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dc.contributor.author郭柏均en_US
dc.contributor.authorKuo, Po-Chunen_US
dc.contributor.author賴明治en_US
dc.contributor.authorLai, Ming Chihen_US
dc.date.accessioned2014-12-12T02:40:30Z-
dc.date.available2014-12-12T02:40:30Z-
dc.date.issued2013en_US
dc.identifier.urihttp://140.113.39.130/cdrfb3/record/nctu/#GT070152201en_US
dc.identifier.urihttp://hdl.handle.net/11536/74409-
dc.description.abstract在本篇論文中,系使用內嵌介面法把一個二維橢圓介面問題推廣到三維。此方法為調整過的有限差分法,其修正項透過介面上的不連續條件而得。藉由由法向量方向所展開的泰勒展開式,在介面附近的網格點,離散差分方程會被調整。因為在介面上不連續條件型態的關係, 在解橢圓介面問題的過程中,必須要解一個線性系統。首先用重新初始化水平集方法來找網格點在界面上的正交投影,接下來我們運用內嵌介面法,廣義最小殘量方法,和最小平方法來解橢圓介面問題。zh_TW
dc.description.abstractIn this thesis, we extend the immersed interface method for a 2D elliptic interface problem to 3D. The numerical method is a finite difference method modified with some correction terms from the jump conditions. By using Taylor's expansions along the normal direction, the discrete difference equation is modified at the gird point close to interface. Because of the types of the jump condition, we have to solve a linear system in the process of solving the elliptic interface problem. We first use the reinitialization of level set method to find the orthogonal projection of the grid point and perform it to check its accuracy. Then, we solve the elliptic interface problem by the immersed interface method, GMRES and least squares method, and make some numerical tests to check the rate of convergence.en_US
dc.language.isoen_USen_US
dc.subject內嵌介面法zh_TW
dc.subject橢圓介面問題zh_TW
dc.subjectimmersed interface methoden_US
dc.subjectelliptic interface problemen_US
dc.title三維橢圓介面問題的數值研究zh_TW
dc.titleAn immersed interface method for 3D elliptic interface problemsen_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
Appears in Collections:Thesis


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