The purpose of this paper is to solve the interface discontinuities in radial basis function (RBF) method for multi-medium boundary value problems (BVPs). The discontinuity of the solution derivatives is not easily handled with RBF method because of infinitely smoothness.
The essence of solving BVP is to construct the continuous potential function surfaces. Hence, from constructing surface aspect, this paper proposed and compared the global and subzone schemes for RBF method. Their implementation schemes and mathematic models can then be derived. Numerical experiments and comparison are carried out for electric and magnetic field calculation.
In the numerical experiments, the subzone scheme has shown its significant advantageous, it can approximate not only the potential function but also its derivative on interface boundary with high accuracy. So the physical characteristics of discontinuities on the interface can be revealed clearly. The overall precision is significantly improved.
This paper proposed an effective subzone scheme for RBF method in multi-medium BVP. It is an improvement for RBF method based on its domain decomposition idea. And it is also a candidate for solving complex BVP.
This work was supported by the National Science Foundation Project of CQ CSTC jjA00017.
Huaiqing, Z., Xin, N., Yu, C. and Zhihong, F. (2014), "Subzone scheme for RBF meshless method in solving multi-medium boundary value problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 6, pp. 2139-2157. https://doi.org/10.1108/COMPEL-11-2013-0353
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