An Efficient Spectral Domain Embedding Method for Elliptic PDE's on ۳D Complex Domain

The aims of this paper, utilize the fictitious domain concept with cuboid embedding to solve elliptic boundary value problems in domains of ۳D complex geometry. Cuboid embedding allows the application of spectral methods in the extended domain to solve elliptic PDE's. Also by finding the Schur complement and Moore-Penrose inverse, the system of block matrices is solved efficiently.Ample numerical examples results are presented to demonstrate the effectiveness of this approach for problems on ۳D complex domains.

Keywords:

Spectral collocation method , Irregular domain , Fictitious domain , Domain embedding method