About: An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential

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About: An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In gravity field studies the complex structure of the Earth’s surface makes the solution of potential problems rather demanding. Green’s functions, integral kernels, reproducing kernels of the respective Hilbert spaces, kernels associated with the integral equation method, but also linear (e.g. Galerkin’s) systems resulting from the use of direct methods are usually constructed for a boundary that is simplified in comparison with reality. The simplification has an essential impact on the convergence of iteration procedures applied in this connection. Often a sphere is used, but it seems this is not an adequate choice. Attempt is made to work with an ellipsoid of revolution. Ellipsoidal harmonics come into play. The structure of the kernels mentioned above similarly as of the entries of Galerkin’s matrix becomes rather complex. Therefore, an approximation of ellipsoidal harmonics is used. The idea is applied to the construction of Green’s function, reproducing kernel and Galarkin’s matrix. In gravity field studies the complex structure of the Earth’s surface makes the solution of potential problems rather demanding. Green’s functions, integral kernels, reproducing kernels of the respective Hilbert spaces, kernels associated with the integral equation method, but also linear (e.g. Galerkin’s) systems resulting from the use of direct methods are usually constructed for a boundary that is simplified in comparison with reality. The simplification has an essential impact on the convergence of iteration procedures applied in this connection. Often a sphere is used, but it seems this is not an adequate choice. Attempt is made to work with an ellipsoid of revolution. Ellipsoidal harmonics come into play. The structure of the kernels mentioned above similarly as of the entries of Galerkin’s matrix becomes rather complex. Therefore, an approximation of ellipsoidal harmonics is used. The idea is applied to the construction of Green’s function, reproducing kernel and Galarkin’s matrix. (en)
Title	An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential (en)
skos:prefLabel	An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential An approximation of ellipsoidal harmonics and the construction of Galerkin's matrix in studies on Earth's gravitational potential (en)
skos:notation	RIV/00025615:_____/09:#0001585!RIV10-MSM-00025615
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC506), Z(CUZ0002561501)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Holota, Petr
http://linked.open.../riv/druhVysledku	A(V) - Audiovizuální tvorba se vzdáleným přístupem
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Výzkumný ústav geodetický, topografický a kartografický, v.v.i.
http://linked.open...dnocenehoVysledku	302696
http://linked.open...ai/riv/idVysledku	RIV/00025615:_____/09:#0001585
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Modelling of the gravity field; Geodetic boundary value problems; Classical and weak solution concept; Green's function; Galerkin's matrix; Reproducing kernels; Ellipsoidal harmonics (en)
http://linked.open.../riv/klicoveSlovo	Green's function Classical and weak solution concept Ellipsoidal harmonics Galerkin's matrix Modelling of the gravity field Geodetic boundary value problems Reproducing kernels
http://linked.open...i/riv/kodPristupu	L
http://linked.open...ontrolniKodProRIV	[9B8A9DE33FEC]
http://linked.open...i/riv/mistoVydani	Vídeň
http://linked.open...in/vavai/riv/obor	DE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Recent dynamics of the Earth
http://linked.open...UplatneniVysledku	2009
http://linked.open...iv/tvurceVysledku	Holota, Petr
http://linked.open...n/vavai/riv/zamer	Research and Development in Geodesy, Cadastre and Geomatics in 2005 - 2011

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