| A SIMPLE NUMERICAL METHOD FOR COMPLEX GEOMETRICAL OPTICS SOLUTIONS TO THE CONDUCTIVITY EQUATION | |
| Du, K ; Du K(杜魁) | |
| 2011 | |
| 关键词 | complex geometrical optics solution R-linear integral equation singular integral fast algorithm global R-linear GMRES |
| 英文摘要 | This paper concerns numerical methods for computing complex geometrical optics (CGO) solutions to the conductivity equation del . sigma del u(., k) = 0 in R(2) for piecewise smooth conductivities sigma, where k is a complex parameter. The key is to solve an R-linear singular integral equation defined in the unit disk. Recently, Astala et al. [Appl. Comput. Harmon. Anal., 29 (2010), pp. 2-17] proposed a complicated method for numerical computation of CGO solutions by solving a periodic version of the R-linear integral equation in a rectangle containing the unit disk. In this paper, based on the fast algorithms in [P. Daripa and D. Mashat, Numer. Algorithms, 18 (1998), pp. 133-157] for singular integral transforms, we propose a simpler numerical method which solves the R-linear integral equation in the unit disk directly. For the resulting R-linear operator equation, a minimal residual iterative method is proposed. Numerical examples illustrate the accuracy and efficiency of the new method. |
| 语种 | 英语 |
| 内容类型 | 期刊论文 |
| 源URL | [http://dspace.xmu.edu.cn/handle/2288/66430]  |
| 专题 | 数学科学－已发表论文 |
| 推荐引用方式 GB/T 7714 | Du, K,Du K. A SIMPLE NUMERICAL METHOD FOR COMPLEX GEOMETRICAL OPTICS SOLUTIONS TO THE CONDUCTIVITY EQUATION[J],2011. |
| APA | Du, K,&杜魁.(2011).A SIMPLE NUMERICAL METHOD FOR COMPLEX GEOMETRICAL OPTICS SOLUTIONS TO THE CONDUCTIVITY EQUATION.. |
| MLA | Du, K,et al."A SIMPLE NUMERICAL METHOD FOR COMPLEX GEOMETRICAL OPTICS SOLUTIONS TO THE CONDUCTIVITY EQUATION".(2011). |
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