A Systematic Approach for Solving Laplace, Helmholtz and Biharmonic Equations Using Degenerate Kernels (II)

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基本資料

Project title

Code/計畫編號

NSC95-2221-E019-065

Translated Name/計畫中文名

以退化核求解拉普拉斯、赫姆茲與雙諧和方程式之系統性解法(II)

Project Coordinator/計畫主持人

Jeng-Tzong Chen

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1311108

Year

2006

Start date/計畫起

01-08-2006

Expected Completion/計畫迄

31-07-2007

Bugetid/研究經費

832千元

ResearchField/研究領域

土木水利工程

本計劃提出一系統性之方法來求解含圓型邊界的工程問題。在零場積分方程中搭配退化核與傅立葉級數展開。其中核函數展開成退化核的形式，把邊界密度用傅立葉級數展開，可把點佈在真實邊界上，且又可避開奇異積分，此乃是本計劃的最大創意。我們的方法有五個優點：良態的模式、不需計算奇異積分、無邊界層效應、指數收歛與無網格法。代入邊界條件後，可得到線性代數系統。解得傅立葉係數後，其解可以表示成積分表示式。這種系統性解法可以應用在赫姆茲(第二年)問題上。本計畫最後提供幾個算例來驗證我們方法的正確性。In this project, a systematic approach is proposed to deal with engineering problems containing circular boundaries. The mathematical tools, degenerate kernels and Fourier series, are utilized in the null-field integral formulation. The kernel function is expanded to the degenerate form and the boundary density is expressed into Fourier series. By collocating the null-field points on the real boundary, the singularity is novelly avoided. Five gains of well-posed model, singularity free, boundary-layer effect free , exponential convergence and mesh-free approach are achieved. By matching the boundary condition, a linear algebraic system is obtained. After obtaining the unknown Fourier coefficients, the solution can be obtained by using the integral representation. This systematic approach can be applied to solve the Helmholtz problems (second year). Finally, several examples are demonstrated to show the validity of present formulation.

Keyword(s)

退化核
傅立葉級數
零場積分方程
無網格
線性代數系統
degenerate kernels
Fourier series
null-field
mesh-free
linear algebraic system

DSpace CRIS

A Systematic Approach for Solving Laplace, Helmholtz and Biharmonic Equations Using Degenerate Kernels (II)

基本資料

Description