The local tangential lifting method for moving interface problems on surfaces with applications

2021 ◽  
Vol 431 ◽  
pp. 110146
Author(s):  
Xufeng Xiao ◽  
Xinlong Feng ◽  
Zhilin Li
Keyword(s):  
Interface Problems ◽  
Moving Interface ◽  
Moving Interface Problems

Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

2014 ◽  
Vol 15 (4) ◽  
pp. 1045-1067 ◽  
Author(s):  
Wenqiang Feng ◽  
Xiaoming He ◽  
Yanping Lin ◽  
Xu Zhang
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Positive Definite ◽  
Algebraic Multigrid ◽  
Interface Problems ◽  
Multigrid Solver ◽  
Immersed Finite Element ◽  
Symmetric Positive Definite ◽  
Moving Interface ◽  
Moving Interface Problems

AbstractThis 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 L2and semi-H1norms 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.

scholarly journals A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow

1997 ◽  
Vol 134 (2) ◽  
pp. 236-252 ◽  
Author(s):  
Thomas Y. Hou ◽  
Zhilin Li ◽  
Stanley Osher ◽  
Hongkai Zhao
Keyword(s):  
Hybrid Method ◽  
Interface Problems ◽  
Moving Interface ◽  
Moving Interface Problems
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