A NEW FORMULATION FOR CERTAIN INTERFACE PROBLEMS IN POLAR COORDINATES AND APPLICATIONS
Date Issued
2005-07-31
Date
2005-07-31
Author(s)
DOI
932115M002004
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 non-smooth or discontinuous solution to a problem with a smooth solution. The
new formulation leads to a simple second order ¯nite di®erence scheme for the partial di®erential
equation and a new interpolation scheme for the normal derivative of the solution. In conjunction
with the fast immersed interface method, a fast Poisson solver has been developed for the interface
problems with piecewise constant but discontinuous coe±cient using the new formulation in polar
coordinates system.
Subjects
interface problems
singular source
delta function
level set function
discontinuous
coefficients
coefficients
polar coordinates
immersed interface method
smooth extension
fast Poisson solver
Publisher
臺北市：國立臺灣大學數學系暨研究所
Type
report
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