Immersed finite elementmethod for interface problems with algebraicmultigrid solver

Wenqiang Feng, Xiaoming He, Yanping Lin, Xu Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

This article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated fromthe algebraicmultigrid solver for both stationary andmoving 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.
Original languageEnglish
Pages (from-to)1045-1067
Number of pages23
JournalCommunications in Computational Physics
Volume15
Issue number4
DOIs
Publication statusPublished - 1 Apr 2014

Keywords

  • Algebraic multigrid method
  • Immersed finite elements
  • Interface problems

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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