Natural Boundary Element Method For Three Dimensional Exterior Harmonic Problem With An Inner Prolate Spheroid Boundary
Hong-ying Huang 1, De-hao Yu 11 LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Received 2005-3-22 Revised 2005-10-12
In this paper, we study natural boundary reduction for Laplace equation with Dirichlet or Neumann boundary condition in a three-dimensional unbounded domain, which is the outside domain of a prolate spheroid. We express the Poisson integral formula and natural integral operator in a series form explicitly. Thus the original problem is reduced to a boundary integral equation on a prolate spheroid. The variational formula for the reduced problem and its well-posedness are discussed. Boundary element approximation for the variational problem and its error estimates, which have relation to the mesh size and the terms after the series is truncated, are also presented. Two numerical examples are presented to demonstrate the effectiveness and error estimates of this method.
Key words: Natural boundary reduction; Prolate spheroid boundary; Finite element; Exterior harmonic problem.