Applications of New Method of Fundamental Solution to the Inverse Cauchy Problems

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Project title

Code/計畫編號

MOST107-2221-E019-006

Translated Name/計畫中文名

新基本解法於反算問題之應用

Project Coordinator/計畫主持人

Ying-Te Lee

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=12621068

Year

2018

Start date/計畫起

01-08-2018

Expected Completion/計畫迄

31-07-2019

Bugetid/研究經費

657千元

ResearchField/研究領域

土木水利工程

基於去年計劃使用新基本解法處理勢能問題成功之經驗，本計劃擬嘗試將新基本解法延伸來求解柯西反算問題。在傳統的基本解法中，為了避免場點與源點碰在一起時所產生的奇異行為，源點總是被放置於領域之外。在我們所提出的新的基本解法中，源點則被放置在真實的邊界上並且透過滿足力平衡與剛體運動的物理規範，影響係數矩陣的對角線項則可被輕易的求得。首先，利用力平衡方程式來求得曳引力影響係數矩陣的對角線項。接著，藉由滿足剛體運動可求得勢能場影響係數矩陣的對角線值。在求得對角線項後，根據問題所給定的邊界條件，我們將可輕易的建構出一套線性代數方程。此外我們也將引入迭代法來求解反算問題。計畫書中所提出的技巧不僅能用於單層勢能法，同時也適用於雙層勢能法。最後，我們將提出幾個數值算例來呈現新基本解法的可行性、正確性與精確性。 AbstractBased on the successful experience of last year project to deal with the potential problems by using the new method of fundamental solution (MFS), this proposal will be attempted to extend the new MFS to solve the inverse Cauchy problems of Laplace equation. In the conventional MFS, the source points are always located outside of the domain for avoiding the singularity of source point and collocation point coinciding together. In the new MFS are located on the real boundary and the finite value of the diagonal terms in the influence matrix can be determined through satisfying the force equilibrium condition and rigid body motion. First, the equation of force equilibrium will be used to determine the diagonal-term values of the influence matrix for traction. Then, the diagonal-term values of the influence matrix for potential will be available by satisfying the rigid body motion. After obtaining the diagonal-term values of the influence matrix, the linear algebraic equation will be easily constructed according to the boundary conditions. Besides, the iterative scheme will be introduced to solve the inverse problem. The proposed techniques will be used not only for single-layer approach but also for the double-layer approach. Finally, several numerical examples will be provided to show the validity and feasibility of the new scheme.

Keyword(s)

基本解法
力平衡
剛體運動
拉普拉斯方程
柯西反算問題
method of fundamental solutions
equilibrium of force
rigid body motion
Laplace equation
inverse Cauchy problem

DSpace CRIS

Applications of New Method of Fundamental Solution to the Inverse Cauchy Problems

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