期刊
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
卷 44, 期 1, 页码 171-202出版社
MALAYSIAN MATHEMATICAL SCIENCES SOC
DOI: 10.1007/s40840-020-00942-7
关键词
Numerical conformal mapping; Boundary integral equations; Multiply connected regions; Neumann-type kernel; Generalized Neumann kernel; GMRES; Fast multipole method; Medical image processing
类别
资金
- Malaysian Ministry of Education (MOE) through the Research Management Centre (RMC), Universiti Teknologi Malaysia [R.J130000.7854.5F198]
- Kurdistan Ministry of Higher Education through Department of General Sciences, College of Education and Language, Charmo University
This paper introduces a fast boundary integral equation method for numerical conformal mapping and its inverse, which can handle regions with complex geometry and high connectivity. The complexity of this method is lower compared to previous algorithms, and it shows potential applications in medical human brain image processing.
In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto a disk and annulus with circular slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. The integral equations related to the mappings are solved numerically using combination of Nystrom method, GMRES method, and fast multipole method. The complexity of this new algorithm is O((M+1)n), where M+1 stands for the multiplicity of the multiply connected region and n refers to the number of nodes on each boundary component. Previous algorithms require O((M+1)3n3) operations. The numerical results of some test calculations demonstrate that our method is capable of handling regions with complex geometry and very high connectivity. An application of the method on medical human brain image processing is also presented.
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