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Statements

Subject Item
n2:RIV%2F00025615%3A_____%2F11%3A%230001777%21RIV12-MSM-00025615
rdf:type
n8:Vysledek skos:Concept
dcterms:description
In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary value problems are mentioned. Subsequently a weak formulation of Neumann’s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin’s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach) based on an approximation version of Legendre’s ordinary differential equation, resulting from the method of separation of variables in solving Laplace’s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations. In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary value problems are mentioned. Subsequently a weak formulation of Neumann’s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin’s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach) based on an approximation version of Legendre’s ordinary differential equation, resulting from the method of separation of variables in solving Laplace’s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations.
dcterms:title
Reprodicing kernel and Galerkin's matrix for the exterior of an ellipsoid: Application in gravity field studies Reprodicing kernel and Galerkin's matrix for the exterior of an ellipsoid: Application in gravity field studies
skos:prefLabel
Reprodicing kernel and Galerkin's matrix for the exterior of an ellipsoid: Application in gravity field studies Reprodicing kernel and Galerkin's matrix for the exterior of an ellipsoid: Application in gravity field studies
skos:notation
RIV/00025615:_____/11:#0001777!RIV12-MSM-00025615
n8:predkladatel
n14:ico%3A00025615
n3:aktivita
n13:P n13:Z
n3:aktivity
P(LC506), Z(CUZ0002561501)
n3:cisloPeriodika
3
n3:dodaniDat
n10:2012
n3:domaciTvurceVysledku
n17:7619413
n3:druhVysledku
n7:J
n3:duvernostUdaju
n15:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
226616
n3:idVysledku
RIV/00025615:_____/11:#0001777
n3:jazykVysledku
n4:eng
n3:klicovaSlova
Earth's gravity field; geodetic boundary-value problems; Green's function; variational methods; reproducing kernels
n3:klicoveSlovo
n9:Green%27s%20function n9:geodetic%20boundary-value%20problems n9:variational%20methods n9:Earth%27s%20gravity%20field n9:reproducing%20kernels
n3:kodStatuVydavatele
CZ - Česká republika
n3:kontrolniKodProRIV
[8D63C07707A5]
n3:nazevZdroje
Studia Geophysica et Geodaetica
n3:obor
n16:DE
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n19:LC506
n3:rokUplatneniVysledku
n10:2011
n3:svazekPeriodika
55
n3:tvurceVysledku
Holota, Petr
n3:zamer
n18:CUZ0002561501
s:issn
0039-3169
s:numberOfPages
17