The Immersed Interface/Multigrid Methods for Interface Problems

Authors:
Loyce Adams;Zhilin Li
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 24

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A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions

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Solving partial differential equations on irregular domains with moving interfaces, with applications to superconformal electrodeposition in semiconductor manufacturing

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Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems

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Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions

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Shape-topology optimization for Navier-Stokes problem using variational level set method

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An interpolation matched interface and boundary method for elliptic interface problems

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Modeling and simulation of electronic structure, material interface and random doping in nano-electronic devices

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MIB method for elliptic equations with multi-material interfaces

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Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

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3D Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients

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A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

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Heterogeneous mixtures of elliptical particles: Directly resolving local and global properties and responses

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A dimension by dimension splitting immersed interface method for heat conduction equation with interfaces

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Abstract

New multigrid methods are developed for the maximum principle preserving immersed interface method applied to second order linear elliptic and parabolic PDEs that involve interfaces and discontinuities. For elliptic interface problems, the multigrid solver developed in this paper works while some other multigrid solvers do not. For linear parabolic equations, we have developed the second order maximum principle preserving finite difference scheme in this paper. We use the Crank--Nicolson scheme to deal with the diffusion part and an explicit scheme for the first order derivatives. Numerical examples are also presented.