The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains (Journal of Computational Mathematics, 2018)
The artificial boundary method is applied to solve three-dimensional exterior problems.Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificialboundary conditions are derived explicitly in terms of an infinite series. Then thewell-posedness of the coupled variational problem is obtained. It is found that error estimatesderived depend on the mesh size, truncation term and the location of the artificialboundary. Three numerical examples are presented to demonstrate the effectiveness andaccuracy of the proposed method.
Keywords: Artificial boundary method; Exterior harmonic problem; Finite element method; Natural boundary reduction; Oblate ellipsoid; Prolate ellipsoid.