A Rigorous Condition Number Estimate of an Immersed Finite Element Method

It is known that the convergence rate of the traditional iteration methods like the conjugate gradient method depends on the condition number of the stiffness matrix. Moreover the construction of fast solvers like multigrid and domain decomposition methods also need to estimate the condition number...

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Vydáno v:Journal of scientific computing Ročník 83; číslo 2; s. 29
Hlavní autoři: Wang, Saihua, Wang, Feng, Xu, Xuejun
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2020
Springer Nature B.V
Témata:
Algorithms
Computational Mathematics and Numerical Analysis
Conjugate gradient method
Domain decomposition methods
Estimates
Finite element analysis
Finite element method
Iterative methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Multigrid methods
Stiffness matrix
Theoretical
Triangulation
Condition number
IFE method
Interface problem
ISSN:0885-7474, 1573-7691
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Shrnutí:It is known that the convergence rate of the traditional iteration methods like the conjugate gradient method depends on the condition number of the stiffness matrix. Moreover the construction of fast solvers like multigrid and domain decomposition methods also need to estimate the condition number of the stiffness matrix. The main purpose of this paper is to give a rigorous condition number estimate of the stiffness matrix resulting from the linear and bilinear immersed finite element approximations of the high-contrast interface problem. It is shown that the condition number is C ρ h - 2 , where ρ is the jump of the discontinuous coefficients, h is the mesh size, and the constant C is independent of ρ and the location of the interface on the triangulation. Numerical results are also given to verify our theoretical findings.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-020-01212-1