedance half space. The method to compute such Green functions presented in Ref. 1, is improved and used in the code. A formulation of the infinite boundary element is proposed. The two BEM approaches for the impedance half space problems are tested by means of examples and the agreement is found to be good.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1080-1081
Author(s):  
Giuseppe Davi ◽  
Rosario M. A. Maretta ◽  
Alberto Milazzo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document