Several meshless methods have been reported, such as the Treffiz method [11-16], the method of fundamental solutions [7,17-19], the element-free Galerkin method , the reproducing kernel particle method [21,22], the meshless local boundary integral equation method
[23, 24], and the meshless local Petrov-Galerkin approach .
Kobayashi, "A fast multipole boundary integral equation method
for crack problems in 3D," Engineering Analysis with Boundary Elements, vol.
Numerical solutions of the above-mentioned equations are considered in the literature through some classical and modern techniques such as finite difference methods (FDMs) [15-18], finite element methods (FEMs) , finite volume methods (FVMs) , dual reciprocity boundary integral equation method
, interpolating scaling function method , and Haar wavelet scheme .
Gross, "A hyper-singular traction boundary integral equation method
for stress intensity factor computation in a finite cracked body," Engineering Analysis with Boundary Elements, vol.
They cover determining the velocity field by conformal mapping methods, calculating flat potential flows by the boundary integral equation method
, calculating vortex flows, the behavior of dust particles in the suction range, specific features of air ejected in a perforated duct with a bypass chamber, air ejection in a porous pipe with linear cross-flow pattern, specific features of air ejection in the elevator handling of grain, and measures for reducing aspiration volumes in the elevator handling of grain.
In this paper, electromagnetic problems for nanoscale antennas are investigated by a boundary integral equation method
with fast inverse Laplace transform (BIEM-FILT) [3,4]; novel antennas are designed to realize ultra-fast and high-density magnetic recording using localized circularly polarized light [5-8].
FMM has been applied to problems in various fields such as boundary integral equation method
(BIEM) and molecular dynamics (MD).
W Kuang, "A new boundary integral equation method
for analysis of cracked linear elastic bodies," Journal of the Chinese Institute of Engineers, vol.
Now Let But for exterior flow problem the equation of indirect panel method for the doublet distribution can be stated as For exterior flow problem, assembling the equation (10) and equation (12) for the indirect boundary integral equation method
can be inscribed as Or When all nodes are in consideration, then equation (14) yields an system of equations which can be written in matrix form in the case of constant and linear elements as Here is the matrix coefficient, is a vector of unknown total potentials "and on the R.H.S is a known vector whose elements are the negative of the values of the velocity potentials of the uniform stream at the nodes on the origion of the body.
The experimental results are compared with the results predicted by a numerical approach based on the boundary integral equation method
(BIEM) and the PHI3D package.
Chengz, "Treatment of body forces in single-domain boundary integral equation method
for anisotropic elasticity," Transformation of Domain Effects to the Boundary, vol.
In combination with the boundary integral equation method
(BIEM) these fundamental solutions were applied to the cell problem for composites with anisotropic inhomogeneities and porous media in [14, 15], while analysis of microstructural stresses in the matrix material was considered in .