Artificial Boundary Conditions for the Simulation of the Heat Equation in an Infinite Domain

Authors:
Alexander Y. Suhov;Adi Ditkowski
Affiliations:
suhuvale@tau.ac.il and adid@post.tau.ac.il;-
Venue:
SIAM Journal on Scientific Computing
Year:
2011

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Abstract

We present Dirichlet to Dirichlet boundary conditions for the heat equation in one, two, and three dimensions. These boundary conditions contain temporal convolution integrals with nonsingular kernels, allowing for an accurate and simple numerical approximation and enabling their straightforward coupling to any numerical scheme. The stability of these boundary conditions is proven using the Kreiss theory.