The fictitious Compress Recuperation Principle in Boundary Value Problems and Its Application in Bjerhammar's Theory
SHEN Wen-bin1,2, NING Jin-sheng1,2, CHAO Ding-bo1
(1.School of geodesy and Geomatics, Wuhan University, Wuhan 430079, China; 2. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China)
Abstract£ºThe fictitious compress recuperation method is further developed, so that it is suitable for any regular harmonic function u. For an arbitrary finite body ¦¸¡¡with a simply closed surface, if the boundary value u|e¦¸ was given, and it is assumed that the function u is harmonic in the region outside the body and regular at infinity, one can precisely and strictly determine the external field u by using the idea of the fictitious compress recuperation. Hence, it is reasonable to generalize the method of the fictitious compress recuperation into the corresponding principle. Furthermore, as an application example, the fictitious gravity anomaly required in Bjerhammar's theory is simply derived out, based on the principle of the fictitious compress recuperation.
Key words£ºregular harmonic function; fictitious compress recuperation; determination of external field; determination of the fictitious gravity anomaly