scholarly journals Complex variable boundary integral equations for perforated infinite planes

2001 ◽  
Vol 25 (3) ◽  
pp. 191-202 ◽  
Author(s):  
J. Helsing ◽  
A. Jonsson
Keyword(s):  
Integral Equations ◽  
Complex Variable ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Variable Boundary

A Complex Variable Boundary Element-Free Method for Potential and Helmholtz Problems in Three Dimensions

2019 ◽  
Vol 17 (02) ◽  
pp. 1850129 ◽  
Author(s):  
Xiaolin Li ◽  
Shougui Zhang ◽  
Yan Wang ◽  
Hao Chen
Keyword(s):  
Boundary Element ◽  
Complex Variable ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Variable Boundary ◽  
Current Implementation ◽  
Element Free Method ◽  
Element Free ◽  
3D Surfaces

The complex variable boundary element-free method (CVBEFM) is a meshless method that takes the advantages of both boundary integral equations (BIEs) in dimension reduction and the complex variable moving least squares (CVMLS) approximation in element elimination. The CVBEFM is developed in this paper for solving 3D problems. This paper is an attempt in applying complex variable meshless methods to 3D problems. Formulations of the CVMLS approximation on 3D surfaces and the CVBEFM for 3D potential and Helmholtz problems are given. In the current implementation, the CVMLS shape function of 3D problems is formed with 1D basis functions, and the boundary conditions in the CVBEFM can be applied directly and easily. Some numerical examples are presented to demonstrate the method.

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