Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9507216 | Applied Mathematics and Computation | 2005 | 7 Pages |
Abstract
A simple way to solve a partial differential equation in a non-rectangular domain Ω is to embed the domain in a rectangle B and solve the problem (more easily) in the rectangle. To apply a Fourier spectral method on the rectangle, it is necessary to extend the inhomogeneous term in the PDE, f(x,y), to B in such a way that the extended function g(x,y) is periodic and infinitely differentiable, and yet is equal to f(x,y) everywhere in the irregular domain Ω. If the boundary of Ω, âΩ, is defined as the zero isoline of a function Φ(x,y), then a suitable extension is g(x,y)â¡f(x,y)H(1â2Φ(x,y)/constant) where H is a smoothed approximation to the step function which is defined in the main text.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
John P. Boyd,