Affiliations: [a] Children's Hospital of Chongqing Medical University
136 Zhong Shan second road, District of Yu Zhong, Chongqing 400014, China | [b] State Key Laboratory of Power Transmission Equipment
and System Security and New Technology, The Electrical Engineering College,
Chongqing University. Chongqing, China
Abstract: A new numerical integral method of the Hankel transform which
included the dual Bessel function in the integrand was presented. Because of
the strong-oscillation and slow-decay properties of the Bessel functions, it is
impossible to use a normal numerical integration method. In our method, the
integral interval [0, ∞) is divided into two parts: [0, λ _0] and [λ _0, ∞). In [0,
λ _0], the integration can be calculated using a
Gauss-Legendre quadrature method between the adjacent zero points. And in
[λ _0, ∞), the Hankel transform is converted to
the Fourier cosine or sine transform, and can be calculated with a polygonal
approximation algorithm. The proper value of the dividing point of
λ _0 was discussed. The simulation results of the
test functions show that the algorithm is correct and accurate. Finally, the
forward problem of the multi-layer medium magnetic induction tomography was
calculated with this new method, and the eddy current distribution in the model
and the induced voltages in the detection coils were simulated.
