The Use of Finite Elements in Physical Geodesy,
Abstract
Currently used methods of computational physical geodesy are compared with respect to their efficiency during production runs on a computer. These methods include: (1) Least Squares adjustment with respect to spherical harmonics; (2) Surface layers, buried masses and related methods; (3) Least squares collocation; (4) Representation of the potential by spline functions; and (5) Explicit integral formulas. As an alternative, the feasibility of applying the finite element method to the fundamental problems of physical geodesy is investigated. The methods listed under (1)-(4) can be dramatically speeded up if the distribution of data and weights satisfies certain symmetry-requirements which are rather stringent. Method (5) relies altogether on a special type and distribution of data. In the absence of data homogeneity and regularity, the finite element method is asymptotically superior with respect to computational efficiency. Let N denote the number of parameters necessary to describe the variation of the potential on the reference surface. The computational effort associated with methods (1)-(4) grows proportional to N cubed. That one resulting from finite elements grows proportional to N to the 3/2 power. The constants of proportionality are, however, unfavorable for the finite element method. Hence its superiority comes through only for large values of N, which, in case of a global solution, corresponds to data averaged over 2 deg x 2 deg blocks. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1981
- Accession Number
- ADA104164
Entities
People
- Peter Meissl
Organizations
- Ohio State University