Sangawi, Ali W. K. and Murid, Ali H. M. and Lee, Khiy Wei (2021) Circular slit maps of multiply connected regions with application to brain image processing. Bulletin of the Malaysian Mathematical Sciences Society, 44 (1). pp. 171202. ISSN 01266705

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Official URL: http://dx.doi.org/10.1007/s40840020009427
Abstract
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 Neumanntype and generalized Neumann kernels. The integral equations related to the mappings are solved numerically using combination of Nyström 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.
Item Type:  Article 

Uncontrolled Keywords:  Boundary integral equations, Fast multipole method 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  94591 
Deposited By:  Widya Wahid 
Deposited On:  31 Mar 2022 15:48 
Last Modified:  31 Mar 2022 15:48 
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