Saad’s paper, The smooth forcing extension method: A high-order technique for solving elliptic equations on complex domains, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper introduces a new high-order accurate approach, the smooth forcing extension method, to elliptic equations in complex geometries using Fourier continuation methods.
The smooth forcing extension method is similar to the immersed boundary smooth extension (IBSE) method introduced by Guy, Stein, Thomases, and co-workers, but it relies on extending the forcing term instead of the solution field from the “physical” to the “non-physical” domain. One consequence of this difference is that the smooth forcing extension method can yield a better conditioned system of equations than the IBSE formulation, which can yield improved accuracy at higher resolutions.