THE TREFFTZ TEST FUNCTIONS METHOD FOR SOLVING THE GENERALIZED INVERSE BOUNDARY VALUE PROBLEMS OF LAPLACE EQUATION

Authors

Chein-Shan Liu, Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, Taiwan, R.O.C.
Yung-Wei Chen, Department of Marine Engineering, National Taiwan Ocean University, Keelung, Taiwan, R.O.C.
Jiang-Ren Chang, Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Taiwan, R.O.C.Follow

Abstract

The issue of data completion is important for the elliptic type partial differential equation. In the inverse Cauchy problem, we need to complete the boundary data by over-specifying Dirichlet and Neumann data on a portion of the boundary. In this paper, we numerically solve the generalized inverse boundary value problems of Laplace equation in a rectangle with one boundary function and two boundary functions missing, which are more difficult than the inverse Cauchy problem. By using the technique of a boundary integral equation method together with a specially designed Trefftz test function, we can complete the boundary data by requiring minimal extra data. Then solving the Laplace equation with the given data and recovered data by the multiple-scale Trefftz method, we can find the numerical solution in the interior nodal points.

Recommended Citation

Liu, Chein-Shan; Chen, Yung-Wei; and Chang, Jiang-Ren (2018) "THE TREFFTZ TEST FUNCTIONS METHOD FOR SOLVING THE GENERALIZED INVERSE BOUNDARY VALUE PROBLEMS OF LAPLACE EQUATION," Journal of Marine Science and Technology: Vol. 26: Iss. 5, Article 3.
DOI: 10.6119/JMST.201810_26(5).0003
Available at: https://jmstt.ntou.edu.tw/journal/vol26/iss5/3