New Formulations for Interface Problems in Polar Coordinates

Authors:
Zhilin Li;Wei-Cheng Wang;I-Liang Chern;Ming-Chih Lai
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2003

Citing 0
Cited 11

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Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities

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Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain

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An interpolation matched interface and boundary method for elliptic interface problems

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Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients

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MIB method for elliptic equations with multi-material interfaces

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The IIM in polar coordinates and its application to electro capacitance tomography problems

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Abstract

In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a nonsmooth or discontinuous solution into a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new interpolation scheme for the normal derivative of the solution. In conjunction with the fast immersed interface method, a fast solver has been developed for the interface problems with a piecewise constant but a discontinuous coefficient using the new formulation in a polar coordinate system.