Green?s Function, Reproducing Kernel and Galerkin?s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F10%3A%230001716" target="_blank" >RIV/00025615:_____/10:#0001716 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Green?s Function, Reproducing Kernel and Galerkin?s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies

Popis výsledku v původním jazyce

In the introductory part the importance of the topic for gravity field studies is outlined. Concepts and tools used for the representation of solutions of boundary value problems are mentioned. A weak formulation of Neumann?s problem is considered with emphasis on function bases generated by the reproducing kernel of Hilbert?s space of functions. The paper then focuses on the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structureis 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 based on an approximation version of Legendre?s ordinary differential equation (limit layer approach) is used. A numerical implementation of the exact structure of the reproducing kernel is mention as a driving impulse of running investigations.

Název v anglickém jazyce

Green?s Function, Reproducing Kernel and Galerkin?s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies

Popis výsledku anglicky

In the introductory part the importance of the topic for gravity field studies is outlined. Concepts and tools used for the representation of solutions of boundary value problems are mentioned. A weak formulation of Neumann?s problem is considered with emphasis on function bases generated by the reproducing kernel of Hilbert?s space of functions. The paper then focuses on the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structureis 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 based on an approximation version of Legendre?s ordinary differential equation (limit layer approach) is used. A numerical implementation of the exact structure of the reproducing kernel is mention as a driving impulse of running investigations.

Druh

A - Audiovizuální tvorba

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

<a href="/cs/project/LC506" target="_blank" >LC506: Recentní dynamika Země</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

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

ISBN

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Místo vydání

Vídeň

Název nakladatele resp. objednatele

European Geoscience Union

Verze

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Identifikační číslo nosiče

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