Boundary approximation method, also known as the collocation Trefftz method in
engineering, is used to solve Laplace boundary value problem on rectanglular domain.
Suppose the particular solutions are chosen for the whole domain. If there is no singularity
on other vertices, it should have exponential convergence. Otherwise, it will
degenerate to polynomial convergence. In the latter case, the order of convergence has
some relation with the intensity of singularity. So, it is easy to design models with
desired convergent orders.
On a sectorial domain, when one side of the boundary conditions is a transcendental
function, it needs to be approximated by power series. The truncation of this power
series will generate an artificial singularity when solving Laplace equation on polygon.
So it will greatly slow down the expected order of convergence. This thesis study how
the truncation error affects the convergent speed. Moreover, we focus on the transition
behavior of the convergence from one order to another. In the end, we also apply our
results to boundary approximation method with enriched basis.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0630109-020518 |
| Date | 30 June 2009 |
| Creators | Lin, Guan-yu |
| Contributors | Hung-Tsai Huang, Chien-Sen Huang, none, Tzon-Tzer Lu, Zi-Cai Li |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0630109-020518 |
| Rights | unrestricted, Copyright information available at source archive |
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