Spectral Smoothed Boundary Methods: The role of external boundary conditions
A. Bueno Orovio, V. M. Pérez-García
Numerical Methods for Partial Differential Equations 22, 435-448 (2006).
Pérez García, Victor M..
The spectral smoothed boundary method (SSBM) is a recently proposed numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of Fourier spectral methods. In this article we explore the robustness and accuracy of the scheme under variations of the artificial boundary conditions that must be imposed on the boundary of the enlarged domain in which the problem is solved. As a test model, we present quantitative numerical results based on a problem of propagation of waves of electrical activity in cardiac tissue for which the method is relevant.