Reproducing Kernel and Neumann?s Function for the Exterior of an Oblate Ellipsoid of Revolution: Application in Gravity Field Studies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F14%3A%230002079" target="_blank" >RIV/00025615:_____/14:#0002079 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11200-013-0861-3" target="_blank" >http://dx.doi.org/10.1007/s11200-013-0861-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11200-013-0861-3" target="_blank" >10.1007/s11200-013-0861-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reproducing Kernel and Neumann?s Function for the Exterior of an Oblate Ellipsoid of Revolution: Application in Gravity Field Studies

Popis výsledku v původním jazyce

The purpose of this paper is to discuss the construction of the reproducing kernel of Hilbert?s space of functions that are harmonic in the exterior of an oblate ellipsoid of revolution. The motivation comes from the weak solution concept applied to Neumann?s problem for Laplace?s partial differential equation in gravity field studies. The use of the reproducing kernel enables the construction of a function basis that is suitable for the approximation representation of the solution and offers a straightforward way leading to entries in Galerkin?s matrix of the respective linear system for unknown scalar coefficients. The serious problem, however, is the summation of the series that represents the kernel. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no straightforward analogue to the addition theorem known for the spherical situation. This makes the computation of the kernel and the set of the entries in Galerkin?s matrix rather demand

Název v anglickém jazyce

Reproducing Kernel and Neumann?s Function for the Exterior of an Oblate Ellipsoid of Revolution: Application in Gravity Field Studies

Popis výsledku anglicky

The purpose of this paper is to discuss the construction of the reproducing kernel of Hilbert?s space of functions that are harmonic in the exterior of an oblate ellipsoid of revolution. The motivation comes from the weak solution concept applied to Neumann?s problem for Laplace?s partial differential equation in gravity field studies. The use of the reproducing kernel enables the construction of a function basis that is suitable for the approximation representation of the solution and offers a straightforward way leading to entries in Galerkin?s matrix of the respective linear system for unknown scalar coefficients. The serious problem, however, is the summation of the series that represents the kernel. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no straightforward analogue to the addition theorem known for the spherical situation. This makes the computation of the kernel and the set of the entries in Galerkin?s matrix rather demand

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia Geophysica et Geodaetica

ISSN

0039-3169

e-ISSN

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Svazek periodika

58

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

31

Strana od-do

505-535

Kód UT WoS článku

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EID výsledku v databázi Scopus

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