Null-field Integral Equations And
Their Applications
Author(s)
J.-T. Chen & P.-Y. Chen
Abstract
In this paper, a null-field equation approach is proposed to deal with boundary
value problems containing circular boundaries. The mathematical tools,
degenerate kernels and Fourier series, are utilized in the null-field integral
formulation. Although we employ the null field equations, we can exactly
collocate the point on the real boundary. Thus, the singularity is novelly avoided
since the kernel is expressed in a degenerate form. Five gains of well-posed
model, singularity free, boundary layer effect free, exponential convergence and
mesh-free approach are achieved. To demonstrate the validity of the present
formulation, some applications are considered: (1) torsion problem, (2) bending
problem, (3) SH wave impinging successive canyons. It is found that previous
results by other investigators are not consistent with ours. After comparing with
other independent solutions, the accuracy and efficiency of our approach is
acceptable.
Keywords: null-field integral equation, degenerate kernel, Fourier series.
1 Introduction
Engineering problems can be formulated as mathematical models. In order to
solve the boundary value problems, researchers and engineers have paid more
attention on the development of boundary integral equation method (BIEM),
boundary element method (BEM) and meshless method than domain type
methods, finite element method (FEM) and finite difference method (FDM).
Among various numerical methods, BEM is one of the most popular numerical
approaches for solving boundary value problems. Although BEM has been
Keywords
null-field integral equation, degenerate kernel, Fourier series.
Related Book
Other papers in this volume
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