Fast space-domain evaluation of geodetic surface integrals |
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| Authors: | R Lehmann |
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| Institution: | (1) Geodetic Institute, University of Karlsruhe, Englerstr. 7, D-76128 Karlsruhe, Germany Tel: +49 721- 6082724; Fax: +49 721 694552; e-mail: lehmann@gik.bau-verm.uni-karlsruhe.de, DE |
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| Abstract: | Geodetic surface integrals play an important role in the numerical solution of geodetic boundary-value problems. In many
cases they can be evaluated using fast methods in the frequency domain (FFT). However, this is not possible in general, because
the domain of integration may be non-trivial (as is the surface of the Earth), the kernel function may not be of convolution
type, or the data distribution may be heterogeneous. Therefore, fast evaluation strategies are also required in the space
domain. They are more difficult to design because only one property is left where a more or less fast evaluation strategy
can be built upon: the potential type of the kernel function. Consequently, the idea is not to replace well-established frequency
domain techniques, but to supplement them. Our approach to this problem goes in two directions: (1) we use advanced cubature
methods where the integration nodes automatically densify in the vicinity of the evaluation points; (2) we use powerful computer
hardware, namely MIMD computers with distributed memory. This enables us to evaluate geodetic surface integrals of any practical
complexity in reasonable time and accuracy. This is shown in a numerical example.
Received: 7 May 1996 / Accepted:17 March 1997 |
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| Keywords: | , Geodetic surface integrals,Numerical integration,Parallel computer |
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