Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F16%3AN0000040" target="_blank" >RIV/00025615:_____/16:N0000040 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/1345_2016_236" target="_blank" >http://dx.doi.org/10.1007/1345_2016_236</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/1345_2016_236" target="_blank" >10.1007/1345_2016_236</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem

Popis výsledku v původním jazyce

The aim of this paper is to discuss the solution of the simple gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. The solution domain is carried onto the exterior of a sphere and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their internal structure is analyzed and modified by using integration by parts. As a result of the transformation a spherical mathematical apparatus may be applied at each iteration step, including the spherical form of Green’s function of the second kind, i.e. Neumann’s function in the integral representation of the successive approximations.

Název v anglickém jazyce

Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem

Popis výsledku anglicky

The aim of this paper is to discuss the solution of the simple gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. The solution domain is carried onto the exterior of a sphere and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their internal structure is analyzed and modified by using integration by parts. As a result of the transformation a spherical mathematical apparatus may be applied at each iteration step, including the spherical form of Green’s function of the second kind, i.e. Neumann’s function in the integral representation of the successive approximations.

Druh

D - Stať ve sborníku

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

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the IAG General Assembly, Prague

ISBN

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ISSN

0939-9585

e-ISSN

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Počet stran výsledku

6

Strana od-do

1-6

Název nakladatele

Springer

Místo vydání

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Místo konání akce

Prague

Datum konání akce

22. 6. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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