Fourier embedded domain methods: periodic and C-infinity extension of a function defined on an irregular region to a rectangle via convolution with Gaussian kernels

2006 - A. Bueno Orovio

Applied Mathematics and Computation, 183, 813-818 (2006).

Abtract

One possible way to solve a partial differential equation in an irregular region ohm is the use of the so-called domain embedding methods, in where the domain of interest is embedded within a rectangle. In order to apply a Fourier spectral method on the rectangle, the inhomogeneous term f(x,y) has to be extended to a new function g(x,y) that is periodic and infinitely differentiable, and equal to f(x,y) everywhere within ohm. Some authors have given explicit methods to compute extensions with infinite order convergence for the cases in where the boundary of ohm, partial derivative ohm, can be defined as the zero isoline of a function psi(x,y). For the cases in where this is not possible, we suggest a new method to build these extensions via convolution with Gaussian kernels. (c) 2006 Elsevier Inc. All rights reserved.