Masters Theses

Author

Wenqiang Feng

Abstract

"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 Ł² 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"--Abstract, page iii.

Advisor(s)

He, Xiaoming

Committee Member(s)

Singler, John
Zhang, Yanzhi

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2013

Pagination

ix, 70 pages

Note about bibliography

Includes bibliographical references.

Rights

© 2013 Wenqiang Feng, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Finite element method -- Computer programs
Interfaces (Physical sciences) -- Mathematics -- Computer simulation
Algebraic number theory -- Computer simulation
Differential equations -- Computer simulation
Numerical analysis -- Computer simulation

Thesis Number

T 10288

Electronic OCLC #

853507806

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