National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 16 Jun 2024 05:50:49 GMT2024-06-16T05:50:49Z5021A study on the method of fundamental solutions using an image concepthttp://scholars.ntou.edu.tw/handle/123456789/2452Title: A study on the method of fundamental solutions using an image concept
Authors: Jeng-Tzong Chen; Hung-Chih Shieh; Jhen-Jyun Tsai; Jia-Wei Lee
Abstract: In this paper, both analytical and semi-analytical solutions for Green’s functions are obtained by using the image method which can be seen as a special case of method of fundamental solutions (MFS). The image method is employed to solve the Green’s function for the annular, eccentric and half-plane Laplace problems. In addition, an analytical solution is derived for the fixed-free annular case. For the half-plane problem with a circular hole and an eccentric annulus, semi-analytical solutions are both obtained by using the image concept after determining the strengths of two frozen image points and a free constant by matching boundary conditions. It is found that two frozen images terminated at the two focuses in the bipolar coordinates for the problems with two circular boundaries. A boundary value problem of an eccentric annulus without sources is also considered. Error distribution is plotted after comparing with the analytical solution derived by Lebedev et al. using the bipolar coordinates. The optimal locations for the source distribution in the MFS are also examined by using the image concept. It is observed that we should locate singularities on the two focuses to obtain better results in the MFS. Besides, whether the free constant is required or not in the MFS is also studied. The results are compared well with the analytical solutions.
Wed, 01 Dec 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/24522010-12-01T00:00:00ZAnalytical study and numerical experiments for Laplace equation with overspecified boundary conditionshttp://scholars.ntou.edu.tw/handle/123456789/2348Title: Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions
Authors: Jeng-Tzong Chen; Chen, K. H.
Abstract: In this paper, the window function, e−αk2, is applied to regularize the divergent problem which occurs in the Laplace equation with overspecified boundary conditions in an infinite strip region. To deal with this ill-posed problem, the corner of the L-curve is chosen as the compromise point to determine the optimal α of the Gaussian window, e−αk2, so that the high wave-number (k) content can be suppressed instead of engineering judgement using the concept of a cutoff wave-number. From the examples shown, it is found that a reasonable solution of the unknown boundary potential can be reconstructed, and that both high wave-number content and divergent results can be avoided by using the proposed regularization technique.
Tue, 01 Sep 1998 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23481998-09-01T00:00:00Z