Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method
Joint Authors
Lo, Wei-Lin
Wu, Nan-Jing
Chen, Chuin-Shan
Tsay, Ting-Kuei
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-02-14
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations.
When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied.
In this research, a numerical integral method is proposed to find the specific length-to-width ratio.
It is conventional to employ the boundary integral method (BIEM) to perform the conformal mapping.
However, due to the singularity produced by the BIEM in seeking the derivatives on the boundaries, the transformation Jacobian determinants on the boundaries have to be evaluated at inner points instead of directly on the boundaries.
This approximation is a source of numerical error.
In this study, the transformed rectangular property and the Cauchy-Riemann equations are successfully applied to derive reduced formulations of the derivatives on the boundaries for the BIEM.
With these boundary derivative formulations, the Jacobian determinants can be evaluated directly on the boundaries.
Furthermore, the results obtained are more accurate than those of the earlier mapping method.
American Psychological Association (APA)
Lo, Wei-Lin& Wu, Nan-Jing& Chen, Chuin-Shan& Tsay, Ting-Kuei. 2016. Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1112262
Modern Language Association (MLA)
Lo, Wei-Lin…[et al.]. Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method. Mathematical Problems in Engineering No. 2016 (2016), pp.1-18.
https://search.emarefa.net/detail/BIM-1112262
American Medical Association (AMA)
Lo, Wei-Lin& Wu, Nan-Jing& Chen, Chuin-Shan& Tsay, Ting-Kuei. Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1112262
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112262