The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains
Keywords:
Artificial boundary method, Exterior harmonic problem, Finite element method, Natural boundary reduction, Oblate ellipsoid, Prolate ellipsoid.Abstract
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 artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.