Numerical algorithms for a free boundary problem model of DCIS and a related inverse problem |
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| Authors: | Keji Liu Yongzhi Xu Dinghua Xu |
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| Institution: | 1. Shanghai Key Laboratory of Financial Information Technology, Institute of Scientific Computation and Financial Data Analysis, School of Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of Chinaliu.keji@mail.shufe.edu.cn kjliu.ip@gmail.com;3. Department of Mathematics, University of Louisville, Louisville, KY, USA;4. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of China |
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| Abstract: | ABSTRACTThe Ductal carcinoma in situ (DCIS) model has wide applications in the diagnosis of breast cancer, and has been attracted much attention in recent years. In this paper, an effective method has been provided for solving the direct problem of the DCIS model. Moreover, the uniqueness result is established for a kind of inverse problems of DCIS model. Based on the uniqueness theorem, an optimization method has been developed for dealing with the related inverse problem of the DCIS model. The numerical experiments show that the algorithms in this paper are efficient, accurate, robust against noise and fast. |
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| Keywords: | Free boundary problem uniqueness analysis numerical methods ductal carcinoma in situ |
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