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Immersed finite element method for i...
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Feng, Wenqiang.
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Immersed finite element method for interface problems with algebraic multigrid solver.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Immersed finite element method for interface problems with algebraic multigrid solver./
作者:
Feng, Wenqiang.
面頁冊數:
81 p.
附註:
Source: Masters Abstracts International, Volume: 52-01.
Contained By:
Masters Abstracts International52-01(E).
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1541170
ISBN:
9781303234613
Immersed finite element method for interface problems with algebraic multigrid solver.
Feng, Wenqiang.
Immersed finite element method for interface problems with algebraic multigrid solver.
- 81 p.
Source: Masters Abstracts International, Volume: 52-01.
Thesis (M.S.)--Missouri University of Science and Technology, 2013.
This thesis is to discuss the bilinear and 2D linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. In contrast to the body-fitting mesh restriction of the traditional finite element methods or finite difference methods for interface problems, a number of numerical methods based on structured meshes independent of the interface have been developed. When these methods are applied to the real world applications, we often need to solve the corresponding large scale linear systems many times, which demands efficient solvers. The algebraic multigrid (AMG) method is a natural choice since it is independent of the geometry, which may be very complicated in interface problems. However, for those methods based on finite difference formulation and a structured mesh independent of the interface, the stiffness matrix of the linear system is usually not symmetric positive-definite, which demands extra efforts to design efficient multigrid methods. On the other hand, the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite. Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and 2D linear IFE methods for both stationary and moving interface problems after the IFE and multi-grid methods are reviewed respectively. The numerical examples demonstrate the features of the proposed algorithm, including the optimal convergence in both L2 and semi- H1 norms of the IFE-AMG solutions, the high efficiency with proper choice of the components and parameters of AMG, the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems, and the relationship between the cost and the moving interface location.
ISBN: 9781303234613Subjects--Topical Terms:
515831
Mathematics.
Immersed finite element method for interface problems with algebraic multigrid solver.
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Source: Masters Abstracts International, Volume: 52-01.
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