Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation

2015 ◽  
Vol 50 ◽  
pp. 360-371 ◽  
Author(s):  
Hakan Dogan ◽  
Viktor Popov ◽  
Ean Hin Ooi
Keyword(s):  
Integral Equation ◽  
Helmholtz Equation ◽  
Boundary Integral Equation ◽  
Dispersion Analysis ◽  
Boundary Integral ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Integral Equation Methods ◽  
Radial Basis

AN IMPROVED LOCAL BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

2010 ◽  
Vol 02 (02) ◽  
pp. 421-436 ◽  
Author(s):  
BAODONG DAI ◽  
YUMIN CHENG
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Computational Efficiency ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Potential Problems

Combining the local boundary integral equation with the improved moving least-squares (IMLS) approximation, an improved local boundary integral equation (ILBIE) method for two-dimensional potential problems is presented in this paper. In the IMLS approximation, the weighted orthogonal functions are used as basis functions. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation and does not lead to an ill-conditioned equations system. The corresponding formulae of the ILBIE method are obtained. Comparing with the conventional local boundary integral equation (LBIE) method, the ILBIE method is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be implemented directly and easily as in the finite element method. The ILBIE method has greater computational efficiency and precision. Some numerical examples to demonstrate the efficiency of the method are presented in this paper.

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