Fundamental solution of Laplace?s equation in oblate spheroidal coordinates and Galerkin?s matrix for Neumann?s problem in Earth?s gravity field studies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F15%3A%230002195" target="_blank" >RIV/00025615:_____/15:#0002195 - 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

Fundamental solution of Laplace?s equation in oblate spheroidal coordinates and Galerkin?s matrix for Neumann?s problem in Earth?s gravity field studies

Popis výsledku v původním jazyce

The motivation comes from the role of boundary value problems in Earth?s gravity field studies. The focus is on Neumann?s problem in the exterior of an oblate ellipsoid of revolution. The approach follows the concept of variational methods and the notionof the weak solution. The solution of the problem is approximated by linear combinations of basis functions with scalar coefficients, i.e. by Galerkin approximations. The aim is to discuss the construction of Galerkin?s matrix for elementary potentialsused in quality of a function basis. The computation of the entries of Galerkin?s matrix is expected to be simple for the elementary functions like these. Nevertheless, the opposite is true. Ellipsoidal harmonics are applied as a natural tool. The problem, however, is the summation of the series that represent the entries. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Thi

Název v anglickém jazyce

Fundamental solution of Laplace?s equation in oblate spheroidal coordinates and Galerkin?s matrix for Neumann?s problem in Earth?s gravity field studies

Popis výsledku anglicky

The motivation comes from the role of boundary value problems in Earth?s gravity field studies. The focus is on Neumann?s problem in the exterior of an oblate ellipsoid of revolution. The approach follows the concept of variational methods and the notionof the weak solution. The solution of the problem is approximated by linear combinations of basis functions with scalar coefficients, i.e. by Galerkin approximations. The aim is to discuss the construction of Galerkin?s matrix for elementary potentialsused in quality of a function basis. The computation of the entries of Galerkin?s matrix is expected to be simple for the elementary functions like these. Nevertheless, the opposite is true. Ellipsoidal harmonics are applied as a natural tool. The problem, however, is the summation of the series that represent the entries. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Thi

Druh

A - Audiovizuální tvorba

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-34595S" target="_blank" >GA14-34595S: Matematické metody pro studium tíhového pole Země</a><br>

Návaznosti

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

Rok uplatnění

2015

Kód důvěrnosti údajů

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

ISBN

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Místo vydání

Vienna

Název nakladatele resp. objednatele

European Geosciences Union

Verze

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Identifikační číslo nosiče

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