NDLI: A new augmented immersed finite element method without using SVD interpolations

Content Provider	Springer Nature Link
Author	Chen, Jinru Ji, Haifeng Li, Zhilin
Copyright Year	2015
Abstract	Augmented immersed interface methods have been developed recently for interface problems and problems on irregular domains including CFD applications with free boundaries and moving interfaces. In an augmented method, one or several augmented variables are introduced along the interface or boundary so that one can get efficient discretizations. The augmented variables should be chosen such that the interface or boundary conditions are satisfied. The key to the success of the augmented methods often relies on the interpolation scheme to couple the augmented variables with the governing differential equations through the interface or boundary conditions. This has been done using a least squares interpolation (under-determined) for which the singular value decomposition (SVD) is used to solve for the interpolation coefficients. In this paper, based on properties of the finite element method, a new augmented immersed finite element method (IFEM) that does not need the interpolations is proposed for elliptic interface problems that have a piecewise constant coefficient. Thus the new augmented method is more efficient and simple than the old one that uses interpolations. The method then is extended to Poisson equations on irregular domains with a Dirichlet boundary condition. Numerical experiments with arbitrary interfaces/irregular domains and large jump ratios are provided to demonstrate the accuracy and the efficiency of the new augmented methods. Numerical results also show that the number of GMRES iterations is independent of the mesh size and nearly independent of the jump in the coefficient.
Ending Page	416
Page Count	22
Starting Page	395
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	2
Volume Number	71
Language	English
Publisher	Springer US
Publisher Date	2015-05-09
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Piecewise constant coefficient Numeric Computing Augmented immersed finite element method Theory of Computation Nonlinear elliptic equations Fast poisson solver Interface problem Algorithms Algebra Numerical Analysis Least squares interpolation using SVD Error bounds Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Immersed finite element Poisson equation on irregular domain
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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