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Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

Published online by Cambridge University Press:  03 June 2015

Wenqiang Feng ,
Xiaoming He ,
Yanping Lin  and
Xu Zhang
Wenqiang Feng*
Affiliation:
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA
Xiaoming He*
Affiliation:
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA
Yanping Lin*
Affiliation:
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong Department of Mathematical and Statistics Science, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Xu Zhang*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
*
Email:fw253@mst.edu
Corresponding author.Email:hex@mst.edu
Corresponding author.Email:hex@mst.edu
Email:xuz@vt.edu
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Abstract

This article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. For the numerical 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 linear IFE methods for both stationary and moving interface problems. The numerical examples demonstrate the features of the proposed algorithms, 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.

Keywords

65F1065N3035J1535K20Interface problemsimmersed finite elementsalgebraic multigrid method
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014 , pp. 1045 - 1067
Copyright
Copyright © Global Science Press Limited 2014

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