| Attributes | Values |
|---|
| rdf:type
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| Description
| - In gravity field studies the complex geometry of the Earth’s surface makes the solution of potential problems rather demanding. Therefore, Green’s functions, integral equations or linear systems associated with direct methods are usually constructed for solution domains slightly simplified compared to reality. The measure of the simplification affects the convergence of iterations applied in the solution. Often a sphere is used, but this seems not adequate for a global approach. In the paper the construction of a reproducing kernel in Hilbert’s space of functions harmonic in the exterior of an ellipsoid of revolution is discussed. Ellipsoidal harmonics offer the corresponding apparatus, but the structure of the kernel becomes rather complex. Two possibilities to overcome the problem are considered. First an approximation of ellipsoidal harmonics based on a simplified version of Legendre’s ordinary differential equation is used. Subsequently an exact numerical approach is applied as an alternative. In spherical case, as a rule, elementary functions, as expm1 and log1p, appear in its implementation. A slightly modified approach is used for ellipsoidal harmonics in the paper. In this way one can overcome instabilities in the reproducing kernel and its gradient computation, which are mostly connected with floating-point arithmetic and a number representation. The suggested evaluation scheme for the reproducing kernel offers high computation efficiency and very positive results concerning precision and accuracy. In conclusions both the evaluation concepts are compared.
- In gravity field studies the complex geometry of the Earth’s surface makes the solution of potential problems rather demanding. Therefore, Green’s functions, integral equations or linear systems associated with direct methods are usually constructed for solution domains slightly simplified compared to reality. The measure of the simplification affects the convergence of iterations applied in the solution. Often a sphere is used, but this seems not adequate for a global approach. In the paper the construction of a reproducing kernel in Hilbert’s space of functions harmonic in the exterior of an ellipsoid of revolution is discussed. Ellipsoidal harmonics offer the corresponding apparatus, but the structure of the kernel becomes rather complex. Two possibilities to overcome the problem are considered. First an approximation of ellipsoidal harmonics based on a simplified version of Legendre’s ordinary differential equation is used. Subsequently an exact numerical approach is applied as an alternative. In spherical case, as a rule, elementary functions, as expm1 and log1p, appear in its implementation. A slightly modified approach is used for ellipsoidal harmonics in the paper. In this way one can overcome instabilities in the reproducing kernel and its gradient computation, which are mostly connected with floating-point arithmetic and a number representation. The suggested evaluation scheme for the reproducing kernel offers high computation efficiency and very positive results concerning precision and accuracy. In conclusions both the evaluation concepts are compared. (en)
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| Title
| - Geometrical properties of equipotential surfaces and their numerical studies for high resolution Earth’s gravity field models expresses in ellipsoidal harmonics
- Geometrical properties of equipotential surfaces and their numerical studies for high resolution Earth’s gravity field models expresses in ellipsoidal harmonics (en)
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| skos:prefLabel
| - Geometrical properties of equipotential surfaces and their numerical studies for high resolution Earth’s gravity field models expresses in ellipsoidal harmonics
- Geometrical properties of equipotential surfaces and their numerical studies for high resolution Earth’s gravity field models expresses in ellipsoidal harmonics (en)
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| skos:notation
| - RIV/00025615:_____/11:#0001785!RIV12-MSM-00025615
|
| http://linked.open...avai/riv/aktivita
| |
| http://linked.open...avai/riv/aktivity
| - P(LC506), Z(CUZ0002561501)
|
| http://linked.open...vai/riv/dodaniDat
| |
| http://linked.open...aciTvurceVysledku
| |
| http://linked.open.../riv/druhVysledku
| |
| http://linked.open...iv/duvernostUdaju
| |
| http://linked.open...titaPredkladatele
| |
| http://linked.open...dnocenehoVysledku
| |
| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/11:#0001785
|
| http://linked.open...riv/jazykVysledku
| |
| http://linked.open.../riv/klicovaSlova
| - physical geodesy; differential geometry; theory of surfaces; Weingarten's theorem; Christoffel's theorem; Brun's equation; gravity field models; vertical datum (en)
|
| http://linked.open.../riv/klicoveSlovo
| |
| http://linked.open...i/riv/kodPristupu
| |
| http://linked.open...ontrolniKodProRIV
| |
| http://linked.open...i/riv/mistoVydani
| |
| http://linked.open...telVyzkumneZpravy
| - International Union of Geodesy and Geophysics
|
| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
| |
| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...vavai/riv/projekt
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Holota, Petr
- Nesvadba, Otakar
|
| http://linked.open...n/vavai/riv/zamer
| |
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